{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":61151,"title":"Scaling vertically functions","description":"Given a real function by the 1×n array, x, of inputs and the 1×n array, y, of outputs, consider shifting vertically its graph by the scale factor k (see figure below). Return\r\ny_scaled, which is the 1×n vector that stands for the outputs of the scaled function;\r\ns = 'strech' or 'compress', if the graph will be away from or towards the x-axis, respectively, becoming narrower or wider relative to the original function's graph. Return s = '', if there is no change in size;\r\nr = 'flip' or 'flat' if the graph will be reflected over the x-axis or collapses the entire graph onto the x-axis, respectively. Return r = '', if the orientation is preserved.\r\ninput: (x, y, k)\r\noutput: [y_scaled, s, r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 489.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 244.988px; transform-origin: 408px 244.994px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a real function by the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of inputs and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof outputs, consider shifting vertically its graph by the scale factor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figure below). Return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_scaled\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vector that stands for the outputs of the scaled function;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'strech' or 'compress', if the graph will be away from or towards the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis, respectively, becoming narrower or wider relative to the original function's graph. Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = '', if there is no change in size;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'flip' or 'flat' if the graph will be reflected over the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis or collapses the entire graph onto the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis, respectively. Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = '', if the orientation is preserved.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(x, y, k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[y_scaled, s, r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 255.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 127.9px; text-align: left; transform-origin: 384px 127.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"369\" height=\"250\" style=\"vertical-align: baseline;width: 369px;height: 250px\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAuIAAAH0CAIAAAD35t9zAAAACXBIWXMAABcSAAAXEgFnn9JSAAAAB3RJTUUH6gEGDhoPSQwuaAAAACR0RVh0U29mdHdhcmUATUFUTEFCLCBUaGUgTWF0aFdvcmtzLCBJbmMuPFjdGAAAACJ0RVh0Q3JlYXRpb24gVGltZQAwNi1KYW4tMjAyNiAxNDoyNjoxNX37Xd8AACAASURBVHic7N17XJRl/v/xa2REyEHAJFE0B9TEXclDHqi1r1CWmqvioTSzhFbck4rH1dwMsFq1zNV1S1N/gmkHM7PNdc2yBTa0cW3XE2keGTcQPCLMECSD8/vjpnEYBhgOM/c9M6/nYx/7kJuZez42zsx7rutzXbfKbDYLAAAA5WkhdwEAAAD2uSimGI3GqVOnzp8/v47bVFRULFiwoHfv3idOnHBNVQAAQMlcEVMqKyu3bt2anZ1d981279798ccfu6AeAADgFtTOfoCysrJVq1Zt3ry57iaYM2fOrFixgkYZAABg4dzRlDNnzkyePHnz5s09e/b08/Or7WZlZWUrV64MDg4eOHCgU+sBAABuxIkxxWg0pqSk5OTkzJkzJzU1tWXLlrXdctu2bdnZ2fPnz+/UqZPz6gEAAO7FuaMpvXr12rNnz4wZM3x9fWu7zdGjRzds2DBu3LiYmBinFgMAANyLE3tTNBrN4sWL676NwWBYtWpVSEhIUlKSWu30RhkAAOBG5EwGZrP5/fff/+abb95+++2QkBAH76XT6Q4dOuTUwgAAgPMMGjQoOjrakVvKub3b0aNH33zzzUmTJg0ePNjxex06dEin0zmvKjTIzp07eTqUY+fOnXl5eXJXASGEyMvL27lzp9xVoApPh6I0aLhBttGUoqKipUuXRkREzJw5U6VSNei+0dHRSUlJTioMDaLT6SZMmDB+/Hi5C4EQQuzcuTMpKYlWdCXIy8ubPHky71QKISV4ng53JFtMycvLu3DhgsFgeOCBB2x+NWbMmICAgG3btkVFRclSGwAAUALZYkpwcPD48ePLy8utD+p0uvz8/NjY2I4dOwYHB8tVGwAAUALZYkqnTp1eeuklm4Pz58+/fv3673//e8ZRAAAAV0gGAAAKRUwBAAAK5aJJn6ioqGPHjtV7s5UrV7qgGDSjhQsXduvWTe4qUGXVqlWhoaFyVwEhhAgNDV21apXcVaBK7969u3btKncVaAw2fkWTtG/fXu4ScAdPh6LwdChHaGiowWCQuwo0BpM+AABAoYgpAABAoYgpAABAoYgpAABAoYgpAABAoYgpAABAoYgpAABAodg3BQC8i06nO3TokNxVuFR5ebnJZNJoNHIX4pkGDRoUHR3tpJMzmgIA3uXQoUM6nU7uKlzKz8+PjOIkzk69jKYAgNeJjo5OSkqSuwqgfoymAAAAhSKmAAAAhSKmAAAAhSKmAAA8UGVl5T//+c+JEydGRkZGRERERUUlJiYeOXLEbDbXcS+j0Th58uTJkycbjcZ6H+LEiRO9e/dev35906vdv39/RETE/v37m36qplu/fr1yiqGFFgDgaYqKimbPnv3VV1+Fh4fPmjWrS5cuOTk5u3btmjBhwqRJk1588UV/f3+5a4RDiCkAAI9SVla2cOHCQ4cOLVmy5LnnnvPx8RFCjBw5ctasWatWrdq8eXOrVq2WLFmiUqlq3lej0bz33nsOPlBUVNSxY8eas3TUwKQPAMCjZGZmZmVlJSYmxsfHSxlF4u/vP3fu3EcfffSjjz7673//K2OFcBwxBQDgOUwm0549e9q0afPLX/6y5niJv7//U089VVpampGRIYTYv39/79699+zZExcX17Vr1ylTpuTn59v0phw+fHjs2LFdu3aNjIxMTU39+OOPLX0b1r0pUnPJ7t27V69ePWDAgIiIiMGDB3/66aeVlZXSeSorK/fs2TNy5EjrXpnc3FxH/lJms3nv3r2PPvpoRETE/fffv3HjxtWrV/fu3fvEiRNCiPXr1w8ZMmT//v2DBw/u3r37/Pnzb926lZ+fv2jRooEDB0ZERHTt2jU2Nvadd96pqKgQVv03+/fvHz58uHTOFStW2LTjlJSULF26NCoqqmvXrk888cTBgwfrbutxEiZ9AACeo6Sk5MKFC506dQoNDbV7g/vuuy80NPT48eOlpaVCiPLy8uTk5EceeeTpp58uLy8PDAy0vvH+/ftnzJjRvn37l156SQixefPmuqeEXn75ZX9//xkzZkg3XrBgQcuWLUeMGCH9+Prrrw8cODA1NbVVq1b79+/ft29fQUHB1q1bg4OD6/5Lbdq0afny5b169Vq2bNnVq1fffvttg8Hg5+dnucHly5cXL148YcKE9u3bh4SEXLt27Ve/+tW1a9eefPLJXr16Xbx4cfv27dLjTpw4UbrLt99+O2/evKFDh/7mN7/JyMjYsGHDyZMn33zzTct2vS+88EJkZOSLL75oNBrXrVv3m9/8Ji0t7YEHHqi71GZHTAEAiNhYuStorKlTRXz8nR9NJlNpaWlQUJD1dI81Pz8/tVptMBhMJpMQoqKiolevXqmpqVJTrfWIgsFgWLduXefOndPT08PCwoQQTzzxxNSpU7/77rvaiomIiNi4cWNAQIAQIjo6esqUKV9++eWIESOKioqysrIefvjhv/71r9IDjRkzJjU1ddeuXXl5eXXHlO+///6dd975xS9+8eabb0pnfuSRRxISEsrLyy23uXXr1hNPPLFgwQJpAOnTTz+9fPny6tWrhwwZIt3g0UcfnTJlyuHDhy0xxWg0Lly4MDExUaVSjRkzJjIycuXKlRkZGaNGjZJu8Pjjj69ataply5ZCiG7duk2fPv3w4cPEFACADDIz5a6gsWJimnqG6Ohouwt/vvvuu1OnTs2aNUvKKEKIkJCQSZMmpaSk1HaqwYMHS0lCunFISMiVK1dKS0uDg4O3bdtmfUuVSlXbeI+N//znP5cuXUpOTracuWfPniNGjNi1a5fNQ1smuUaPHj169Gjr3wYHB991113WR7p37z527FjpLiqVauTIkdu2bTt48KAlpjzxxBNSRpFufM8995w7d86RgpsXMQUA4DlUKpVarb59+3ZtN5CulhwQEKBWV30CdunSxe4ti4uLy8vLu3XrZn2wY8eOdTy65ZxCCF9f36CgIJPJZGnpqKysLCwsPHXq1IULF7Kzs48cOdKiRf0dooWFhRqNpn379pYjNSOORqMJCQmxuaPRaDx37pxerz98+PDBgwfz8vIGDBhg+W3btm2tw5lGowkMDLx48aJlPMmSUaS/lyOlOgMxBQDgOYKDg3v27Hno0KH8/PwePXrUvEFubu61a9fGjh3bunVr6Yj157GTmM3mL7/8ctGiRTdu3BBCBAYGRkVFWXpgm06lUlnHiKKiopdeeukf//iH2Wz28fG59957+/btKz103dRqtd112jIipgAARFqa3BU0llZb7Ue1Wj1y5Mgvvvhi+/btNTdHKSsre/fdd1u1ahXrQDNOYGCgn5/fuXPnhg4dajl4+fLlRhR59uzZP/7xj926dVu2bNm9994r9c2sX7/ekZgSGhpqNBovX74cFRXlSBlms3nt2rVffPHF0qVLx4wZI7XEXrly5T//+Y/1zW7evHnr1i3Lj9evX7927Vrv3r0t6U0hiCkAgGpdqO5u6NCh48ePf++99zp37mzZ3k0IUVZWtmrVqi+//HLq1Kn9+vWr9zyRkZE9e/bcuXPnqFGjpPYUg8Gwe/fuRpT0v//97+rVq88++2x4eLh0pKioKDMzs7y8vLi4uO77PvDAAx07dnznnXcGDRoktafk5eX961//qu32paWl3333XUhISGxsrJRRzGazTqcrLCy8efPmjz/+KN3s/PnzBw4ckDpRzGbz/v37i4uLhw8f3oi/nVMRUwAAHqVly5YvvPBCSUnJyy+/vGPHjri4uLCwsFOnTu3evTsvL2/SpEmWFTF1CwgI+O1vfztjxozJkyc///zzQojNmzeXlZU1oqQePXqEhYVt3LixpKSkd+/e0s79RUVFFRUV1gt27JLC1vLly6dMmTJ58uSrV69u2bKljvo1Gs3AgQN1Ot3cuXPHjh0rhNizZ8+hQ4fMZvMPP/wgbZ0ihKioqFiwYME333zTv3//3bt3f/nllxMnTnzooYca8bdzKmIKAMDTBAQErFmzZty4cW+//faqVatu3brVunXr6Ojo1atX9+nTx/H2i0cffXTz5s2vvPLK0qVL77rrrqeeeurnP//5/PnzG1pP586d161bl5qampaWdvv27XvvvXfOnDkRERHTpk3LycmxnlSy6/nnn2/fvv1rr732wgsv3H333dOnTy8tLU2rfaLu17/+tRDi3XfffeGFF1q3bj1kyJB//OMf69ev1+l0RUVF0vrnzp07z5s376233tq6dWvHjh1feumlp556ygVtOg2lkmVTuaZYs2aNECIpKUnuQiCEEAUFBQEBAZbtgCCv77//vkOHDtZrDSAXk8lUUFDQuXNnuQuxg3fRpli/fv26deu2bdtm3SnievPnzz98+PCOHTvuueeeht7XaDROnz49Pz+/cXe30Yh/Tg26C5vlAwBgx5UrV0aMGLFy5UrL93mDwZCZmdm2bdt27dq5rIwTJ04MGTJk+/btliN5eXlHjhwJCwuz2QrFI/GtCwAAO9q2bfvAAw+8/fbbBQUFMTExP/zww3vvvZeTk7No0aIOHTq4rIzw8HCtVvvKK6989913/fv3v3bt2ubNmy9fvvzCCy94w0g2MQUAADvUavWiRYsCAgL+9re/7dq1y8fH52c/+9nWrVsffPBBV5ah0WhWrlz5xhtvfPLJJ1u2bPH19e3bt+/GjRvvu+8+V5YhF2IKAAD2aTSahQsXLly4UN4yQkJCli9fvnz58mY5m0ajqfsCiopCbwoAAFAoYgoAAFAoYgoAAFAoYgoAwNOUlZW98847TzzxRPfu3SMiIvr27Ttr1qwzZ840y8nXr1/flKsGNvHuzchoNE6ePHnIkCFXrlyRu5Za0UILAPAoBoNh1qxZWVlZHTt2HDNmjK+v76lTp/bu3fv555//+c9/HjFihNwFogGIKQAAj5KZmfmvf/1r7ty5v/3tby3XHTx16lRCQsKaNWv69+8fEhIib4VwHJM+AACPcvDgQY1GM2TIEEtGEUL07NlzwoQJly5dys/Pl7E2NBQxBQDgUbp06VJeXq7X622Oz58///jx43369JF+LCsr27Jly+DBgyMiIiIjI6dNm2ZpXqmsrNyzZ8/IkSMjIyMjIiKioqISExNzc3PtPlxFRcU777xjOc/MmTOtk5DZbD548OATTzzRtWvXqKiol19+ubS0tI7ijUbjihUr7r///oiIiOHDh3/++eeTJk2aPHmy0WiUWknmzZu3efPmyMjIqKioTz/9VAhx5syZxMTEvn37RkREdO/e/Yknnti7d6+0wf+VK1eGDBkyb9683bt3R0dHR0REREdHv/POO5brJEtOnz49adKk7t2716xfdkz6AACESE+Xu4LGiokRWq31gUceeSQtLW3u3Lk7duyIi4t76KGH2rdvb3NV5IqKipdffnn79u2DBw+eP39+Xl5eenr6M888k5aW1qtXr82bN7/++usDBw5MTU1t1arV/v379+3bV1BQsHXrVunywtbnSU5O/uCDD6KiombOnHn16tX09PT4+Pj09PSwsDAhxGeffTZnzpz27du/9NJLQojNmzcXFhb6+fnZ/asYjcbf//73Bw8eHD169MMPP/zVV1/NnDnTbDb379/fcpv9+/cfP378pZdeunz5clRUVE5OTkJCwl133ZWYmNilS5ecnJwdO3bMmTMnODg4OjracpesrKxRo0b17t17586dKSkpZ86cSUlJkX6bl5eXmJg4cuTIZ5555sCBAzt37rx06VJ6enpAQEDTnpjmQUwBAAiRkCB3BY2VkiKSk60P3HfffR988MEf/vCHAwcOZGdnCyFat24dGxubkJDQp08fKa8cPHhw586dv/vd7+bOnSsd+cUvfjFjxoyMjIywsLCsrKyHH374r3/9q7+/vxBizJgxqampu3btysvLs4kp0nnGjx//pz/9qWXLlkKIwYMHJyYmvvbaa2+88UZZWdmmTZs6d+5sSS1Dhw6Nj4+vbWVNRkbG119/vWDBgsTERJVKNWbMmN69e6emplrfpry8/MUXXxwyZIj04+rVq319fTds2NCjRw8hxMiRI6Ojo6dPn3706FFLTPnxxx+XL18u9Q6PHDly8eLFn3766dixY6W7CCH+9Kc/jRs3Tgjxy1/+0s/Pb9euXXq9Xt5LQFsw6QMA8DTh4eE7duzQ6XQrV6584oknhBB///vfJ0yYsGTJEmm+IzMzMzAwcPTo0ZZRlr59+x44cGDmzJnBwcHbtm37f//v/0kZRQihUqlCQ0PtPtBnn33m4+Pz1FNPSRlFCNG7d++YmJhvvvnm0qVLFy5cOHv27JgxY6SMIoQICwsbM2aM3VOZTKZ9+/aFhYWNGjVKqkqlUo0YMaJ79+7WNwsNDe3Zs6flx9mzZx84cMASOIQQbdu2tRmtiY6OjomJkf7csmXLp556ymQyHT16VDrSsWNHS6BRqVSDBg0yGAyXL1+u/b+uSzGaAgDwTCEhIePGjRs3bpzZbP7uu+8WLVr0/vvvDxo0aNSoUQaDwd/fPzAwsLb7VlZWFhYWnjp16sKFC9nZ2UeOHGnRwvaLfWlpaX5+fuvWrc+fP289QFJZWWkwGIqKiq5evWo0GiMjI63vZfOjRXl5+Y0bNzp06GA92+Lv79+2bVvrm3Xo0OGuu+6yuW9JScnJkycvXrx46NAhnU5nMBisf9uuXTtL5BJCBAUFaTSaU6dOST+2aNFCrb4TBix5SyGIKQAAIX76tu1+unSx/knqJ33ooYeWLVtmOahSqXr27PnKK69MmTJF6tKo43xms/nLL79ctGjRjRs3hBCBgYFRUVF2N2Qzm80mk+n69euLFy+ueZ6rV682/i9VO5u0lJeXN2/evMOHDwshfH19u3bt2q9fv3/+85/1nkdpcaQ2LoopUltQSEjIypUrbX515syZ1157LTs7+9atW4GBgcOGDZs5c6ZlfAwA4AoZGXJX0DzatWvXunXrI0eOXL161WZ/FD8/v1atWkkfzwEBAWVlZcXFxffcc4/02+Li4ueffz48PDwhIeGPf/xjt27dli1bdu+990qrmtevX18zpmg0mi5dunz//ffbt2/v2LFjzWJOnDgREBBw9OjRoUOHWg6eO3fObuV+fn5t27b99ttvDQaDRqORDt66devmzZtBQUF271JWVrZ06dILFy5s2LDh4YcfbtWqlfSgX331lfXNbt68+eOPP0q/FUJcvny5uLi4W7duds+pNK7oTamsrNy6davUx2Rj7969o0ePzsrK6tev31NPPdW2bdsPP/wwPj5eUauhAADuom3btqNHjz5z5syyZctKSkosx8vKyjZv3lxcXPx///d/QoiYmJji4uL9+/dLC3eFEP/6179ycnLuv//+goKCq1evDh48ODw8XMooRUVFmZmZ5eXlxcXFNg/30EMPXb58+e9//7vlPAaD4bnnnnv00Udzc3O1Wm23bt327t2bl5cn/baoqGjfvn12K1er1cOGDcvPz9+9e7flbAcOHDh//nxtf1mDwXD69OmuXbtGR0dLKaSysjIrK8umueTw4cMnT56U/lxRUfG3v/2tTZs2gwcPdvA/qbycPppSVla2atWqzZs3W/6jW1y9enXt2rUBAQHr169/4IEHhBCVlZUbNmxYuXKl1CNtPVsGAIAjnnnmmZycnE8++eQf//jHgAEDOnfufP369YMHD/7www9PP/20NLDx0EMPjR8/fuXKlTqdbuzYsceOHfvoo4969uw5YsSI8vLysLCwjRs3lpSU9O7dOycnZ9euXUVFRRUVFeXl5TaPNXz48K+//nrFihUHDhwYO3ZsSUnJBx98cPr06YULF2q1WpVKtWTJksTExIkTJ06fPl3UtyA5Njb2wQcffP3110+fPi0tSN6/f39tNxZCtG3btk+fPn//+9//8Ic/PP744yUlJTt37vzuu+9UKpV1e4rBYIiPj3/++ee7dOmyZcuW48ePL1y48L777qt7BxeFcG4OOHPmzMKFC48fP96zZ88LFy7Y/DYnJ+f06dPPPvtsv379pCM+Pj4TJ07cvXv30aNHb9y4YRmLAwDAQQEBAWvWrBk5cuTGjRsPHz584MABX1/f3r17//rXv7ZsTduyZcslS5b06NFj48aNc+fObd269ejRo+fPny+tN163bl1qampaWtrt27fvvffeOXPmRERETJs2LScnx3r6xvo86enp8+bNa9GiRffu3f/yl78MHz5cWq3Tp0+fd99996WXXnrllVd8fHwee+yx6dOnv/baa3Yr12g0a9euXb169Y4dOz755JMePXq88cYbmzZtqu1vqlarU1JSNBrNp59++tlnnwUGBo4ZM2b16tV//OMfc3NzLUll4MCBcXFxq1evvnr1ateuXa3LUz5VzUGO5mI0GqdPn3748OGkpKQHH3zw+eeff+yxx6x7U959992VK1cmJyfHxcVZ32vatGkFBQU7duywG1PWrFkjhEhKSmq2QtVqYTI129m8TEFBQUBAgGUaFfL6/vvvO3TowDCkEphMpoKCgs6dO8tdiB3N/y4Kp7ly5cqTTz45YMCAmp2djt89LCxsw4YNTnqjbsQ/pwbdxbm9Kb169dqzZ8+MGTN8fX1r/vaZZ545cuSIdUYRQpw+ffrkyZNhYWE1F1w1v8xMoVKJykqhUonwcJGZ6fRHBACgFhs3bhw+fPjZs2ctRw4dOlRYWOgu7a7O4MRvXRqNxu4arToYDIY1a9aUlpZOmDDB6V/Q9XphvbWfXi9iY0V8vEhLc+7jAgBgz4MPPrhhw4Zp06Y9//zz7dq1++abbz766KPw8PDRo0fLXZpsFDQ4bDQak5OTs7OzJ02aVPeidp1OV/PgsGHDatsl0C6/zz7zqzl8kp4uMjNFfPxNhkMdU1JSUllZaWLWTBmKi4v9/f2Z9FECk8lUXFyskKui2CgvL6+jKxMy6tWr11tvvbVy5cply5ZJm3Q8+eSTs2fPbtOmjdyl1aW8vPzmzZt2f1VYWFhzZZNOp7Pse1svpbydFRUVzZ49+6uvvoqLi1u8eHEjtp1pUEYRer361Vdr+5VISdFs2mRcu9aN9zuCV1KpnNhthgYxm83u0qIIRRkwYMD27dub62z33HNPVlZWc52tERr20WyPImLK2bNnZ86cefbs2WnTpi1YsKDejBIdHd3U5q+jR8VPq9iFECI+3ubqoOq8vKCxY2te0Qo2ysrKaKFVDoPBEBwczGiKEphMpvLy8tp25ZIXQyloXn5+fnX8U2/i57X8b2fZ2dlz5swxGAwvvvjic889Jy0Vcy69vtq1QGNiRFqaSE4WW7aIny5sXSUlRaSni/h4wgoAT2J36hxohAbN4DSCzFdIPnr06Jw5c27duvXWW28lJCS4IqMIUa1zVqutiiDSH3JzhVZb7cZ6vUhJEbGxQq93RW0A4GSDBg1y6ueKAplMJqPRKHcVnik6OnrQoEHOO7+coyn5+fkLFiwQQmzevFnahdYV9Ppq8zsxMdUaULRakZsrUlNth1UyM0V4OHNAADxAdHS0t8UUo9FoMBg6dOggdyFoMDljyo4dO86fP+/r6zt79mybXrOOHTuuXbvW5qpRzcN6uscylGIjOVlMnSoSEmx3UpHmgNLSaK0FAMAFZIspRqPx3//+txDi1q1bNS806KwFC5mZ1ZJHTIztFI+FVisyMkRmpkhIqDbdI22vIrWz1HZfAADQHFwUU6Kioo4dO2Z9RKPRvPfee6559DtsulLq3cktJoY5IAAA5CJzC61L2QylOJ4wpNbamhM9KSlssQ8AgPN4TUyx2RpfqxXx8Q24uzQHVHP0RZoDsu53AQAAzcRrYorNUErjLtwTHy9yc20ngIQQ6ekiPLxaDAIAAE3mHTGl5lBKo5fqWLZXsTmDtL0Kc0AAADQf74gpmZnVVus0/RrI0hxQzWEVaQ6IYRUAAJqDF8SUmlvjN9euJ9KwSs2wIg2rAACApvGCmGJ3a/zmIp0wI8POFvskFQAAmsbTY0rdW+M3F2l7FZthFZIKAABN4+kxxZGt8ZtLzdZaqVUFAAA0ikfHFMe3xm8u0s621kklM5OkAgBA43h0TGno1vjNouYDkVQAAGgUz40pjd4av+m0WpGba1sMSQUAgAby0JjSxK3xm46kAgBAk3loTGmWrfGbiKQCAEDTeGJMacat8ZuIpAIAQBN4Ykxp9q3xm4KkAgBAY3lcTHHe1viNRlIBAKBRPC6mOHVr/EaTLlVojaQCAEB9PCumuGZr/MaJiSGpAADQIJ4VU1y5NX4jkFQAAGgID4oprt8avxFIKgAAOMyDYoosW+M3AkkFAADHeEpMkXFr/Eawm1SsZ6wAAICHxBTZt8ZvhJpJJT2dpAIAgDWPiCnuNZRiQVIBAKBO7h9T3HEoxYKkAgBA7dw/pihqa/xGIKkAAFALN48pCtwavxFIKgAA2OPmMUWZW+M3gt2kYr2jLgAA3sedY4qSt8ZvhJpJJSGBpAIA8GbuHFMUvjV+I8TE2PbWkFQAAF7MbWOKXu8GW+M3Qnw8SQUAAInbxhSboRS3W+BTB5IKAABCCHeNKW66n5vjSCoAALhpTBn02Wd3fnCv/dwcZzepWIczAAA8nVvGlOjy8js/eN5QikXNpBIbS1IBAHgPt4wpd3jqUIpFfLxISal2hKQCAPAabh5TPKlztjbJybZRjKQCAPAO7hxT3H0/N8elpZFUAABeyC1jim74cA/Zz81xJBUAgPdxy5hyaPhwkZvrLUMpFiQVAICXccuY4r1IKgAAb0JMcTckFQCA1yCmuKG0NNsJL5IKAMATEVPcU0YGSQUA4PGIKW6LpAIA8HQuiilGo3Hq1Knz58+v+av8/PyZM2dGRkZGREQMHjz4nXfeqaiocE1Vbo+kAgDwaK6IKZWVlVu3bs3Ozq75q5MnT44bN+6zzz7r16/fuHHjTCZTSkpKcnIyScVRJBUAgOdyekwpKytbvnz5ypUrzWazza8qKirWrVtXXFz8l7/85b332wK1yAAAIABJREFU3lu5cuUXX3wxePDgjz/+WKfTObswz1EzqXAtZQCAR3BuTDlz5szkyZM3b97cs2dPPz8/m99euHBBp9NFR0fH/PQpGxAQkJSU5Ovr++mnn9aMNaiVTVLR60kqAAAP4MSYYjQaU1JScnJy5syZk5qa2rJlS5sbnDp16vr16/379/f397ccDA8P79Sp07fffltUVOS82jwQSQUA4HGcO5rSq1evPXv2zJgxw9fXt+ZvCwsLhRCRkZHWB319fYOCgoqLi41Go1Nr80AkFQCAZ3FiTNFoNIsXL77vvvtqu8HFixdrHmzdunVoaKjRaCwuLnZebR6LpAIA8CBqGR/b7nIelUrVokU94clug+2wYcNCQ0ObpzK3tmuX34gRfpb/RHq9SEgoX7euPDraGY9WUlJSWVlpMpmccXI0VHFxsb+/v1ot5+saEpPJVFxcHBAQIHchEEIIo9FYWlpq3WAA1ygsLNy3b5/NQakt1cEzyLm9W81uFSGE2Wy+fft2I85GRrEo37vXZkxFnZgoWzVwIZVKRe+5QpjNZpVKJXcVgMya/tEs57euLl261DxYWlpaWFio0WgCAwNru2N0dHRSUpIzS3N/GRnWG6io8/KC+vYVubnN/jhlZWUBAQEajabZz4xGMBgMwcHBjKYogclkKi8vDwoKkrsQCCGEWq328fHh6ZBFEz+v5RxNkWLKuXPnrA/eunXr5s2bgYGBfPI1Vc0+lfBw2YoBAKDh5Iwp3bp1a9eunU6nKysrsxw8f/68Xq//+c9/HhwcLGNtHsLmWsokFQCAW5EzpnTq1KlPnz46nW7//v3ShLrBYFi7du3t27dHjx7NtG4z0GpJKgAA9yXnHLa/v//vfve7I0eOzJ079/333+/YsWN2dvaVK1cmTZrkeA8w6iElFetlyVJScUKfCgAAzUvO0RQhRJ8+fT788MMhQ4b897///fjjj9VqdUpKit0ta9F4jKkAANyTi0ZToqKijh07ZvdX4eHhmzZtck0Z3svumEpsrMjIkLMqAADqJPNoClyn5phKZqaIjZWtHgAA6kNM8SZSUrFGUgEAKBgxxctotbbNsyQVAIBSEVO8D0kFAOAmiCleiaQCAHAHxBRvRVIBACgeMcWLkVQAAMpGTPFuJBUAgIIRU7yeVmu7yRtJBQCgDMQUCBETQ1IBACgQMQVCCJIKAECJiCn4CUkFAKAwxBRYsZtUEhJkqgYA4O2IKaiuZlJJTyepAABkQUxBDSQVAIAyEFNgD0kFAKAAxBTUgqQCAJAbMQW1I6kAAGRFTEGd7CaV1FSZqgEAeBdiCupTM6mkpIj0dHmKAQB4E2IKHFAzqSQkkFQAAM5GTIFjYmJEWlq1IyQVAICTEVPgsPj4mknFf/t2maoBAHg+YgoaokZSCZozx++DD+QqBwDg2dRyFwB3Ex8vhLBelqxOTBSvvnrnV0OGiJgY19cFAPA8xBQ0XI2kIvR6IYRISblzRKsVMTFCqyW1AAAajZiCRqmZVGzo9dUabLXaquAiGG4BADiKmILGio8X8fFCpXLoxnq90OtFZuadIwy3AADqQ0xBkxRcuhRw/brm2jWRlWUni9SB4RYAQH2IKWgyrVb06lUtWOj1YssWIYTIzGxAamG4BQBQHTEFTqDViuRkIUTV/0sRRBpuycys6retV23DLV263Bl3AQB4NGIKnM96Qkf8tCyoWYZbWAINAB6NmAKX02qFEPaHWxxPLdK9bJZAW4ZbpNkiAICbI6ZAASwJw5JaRJOHW6SYwnALALgzYgqUx+5wS2amuHixYalF1NhxTgpDpBYAcBPEFLgDSxuKzSSRYLgFADwZMQVuyLont3mHW1gCDQBKQkyBR2iu4RZ2nAMAJSGmwBM113ALO84BgKyIKfAOtQ23sME/ACgYMQVeyWbHOcEG/wCgRMQUQAhR5wb/1iModWODfwBoVsQUwB7r4Za0NDb4BwBZEFMABzTLjnOi9g3+SS0AYA8xBWiUmj25gg3+AaCZEVOA5uC8Df7pyQXgxeSPKWfOnHnttdeys7Nv3boVGhqakJAwZcoUf39/uesCmoYd5wCgyWSOKdnZ2b/97W/Ly8sHDBhw7733fv3118uWLfvqq6/efPPNgIAAeWsDmhM7zgFAw8kZU4xG41tvvVVRUfGXv/xlxIgRQoiysrIlS5bs2rUrMzNz1KhRMtYGOJ0Tdpzr0KmTz69/LV58sdmLBQBZtJDxsX/44Yf8/Pw+ffo8/PDD0hF/f//hw4ebzeaDBw/KWBggA2lcJDlZpKWJjAxhNovcXJGSIlJSHB8mUeflqZYsEeHhDVh8BAAKJudoikqlUqvVN2/eLCsr02g00kGj0SiEuPvuu2UsDFCEOnacy8ys6re1S68XsbEiI4NpIADuTs7RlHbt2k2cOPHs2bPLli0rKioym81HjhxZtWrV3XffPXz4cBkLA5TIerglN7fqf3UMt8TGitRUVxcJAM1K5tGUX/3qV4GBgcnJyZ988ol0sHfv3suXL+/Ro4eMhQFuwN4SaNOzz6qzs+/cJiVFZGaKjAwZygOA5iBnTDGbzRkZGa+//roQYujQoW3btj18+PCxY8deffXVN954IyQkpLY76nS6mgeHDRsWGhrqxHJhT0lJSWVlpclkkrsQCBEUlLduXaclS4J+Cv1CCJGZKcLDy9etK4+Olq8yb2QymYqLi1mxqBBGo7G0tJStLlyvsLBw3759Ngd1Ol20w+9Ick765OTkzJs3Lzg4eO/evRs2bFi+fPnnn3++YMGCAwcOLF26tKKiokFnI6MAKpWqYsMG08aN1Y7q9X4jRjTgAopoDmazWaVSyV0FILOmfzTLOZqyb98+g8GQmpoaHh4uHfHx8YmPjz906NChQ4f0en337t3t3jE6OjopKcmFlaJWZWVlAQEBlg5oyMtgMAQHB6unTRNDh4qfXlaSoDlzxLFjIi1Nrtq8jclkKi8vDwoKkrsQCCGEWq328fHh6ZBFEz+v5RxNKSwsFELYfML5+/u3a9fuxx9/LC8vl6kuwP1ptSI317a1Nj1dxMbKUw8ANIqcMUUaC7p06ZL1wbKysmvXrknJV6a6AI+g1YqMjGpXCBJVrSrsqgLAXcgZU2JjYzUazdatW3Nzc6UjZrN5z549Op3ugQceCK8+ZA2gMaQFzNakXVVoVQHgDuTsTenXr9/MmTNfe+21ESNGDBgwICws7L///e/58+fDwsJmzZpFSzbQPOLjRUyMiI2ttiNcQoLIyqJVBYDCyTmaolKppk2b9u677/bu3fvw4cMffvhhUVHRr371q08++aRXr14yFgZ4GmkCiFYVAO5G5iskq1SqgQMHbt++Xd4yAM8nJZXU1GrdKlKrSloa2+oDUCY5R1MAuFpysu2mtFKrCtvqA1AkYgrgZWJiRG5u1V77FikpIiFBnnoAoHbEFMD71NaqwvI6AApDTAG8kt1dVfR6dlUBoCjEFMCL0aoCQNmIKYB3k1pVbCaAUlJYqwxACYgpgNez26oirVW23hEOAFyOmAJACCHst6rExtKqAkBGxBQAP6FVBYDCEFMAWKFVBYCSEFMAVEerCgDFIKYAsIdWFQAKQEwBUAtaVQDIjZgCoHa0qgCQFTEFQJ3qaFVhAgiAkxFTADiAVhUAciCmAHBMzVYVIWhVAeBUVTGlrKzszJkzFRUV8lYDQNFoVQHgWlUxxWAwJCYm9uvXb8GCBUeOHKmsrJS3LAAKJbWqxMdXO0irCgDnqIopfn5+999/f0VFxc6dO8ePH9+3b9+lS5fm5uaazWZ56wOgRGlpIi2t2hFaVQA4QVVMadOmzdq1a0+cOLFly5ZHHnnk1q1b6enpjz766IMPPvjGG2/k5eWRVwBUEx9PqwoAZ6vWQtuyZcuHH35406ZNUl4ZOXLkzZs333zzzf/7v/8bOnToxo0br169KlehABSHVhUATmZ/pY+UV6TxlZ07dz799NNlZWXLli2Ljo5+/PHHP/roI6PR6OJCASgRrSoAnKmeBclXrlw5fPjwkSNHpHEUs9l87ty5P/zhDw8++ODGjRtZGQRACFpVADiLuuYhs9mcn5+/ffv2Xbt2Xbp0SQihUql69eo1derUxx57TAixb9++P//5z8uXLy8tLZ09e7arSwagQPHxQqu1ne6JjRXx8bYJBgAcdiemmM1mvV7/4Ycf7tq168qVK9LB8PDwSZMmTZgwITg42HLLCRMmdO7cOTEx8fPPPyemAKgitaokJFQbRElPF3q9nWZbAHBAVUy5evXq1KlTv/vuO+nHjh07Tp48ecyYMWFhYXbvFh4eHhwc/OOPP7qoTABuQWpVSU2ttrO+1KqSlmbbbAsA9amKKWazubS09O677x47duxzzz0XFhamUqnquFtFRcXTTz/dp08flxQJwK0kJ4suXURCwp0jUqtKWpptsy0A1KkqpgQEBLz77rsdOnTw8fFx5G5hYWG/+c1vnFkYAHcWHy9iYkR4eLWDCQkiK4tWFQCOq1rp4+/v36lTJwczCgDUT6u1s6tKejq7qgBwHFdIBuA0UquKdZ+KYFcVAA1ATAHgZMnJtit9pFaV9HR56gHgPogpAJxPWqus1VY7mJBQrc0WAGogpgBwCWkCqGarik2bLQBYIaYAcBW7rSp6Pa0qAGpDTAHgWrW1qqSmylQQAOUipgBwObutKikprFUGYIOYAkAOdltVpLXKer0sFQFQIGIKAJnU1qoSG0urCgAJMQWArGhVAVA7YgoAuUmtKjYTQLSqACCmAFAEWlUA2ENMAaAYtKoAqI6YAkBJaFUBYIWYAkBhaFUB8BNiCgDlqaNVhQkgwJvIH1NKSkpWrFgxYMCAiIiIqKioRYsW5efny10UAAWgVQXwejLHlEuXLk2dOvXtt99u06bNU089FRERsWPHjvj4eJIKACHstaoIQasK4D3kjClms3nTpk3Hjx9fsGDB559/vnz58k8++WThwoUXLlzYtGmTjIUBUBBaVQAvJmdMOXfu3N///veHH344Pj7ex8dHCKFSqUaNGnXvvfeePXu2pKRExtoAKIjUqhIfX+0grSqAF1DL+Njnzp27du1aXFycv7+/5WCHDh0yao7xAkBamhgyRCQk3DkitarUbLYF4CnkHE05f/68RqPp0qXL3r17H3/88a5du9JCC6Au8fG0qgBeRc6YotfrhRDr16+fPXt269atn3zyyXvuuefDDz+khRZArWhVAbyJnJM+Qgij0ZiVlbV69eoRI0YIISorKzds2LBy5crXXnvtjTfeUKvtl6fT6WoeHDZsWGhoqHPLRQ0lJSWVlZUmk0nuQiCEEMXFxf7+/rW9cDxHUJDYtUs9bZpm5847BzMzRXh4+bp15dHR8lV2h8lkKi4uDggIkLsQCCGE0WgsLS21bjCAaxQWFu7bt8/moE6ni3b4dSr/vimTJk0aPny49GcfH5/Jkyfff//933zzzaVLlxp0HjIKoFKpzGaz3FW4iGnTJtPGjdUO6fV+I0YopKnWbDarVCq5qwBk1vSPZjm/dbVs2VII0b17d+sXc2BgYNeuXS9cuFBcXFzbHaOjo5OSklxRIupTVlYWEBCg0WjkLgRCCGEwGIKDgz1/NMVi2jTRrZvNdE/Q2LEiJUUkJ8tVlMRkMpWXlwcFBclbBiRqtdrHx4enQxZN/LyWczSlW7duQojy8nLrg2az+fbt2zJVBMDd0KoCeDQ5Y8r999/v5+f31VdflZWVWQ5eu3bt5MmTbdu2bdeunYy1AXAb0q4qNtvqs6sK4BHkjCk9e/bs06ePTqfbs2ePNKFeWVn50UcfnT17NjY2ll4TAA2QnCzS0qodkXZVSU+Xpx4AzUHOmKLRaBYvXnzPPfcsXLgwLi5u0aJFjz/++Ouvv96zZ89p06bRfQagYeLjRW6u7cGEhGo7wgFwKzKv9OnVq9f777//5JNP/u9///vwww9LSkp+/etfv/feex07dpS3MABuSau106qSnk6rCuCm5F+QHBYWtnz58iNHjly4cOHw4cMLFy5s06aN3EUBcFu0qgAeRP6YAgDNLznZdlt9WlUAN0RMAeChpLXKWm21g7SqAG6FmALAc0kTQLSqAG6LmALAo9GqArgzYgoAL1Bbq0pqqkwFAXAIMQWAd7DbqpKSQqsKoGTEFABeo7ZWlfBwodfLUhGAuhFTAHgTu60q0gQQrSqA8hBTAHgfWlUAN0FMAeCVpFYVmwmglBTWKgOKQkwB4K3stqpIa5VpVQGUgZgCwLvRqgIoGDEFgNejVQVQKmIKANCqArhKA2dUiSkAIISgVQVwJr2+6nJa4eGdXnzR8fsRUwDAit1WFS4ABDSOXi8yM0VCgggPFwkJ0utovNHo+AmIKQBQXc1WFSFoVQEaRq8XqakiNlbExor09EafhpgCADXQqgI0jtXkjkhJsTthmqdWO36+BtwUALyI1KpiszJZalVJS7NNMICXkyZ3srLqGjjRakVMjBgyZGdxseMnZjQFAGrHripA3fT6O60ntWUUrVakpIjcXJGWJuLjG3R6RlMAoE7JyWLIENvpnthYkZIikpNlqgmQm14vtmwR6el1rYPTakV8vBgypCmjj8QUAKiP1Kry0zqFKikpIjPTTrMt4MGkyZ0tW+oaUJQmd6ZObZa5UWIKADhAalWxGdamVQVewpHWEyGq0kkDp3XqRkwBAIelpYkhQ0RCwp0jUqtKzX3hAM8gTe7YdGjZkCZ3pk4VWm2zPz4xBQAaIj5eaLW0qsDDSekkM9Nlkzu1IaYAQAPRqgJP5XjryZAhzTu5UxtiCgA0HK0q8DBSOqm79USa3HHtqCExBQAaq7ZWlbQ0MWWKfGUBDnPVuuJGI6YAQBPEx4uYGBEeXu1gQoI6K0ssXSpTTUB9XL6uuNGIKQDQNFqtnVaV9PSQ774TX38tW1VATQ3Z0t41rSf1IqYAQJNJrSqpqdbrNv10OqFSVQ2YC8E6IMjJ8XXFCvuHSkwBgGaSnCy6dKnWqiKE0OurPhtSUogscDUH1xXL13pSL2IKADQfqVUlNtZ+QyKRBa7hPq0n9SKmiJ/9TEycqNgcCcDdaLUiI8O0erV6zZq6bmYTWWJihFbrpH084S3k29Leebw3pljP01lm6/h6A6AZaLVi5crv583rXFlZ/5C7EEKvr/pcsY4sfHmC4xxfV+xuUdhLY0pmpkhIsPNs2v16w3sFgEbSakVyctX3Hke6BIRVZJHubll2wdsQalLMlvbO43UxxZFmZ8stea8A0GxqRhYh6nkz0uurhvEFb0Oworwt7Z3Hu2KKtD+kzSCK9Nqv9+uN5b1CKL0tGoDiSZFFCJGcTGRBA+j1IjVVgVvaO4+3xJTaBlFiYkRaWtU8nYMjssJqbkhYtbO423wfAGVoYmQRfHPyAorf0t55VGazWe4aGmbNmjVCiKSkJMfvotfb7g8p6oubDr5X2JC+4bhPA3UzKCgoCAgI0Gg0chcCIYT4/vvvO3TooFZ7y9cPJTOZTAUFBZ07d278KaQgcvFiPR9ONjz0s6qJjEajwWDo0KGD3IU0kAetK7bWoM9xz387q74tZBVpx8g6Bj9svt7o9SIry6HWN+kfVUJC1Rm8J68AaGbWKw8tkcWRtyGbwV4ii9txcEt77/ha7Mkxxe5ETyPm7CyzwNJ7hRCOdusnJIjUVHdc/wVAYWwii+PfnGwiS5cuHv+p5t4c39Leaz5XPHbSx+6S43oHURrK8bkhz2ppuoNJH0Vh0kc5mmHSxxGORxZr3rdDlNInfdx/S/sGadCkjwfGlNrCaEqKc1+SlkHZOiKL54VgYoqiEFOUw0UxxRqRpXYKjSke2npSL6+OKbUtOXbxSEZqqkOx2APeFogpikJMUQ4ZYooNx9cuWnjuwkVlxRQpUEord+rguR2OXhpTHFly7GKOTDKmpLj3GB4xRVGIKcohf0yx1rjI4kH7cCslpnjulvYN4q4rfSoqKhYvXvz5559v27YtKiqqQfdtxJJjF7DsOSmN6tnNzVKIkb1UAJ6MPfvl5QVb2juPgmLK7t27P/7440Z8L2/ckmNXiompWihUW4yW+vGlCwl56CAfAGVoXGRhA9xG8KYt7Z1HKTHlzJkzK1asaOgMVHMtOXYNy5tDHZNBLGMG4DpcZshJvG9Le+dRREwpKytbuXJlcHBweHj4qVOnHLyXa5YcO4P0zjB1qkODK/wzBuAK7NnfdF68pb3ztJC7ACGE2LZtW3Z29vz58zt16uTI7aWcWnNFT0qKyM1VekaxkN4TcnNFbm6tbwVSXgkPF6mpDdgsGwCaxDLKYjZXvUNJX5vqJr1hxcYKlarqbcvxjl23JvXxxMaK8HCRkmL/zVpKJxkZIjdXJCeTURwn/2jK0aNHN2zYMG7cuJiYmM8++8yRu/z1r+NNpmpH3HrUwfKGUNsyZgZXAMjGZpTFwcsMecOe/Wxp7xIyxxSDwbBq1aqQkJCkpCTHV1GaTNUGXWRccty8HOlckfKKuy9jBuCWmmvPfnd//2JLexeSM6aYzeb333//m2++efvtt0NCQhpxBrU6LzLyUFxc3t/+JoYNGxYaGtrsRbpeUJBIShJJSSI9XWRnq3futLP0yXoZc1LSTRdXaK2kpKSystJkM7oFmRQXF/v7+7NvihKYTKbi4uKAgAC5C3GaoCDRp4/o00ckJVmaVPwOHfLT6eq6V83IIsTNhlzxvnGMRmNpaam/v39TTqLOy/P74AP1gQN1xDJTp07lgwaZpky5k8NuyvkWLbvCwsJ9+/bZHNTpdNHR0Q6eQc63s6NHj7755puTJk0aPHhwg+7o56crL4/WasWMGYfU6jzpoGdkFGvx8SI+3pSSYty5U1Nnp21Qp06mefOMjClCpXK/DRs9ldlsVqlUclfhKj8t+SkXwpSXp87L8zt0yPFRlqCUFFOnTsbx44Vw4AJpriclsO3b60pgWq2IiTH94hfGCRNcWJkbaPpHs2xvakVFRc8//7wQYvPmzcHBwdLB+fPnf/HFF3Vv7ybtXhcYmORtn8r1jjLKMsTILrSKwi60yqGsXWhl1JQ9+5uvEa8xu9B6/Zb2zuMem+WfOHFiypQpBoPB7m8DAgJqCysN+ut5HsfXu7mm05aYoijEFOUgptjRlD37m/YNrGExhS3tncw9NssPDg4eP358eXm59UGdTpefnx8bG9uxY0fLEAusObhHXEqKSE/nRQRASZqyZ7+01tGplxny1usVK5yyZrIdn/Tx2tGUmuS9GjOjKYrCaIpyMJrSAI0bZWnIBrh1jaY4uK6YLe2bj3uMpqC5sIwZgHuTa89+trR3B8QUD2F5maen1/qtgKsxA1C6Ju7ZL01y1701C1vauxVlTfo4gkkfRzj4Mmx6fzqTPorCpI9yMOnTzByMLDZ+ShvG/v0NJ050OH2a1hMlcI+VPo1GTGkQZy9jJqYoCjFFOYgpTuT4nv0OYkt712rQ57giLj0I57Fc4LC2C4dZrm4oXSkMAJTOMnUtXbs1LU2kpDRy/EOrFSkpIiNDZGSQUZSJmOIVuBozAM9kiSzSxYczMhyKLDbXK2bbBgUjpngXBlcAeCyps6SOyCKlk7S0qjEYGlDcATHFGzk+uKJSVe3LAgDupHpkKd+7t+DSpap0wuSOWyGmeDUpr5jNdb1yU1JEbCyDKwDcllZrauAFbqEcxBQIIe6Mg9Y9GaRSifDwejZDAgCguRBTcIeDk0EJCXTaAgBcgZgCOxzvtB04MGT5cr/09KrLcRBcAADNiG2gUCtHrsacl6d+9VX797X8Qfqz9P9dutz5s+VXAADYRUxB/aS8MnVq/RvwW1hu48iNrXOMdXbp0oVAAwBejZgCRzkyuNI4UpQh0AAAbBBT0GDWV2POyyvZt+8utVotXaPU2RoaaIS9WSebrAMAUCxiChovPl4UFJTOnt3C+tKD1klCrxcXL945bjnoskAjGjhIQxsNACgKMQXNzPFRCuskIWOgEcw6AYBSEVMgG+t5mXrZBBcp09iM3Chw1olAAwBNQUyBe2joII1CZp2apY1GkGkAeCtiCjyNmwYa0YRBGksbzbVrfnFxzV0fAMiHmALv1eg2GmE162STdZytvgcKEULExFRdGhYA3B0xBaife7XRSBcukC50EB8vpk5lwgiAuyKmAM1MObNO0qWXLHllyBARE9P4swGA6xFTANm4LNBIeUV6rJiYqg36AED5iCmAG3Aw0Hz9dcGePSEtW6pru5SBXi/S04UQTAkBcA8t5C4AQLPp1MmUkiKSk4XZLHJzq7JIbaQhlvBwER4uUlNFZqbLygQARxFTAM8kzezk5lbllTq6UqS8EhtblVek4RYAUAJiCuDhpLySkVGVV+Lja72llFcSEoRKVRVZAEBexBTAW0h5JS1NmM0iI0PU1r8ikSKLJa8wJQRAFsQUwBtJ+7853sJimRIirwBwJWIK4NUa18ISG8uUEABXIKYAEKJ6C0vdU0J6fdUut5YpIRdcJQCAdyKmAKhG2gKOVc0AlICYAqBWjV7VzJQQgGZBTAFQP5tVzXVPCUk3YEoIQNMRUwA0gJRXrKeE6sCUEIAmIqYAaCQpsljyChvdAmh2xBQATWUzJVRvXpE2umVVM4B6EVMANBtLXnFko1tWNQOoFzEFgFOwqhlA0xFTADgXG90CaDRiCgAXadCqZqaEAAhiCgDXq7mqmSkhAHYRUwDIiY1uAdSBmAJAEWymhOLja71lzY1uAXgqYgoAZZHySlqaQ6uapchiyStMCQEehpgCQLkauqrZMiVEXgE8AzEFgBtoRAsLG90CHkD+mHLmzJlp06ZFRkZGRET07dt30aJF+fn5chcFQKGsW1jY6BbweDLHlL17944ePTorK6tfv35PPfVU27ZtP/zww/j4eJIKgLpptWx0C3g+OWPK1atX165dGxAQ8MEHH7z33nvLly///PPPFyxYcOHChddee80KjiP9AAATg0lEQVRkMslYGwA30rhVzQkJTAkBSidnTMnJyTl9+vTIkSP79esnHfHx8Zk4cWKPHj2OHj1648YNGWsD4I4atNFtejpTQoDSyRlTLl261KZNmz59+qhUKstBX1/fNm3ayFgVAA9Qc6PbOjAlBCiWnDHlmWeeOXLkSFxcnPXB06dPnzx5Miws7K677pKrMACeRIoslrzi+Ea36ekuqxGAfWq5C6jGYDCsWbOmtLR0woQJGo1G7nIAeBTLEIteL7ZsEZmZtQ6cSHlFCJGQIGJiqnp1ATSUNJcqvdCysoReL/R6UVg4aPnyQw6eQUExxWg0JicnZ2dnT5o0adSoUXXcUqfT1Tw4bNiw0NBQp1UH+0pKSiorK+l3Voji4mJ/f3+1WkGva2UKChJJSSIpSQhRFVbWrAmq7cbSDaSVRPHxYtCg8ujo8nofwmQyFRcXBwQENGPZaDSj0VhaWurv7y93IZ4sL08thNDp/IQQBw6opeuc1yJaCHeLKUVFRbNnz/7qq6/i4uIWL17csmXLhp6BjAKoVCqz2Sx3FW5GGixJSbmZl6feuVOTnl5rL+1PQyx+nTqpx483Snesjdlstu66AzyJNCgi/S8vT52fr5bSiTMoIqacPXt25syZZ8+enTZt2oIFC+rNKNHR0UnS9yDIraysLCAggBk6hTAYDMHBwYymNE5QkOjVy6Epobw89Zo1QWvWCK32zvYtNkwmU3l5eVBQrYM0cCW1Wu3j48PT0QiWOJKVVfWji3vM5X87y87OnjNnjsFgePHFF5977jkfHx+5KwLg1axbWDIzxcWLtS4Ukt6+raeEpk6ta5c5QMmcl0ikQK/ViiFDhBDiP//Z6fh9ZY4pR48enTNnzq1bt956661HHnlE3mIAwJqUPIS4M8RS75SQJa8MGaLu2tV1pQKOk/4NWxKJdZdrE0kZ3ZJIpB9rzo0WF+c5fk45Y0p+fv6CBQuEEJs3b37ggQdkrAQA6taIVUKdOnVQq+98jxRCdOlS7UfA2ewutGmWnQytI4iUSJz0D1vOmLJjx47z58/7+vrOnj3bptesY8eOa9euDQkJkas2ALDLJq9Iu9naJS18qO0jwfp7p3WIsRwEGsQDEoldssUUo9H473//Wwhx69atmhcaZMECAIWT8ooQIi1NZGaKrKx69rq1YRl4r+P8opYcU8cKI3gDT00kdskWUzQazXvvvSfXowNAM7JsAVfvlJDjGp1jZP9cQTOyRJCLF++0bDcLyz8VrbbqX44y46/8K30AwGNYpoTOnTMdPVpkNIZcvChE9X0mmosjOcYmtUjrLMgxyuSyhTaKTSR2EVMAoPlptaJVq/LOne38ynqdhXWIsf5Ds6j7bEwqyYhE4jhiCgC4lCUf1KaOHNOMO2sxqeQCsi/99QDEFABQlkbnGNdPKglyzE+c3dZqnUi86r8wMQUA3IwjOUb6gJTmFMRPH5+uzDEevOLaqxbayI6YAgCexvLZZpkFsL7qkMInlYSSJi9IJLIjpgCAd2FSqbZ6vHzprzIRUwAA1bhRjmncimsW2rgRYgoAoGHqzjEKXHHdvr26vNy/uJhE4n6IKQCA5qTIFdd+Qvg1+lTWiURp3TMej5gCAHAphUwq1VGYdy79VSZiCgBAWVyw4pqFNu6CmAIAcDMNXXF97pzJx6dCpfInkbgdYgoAwKPUHIwxGssNBkOHDv7yFIQmaCF3AQAAAPYRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgEIRUwAAgELJH1Py8/NnzpwZGRkZERExePDgd955p6KiQu6i4KjLly/LXQLu4OlQjsLCQrlLwB08He5L5phy8uTJcePGffbZZ/369Rs3bpzJZEpJSUlOTiapuIsVK1bs27dP7ipQZe7cubwdK8czzzwjdwmocuzYsblz58pdBRpDLeNjV1RUrFu3rri4+C9/+cuIESOEEAaD4fe///3HH388YsSIhx9+WMbaAACA7OQcTblw4YJOp4uOjo6JiZGOBAQEJCUl+fr6fvrpp2azWcbaAACA7OSMKadOnbp+/Xr//v39/f0tB8PDwzt16vTtt98WFRXJWBsAAJCdnDFFmkSPjIy0Pujr6xsUFFRcXGw0GmWqCwAAKIKcMeXixYs1D7Zu3To0NNRoNBYXF7u+JAAAoBwyt9DWPKhSqVq0qCc86XQ651SEBsvPz9fpdHl5eXIXAiGEyMvL27lzp9xVoEpeXt6aNWvkrgJCCKHT6fLz83k6FEJqS3XwxnLGlJYtW9Y8aDabb9++Xce9Bg0a5LSK0GDjx4+XuwTckZSUJHcJuIOnQzkc/1CEC0RHRzv+US5nTOnSpUvNg6WlpYWFhRqNJjAw0O69oqOj+QcHAIA3kLM3RYop586dsz5469atmzdvBgYGajQameoCAACKIGdM6datW7t27XQ6XVlZmeXg+fPn9Xr9z3/+8+DgYBlrAwAAspMzpnTq1KlPnz46nW7//v3SZm4Gg2Ht2rW3b98ePXq0SqWSsTYAACA7lbybvR49ejQxMfHmzZsDBgzo2LFjdnb2lStXJk2alJqaarfBFgAAeA+ZY4oQIjc399VXX83Ozr5161bHjh2nT5/+9NNPk1EAAID8MQUAAMAuOXtTAAAA6kBMAQAACkVMAQAACuVOMeXMmTOTJk3q3r17165dH3/88b1799JYI5ezZ88OHDgwoob169fLXZp3ycnJGTBgwP79+22OV1ZWfvrpp4MHD46IiIiMjJw2bVpubq4sFXqP2p6Ld999t+YrpXfv3idOnJClTs925syZadOmRUZGRkRE9O3bd9GiRfn5+dY34KXhSvU+HY68OuTcLL9B9u/fP2fOnIqKitjY2FatWmVlZc2YMWPhwoWJiYnssOJ6eXl5169fDwwMDAgIsD5u8yOcqqioaMWKFdevX7c5bjKZXnnlla1bt4aEhIwbN+7SpUtZWVnHjh3buHFjnz59ZCnV49X2XAghcnJyVCpVSEiIr6+v5WBAQIBa7TZvv+5i7969c+bMqaysHDBgwL333nv48OEPP/zwP//5T3p6elhYmOCl4Vr1Ph3CwVeH2R3cuHEjLi6uf//+R44ckY7k5eUNHTp04MCBp0+flrc277Rp06aIiIh//vOfchfivb7//vu4uLjw8PDw8PAvvvjC+lc6nS4qKurZZ58tKSmRjvzjH//o0aNHYmLiDz/8IEexHq6O58JoND777LOPPPLIlStX5CrPS1y5cmXEiBH9+/f/5ptvpCMmk+mtt96KiIiYNWtWRUWFmZeGCznydDj46nCPSZ/jx4+fPHly5MiRvXv3lo6EhYXNmjXr2rVr//znP+WtzTudOnUqKCioffv2chfijaRR67i4uHPnzv3sZz+z+a3ZbN67d++PP/74q1/9yjK49dhjjw0bNuzQoUM2l9BCE9X9XAghSktLL168GBYWdtddd7m+PK+Sk5Nz+vTpkSNH9uvXTzri4+MzceLEHj16HD169MaNG7w0XKnep0M4/Opwj5hy+PDhioqKQYMGWc/vREZG3n333d98882PP/4oY21eyGg05uXltW/fPjQ0VO5avNHJkyeXLFni4+Pz9ttv//KXv7T5bUlJybFjx+65557u3btbDqrV6oEDBxoMhuPHj7u2WA9X93MhhCgoKCgqKuratWvr1q1dX55XuXTpUps2bfr06WP9MeHr69umTRvpz7w0XKnep0M4/Opwj5hSWFgYEBDQqVMn64OBgYH+/v7Xr18vLy+XqzDvVFJSkp+fHxAQsHbt2gEDBkRERAwYMGDFihUlJSVyl+YVfHx8nnvuuS+++OKhhx6q+dsff/zxxo0bnTt3tn47EEJIQ18FBQUuqtI71P1cCCEuXbpkNBpv374tNRJK7f979uyprKx0cake75lnnjly5EhcXJz1wdOnT588eVL6vs5Lw5XqfTqEw68ON+jhKi0tvXLlSs3jd911V4cOHQoKChhNcbH8/Pzr16/n5+dfuHAhOjq6VatW2dnZb7/9dlZW1saNGy29UXCSn/3sZ3bnFyTXrl0zGo01j4eEhGg0msLCQmeW5nXqfi6EEN9++60QYtu2bV27do2Li7tx48a//vWvWbNmPf3008nJyVwVxKkMBsOaNWtKS0snTJig0Wj+97//8dKQkc3TIRx+dbhBTJFab+z+qkUL9xgN8jDFxcWtWrUaM2bMSy+95O/vL4QoKytbunTp9u3b//rXv7788sssYZBRZWWl3ddLixYtWBPnYpWVlSUlJRqN5tVXX/3lL38p/ffPzc2dPn36jh07fvGLX4wYMULuGj2W0WhMTk7Ozs6eNGnSqFGjBC8NWdl9Ohx8dbjBx7xKpartY+/27dsuLgZCiKFDhx45cmTZsmVSRhFC+Pv7/+53vwsLC5OucS1veV7Ox8fH7uvl9u3bZvYZci0fH5+lS5ceP3581KhRlg/C8PDwWbNmmUwmaU2QvBV6qqKiot///veffPJJXFzc4sWLpe/lvDTkUtvT4eCrww1iSuvWre+5556ax3/44YeCgoK2bdu2atXK9VXBRnBwcOfOnUtKSuxuHQGXadeunTSgauPq1atGo5GuZyXQarXSLENpaanctXigs2fPPv3009nZ2dOmTVuxYoXl5cBLQxa1PR21qfnqcIOYIoTQarUGg+Hy5cvWB4uLi8vKyu6++24/Pz+5CvNaBoOhoqLi/7d3PyFN/3Ecxz/f9v162iSq7yE9SH2jjCB2cNRBHIiaAw9qQWYQFRlkDlqgO+Ql8CAWSYxpiAjdVg0LozpkhDQQHP3xkEYRxugrguKoacFcrcNgiL/fr98Osc/X9nwcP6fX+PBmr+37+X6//1xXVdVms+U/D7IyZ7ZM0/z27dv69cz47Ny5U1KuAvXjx48vX7786491VVW51vDHRSKR1tbWT58+dXd3+/3+9ad/GI38+812iJynY3PUFKfTqWlaJBJZ/3nevn27tLRUUVHBvyn5lEqlOjo6nE7nxMTE+nXTND98+MBdytLZ7fb9+/cvLCzMzs5mF1Op1OTkpMPhOHjwoMRshSYWi1VVVTU2Nm44nvn69etEIsFdyn/cmzdvfD5fMpkcGBg4c+bMhp9MjEae/X47cp+OzVFT9u3bZxjGo0ePXr16lVkxTTMYDOq6Xl1dLTdboVFV9ciRI0KI27dvx+PxzGI8Hu/p6VleXm5qatq2bZvUgBDV1dWKogwPD2c36OnTp+Pj44cOHdqzZ4/cbAWlpKSkoqIiFos9ePAge4/ly5cvA4HA9u3bjx49KjfeX8Y0zc7OTiHEyMjIf30vMBp587/bkft0bI47MnRd93q9Pp/v5MmTVVVVmXf6rK6u+v3+9Q/qQX7U19cfP348FAq53W632y2EmJiYWFlZaWxsPHHihOx0EIcPH25ubg6FQh6Pp7Kycn5+PhqNbt26tb29PXvqGXmgqmpXV9fMzMy1a9fC4bDL5YrFYtFo1Gaz9fT0HDhwQHbAv8q9e/c+fvxYVFR06dKlDVfTSkpKAoGAruuMRt7ksh05TsfmqClCCI/Hs2PHjr6+vufPn//8+dMwDJ/PV19fz8Xd/NM07erVqy6Xa3Bw8PHjx0IIwzAuXLjQ0NDAcyCsILNB5eXlQ0NDo6OjRUVFbrf7ypUru3btkh2t4JSWlt65c+fWrVv379+/e/duZi+8Xm/2vR/4I1ZWVqampoQQyWRywzt4hRCKomQODDAa+ZHjduQ4HQo3YgEAAGvaHGdTAABAAaKmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAAAAi6KmAJAskUi0tLTs3r27u7s7lUpl10dHRw3DqK2tNU1TYjwAElFTAEjmcDj8fr/D4QiHw5OTk5nFz58/B4NBTdMuX75cWloqNyEAWagpAORzOp2nTp1KJpPBYDCRSKytrd28eXNubq65ubmmpkZ2OgDSqLIDAIBQFOXs2bORSCQajY6NjRUXF4+NjRmGcfHiRU3TZKcDII2STqdlZwAAIYR48eJFW1ub3W7fsmXL169f+/v7PR6P7FAAZOKiDwCrqKysbG1tXV5eXlpaOnbsWG1trexEACSjpgCwCkVRXC6XpmmKopSVlakqV6WBQkdNAWAVi4uLgUAglUrZbLbh4eH379/LTgRAMmoKAEtIp9ODg4Pv3r1ramo6ffr04uLi9evXv3//LjsXAJmoKQAsYWpqKhwO67p+/vz5tra28vLyZ8+ePXnyRHYuADJRUwDIF4/He3t7V1dXz507t3fvXl3XvV6vqqo3btyYm5uTnQ6ANNQUAJKl0+lQKDQ9Pe1yuVpaWjKLNTU1dXV18/PzAwMDa2trchMCkIWaAkCy6enpkZERu93u8/kcDkdmUdM0r9er6/rDhw/Hx8flJgQgC493AwAAFsW/KQAAwKJ+ASB+OXeEZTplAAAAAElFTkSuQmCC\" alt=\"Scaling function's graph\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y_scaled, s, r] = scaling(x,y,k)\r\n  y_scaled = x;\r\n  s = x;\r\n  r = x;\r\nend","test_suite":"%% \r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [4 4.6 4.4 3.4 3.1 1.8 1.4 2];\r\nk = 2.62; \r\ny_correct = [10.48  12.052  11.528  8.908  8.122  4.716  3.668  5.24];\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi/2:pi/12:pi/2;\r\ny = sin(x).*cos(x);\r\nk = 2;\r\ny_correct = sin(2*x);\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi/2:pi/12:pi/2;\r\ny = 1 - cos(2*x);\r\nk = 0.5;\r\ny_correct = (sin(x)).^2;\r\ns_correct = 'compress';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi:pi/6:pi;\r\ny = (sin(x)).^2;\r\nk = - 1;\r\ny_correct = (cos(x)).^2 -1;\r\ns_correct = '';\r\nr_correct = 'flip';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -5:5;\r\ny = atan(x);\r\nk = 0;\r\ny_correct = 0.*x;\r\ns_correct = 'compress';\r\nr_correct = 'flat';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nfiletext = fileread('scaling.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = -2:0.5:2;\r\ny = polyval([1/3 0 -1 0], x);\r\nk = 3;\r\ny_correct = [-2 9/8 2 11/8 0 -11/8 -2 -9/8 2];\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(isequal(s, s_correct))\r\nassert(isequal(r, r_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-11T13:38:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-06T11:12:26.000Z","updated_at":"2026-03-28T12:45:32.000Z","published_at":"2026-01-11T13:38:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a real function by the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of inputs and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof outputs, consider shifting vertically its graph by the scale factor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figure below). Return\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_scaled\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector that stands for the outputs of the scaled function;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'strech' or 'compress', if the graph will be away from or towards the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis, respectively, becoming narrower or wider relative to the original function's graph. Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = '', if there is no change in size;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'flip' or 'flat' if the graph will be reflected over the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis or collapses the entire graph onto the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis, respectively. Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = '', if the orientation is preserved.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(x, y, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[y_scaled, s, r]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"250\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"369\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Scaling function's graph\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61165,"title":"Breaking straight lines","description":"Let P be a point in Oxy plane and let p be a 1×2 array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\r\nBreak the given line by building a piecewise linear function constituted by two branches:\r\none branch stands for the parent polynomial p;\r\nand another branch stands for the perpendicular line, r, to p that passes by the point P (see figure below).\r\nGiven (P, p), find\r\nR, the breaking point;\r\nr, the 1×2 array that represents the perpendicular line. If r violates the definition of a function, return r = ''.\r\ninput: (P, p)\r\noutput: (R, r)\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 508.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 254.275px; transform-origin: 408px 254.275px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a point in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOxy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e plane and let \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBreak the given line by building a piecewise linear function constituted by two branches:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eone branch stands for the parent polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand another branch stands for the perpendicular line, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that passes by the point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(P, p)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the breaking point;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array that represents the perpendicular line. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e violates the definition of a function, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er = ''\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(P, p)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(R, r)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 213.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 106.9px; text-align: left; transform-origin: 384px 106.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"251\" height=\"208\" style=\"vertical-align: baseline;width: 251px;height: 208px\" src=\"data:image/png;base64,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\" alt=\"Break line\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [R, r] = breaking(P,p)\r\n  R = x;\r\n  r = x;\r\nend","test_suite":"%%\r\nP = [1 1];\r\np = [2 1];\r\nR_correct = [0.2 1.4];\r\nr_correct = [-0.5 1.5];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.5 1];\r\nR_correct = [0.8 0.6];\r\nr_correct = [2 -1];\r\n[R, r] = breaking(P,p);\r\nassert(all(isapprox(R,R_correct), 'all'))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.5 1.5];\r\nR_correct = [1 1];\r\nr_correct = [2 -1];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [1 -1];\r\nR_correct = [1.5 0.5];\r\nr_correct = [-1 2];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nfiletext = fileread('breaking.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nP = [1 1];\r\np = [0 2];\r\nR_correct = [1 2];\r\nr_correct = '';\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.2 2];  \r\nR_correct = [15/13 23/13];\r\nr_correct = [5 -4];\r\n[R, r] = breaking(P,p);\r\nassert(all(isapprox(R,R_correct), 'all'))\r\nassert(isequal(r,r_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-29T17:18:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-01-29T17:18:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-15T15:30:33.000Z","updated_at":"2026-04-09T10:19:31.000Z","published_at":"2026-01-26T14:18:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a point in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOxy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e plane and let \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBreak the given line by building a piecewise linear function constituted by two branches:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eone branch stands for the parent polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand another branch stands for the perpendicular line, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that passes by the point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(P, p)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the breaking point;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array that represents the perpendicular line. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e violates the definition of a function, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(P, p)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(R, r)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"208\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"251\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Break line\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":61151,"title":"Scaling vertically functions","description":"Given a real function by the 1×n array, x, of inputs and the 1×n array, y, of outputs, consider shifting vertically its graph by the scale factor k (see figure below). Return\r\ny_scaled, which is the 1×n vector that stands for the outputs of the scaled function;\r\ns = 'strech' or 'compress', if the graph will be away from or towards the x-axis, respectively, becoming narrower or wider relative to the original function's graph. Return s = '', if there is no change in size;\r\nr = 'flip' or 'flat' if the graph will be reflected over the x-axis or collapses the entire graph onto the x-axis, respectively. Return r = '', if the orientation is preserved.\r\ninput: (x, y, k)\r\noutput: [y_scaled, s, r]\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 489.987px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 244.988px; transform-origin: 408px 244.994px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven a real function by the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e of inputs and the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eof outputs, consider shifting vertically its graph by the scale factor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ek \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figure below). Return\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 102.188px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 51.0875px; transform-origin: 391px 51.0938px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ey_scaled\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, which is the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003en\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e vector that stands for the outputs of the scaled function;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'strech' or 'compress', if the graph will be away from or towards the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis, respectively, becoming narrower or wider relative to the original function's graph. Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003es\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = '', if there is no change in size;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 40.875px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4375px; text-align: left; transform-origin: 363px 20.4375px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = 'flip' or 'flat' if the graph will be reflected over the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis or collapses the entire graph onto the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ex\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e-axis, respectively. Return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e = '', if the orientation is preserved.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(x, y, k)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e[y_scaled, s, r]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 255.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 127.9px; text-align: left; transform-origin: 384px 127.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"369\" height=\"250\" style=\"vertical-align: baseline;width: 369px;height: 250px\" src=\"data:image/png;base64,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\" alt=\"Scaling function's graph\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [y_scaled, s, r] = scaling(x,y,k)\r\n  y_scaled = x;\r\n  s = x;\r\n  r = x;\r\nend","test_suite":"%% \r\nx  = [0 1 2 5 10 15 20 25];\r\ny = [4 4.6 4.4 3.4 3.1 1.8 1.4 2];\r\nk = 2.62; \r\ny_correct = [10.48  12.052  11.528  8.908  8.122  4.716  3.668  5.24];\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi/2:pi/12:pi/2;\r\ny = sin(x).*cos(x);\r\nk = 2;\r\ny_correct = sin(2*x);\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi/2:pi/12:pi/2;\r\ny = 1 - cos(2*x);\r\nk = 0.5;\r\ny_correct = (sin(x)).^2;\r\ns_correct = 'compress';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -pi:pi/6:pi;\r\ny = (sin(x)).^2;\r\nk = - 1;\r\ny_correct = (cos(x)).^2 -1;\r\ns_correct = '';\r\nr_correct = 'flip';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nx = -5:5;\r\ny = atan(x);\r\nk = 0;\r\ny_correct = 0.*x;\r\ns_correct = 'compress';\r\nr_correct = 'flat';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(strcmp(s, s_correct))\r\nassert(strcmp(r, r_correct))\r\n\r\n%%\r\nfiletext = fileread('scaling.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = -2:0.5:2;\r\ny = polyval([1/3 0 -1 0], x);\r\nk = 3;\r\ny_correct = [-2 9/8 2 11/8 0 -11/8 -2 -9/8 2];\r\ns_correct = 'stretch';\r\nr_correct = '';\r\n[y_scaled, s, r] = scaling(x,y,k);\r\nassert(all(isapprox(y_scaled, y_correct), 'all'))\r\nassert(isequal(s, s_correct))\r\nassert(isequal(r, r_correct))\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-11T13:38:18.000Z","deleted_by":null,"deleted_at":null,"solvers_count":14,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-06T11:12:26.000Z","updated_at":"2026-03-28T12:45:32.000Z","published_at":"2026-01-11T13:38:18.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a real function by the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e of inputs and the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003eof outputs, consider shifting vertically its graph by the scale factor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ek \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figure below). Return\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey_scaled\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which is the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e vector that stands for the outputs of the scaled function;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'strech' or 'compress', if the graph will be away from or towards the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis, respectively, becoming narrower or wider relative to the original function's graph. Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003es\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = '', if there is no change in size;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = 'flip' or 'flat' if the graph will be reflected over the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis or collapses the entire graph onto the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e-axis, respectively. Return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e = '', if the orientation is preserved.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(x, y, k)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e[y_scaled, s, r]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"250\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"369\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Scaling function's graph\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":61165,"title":"Breaking straight lines","description":"Let P be a point in Oxy plane and let p be a 1×2 array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\r\nBreak the given line by building a piecewise linear function constituted by two branches:\r\none branch stands for the parent polynomial p;\r\nand another branch stands for the perpendicular line, r, to p that passes by the point P (see figure below).\r\nGiven (P, p), find\r\nR, the breaking point;\r\nr, the 1×2 array that represents the perpendicular line. If r violates the definition of a function, return r = ''.\r\ninput: (P, p)\r\noutput: (R, r)\r\n","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 508.55px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 408px 254.275px; transform-origin: 408px 254.275px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a point in \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eOxy\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e plane and let \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e be a \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eBreak the given line by building a piecewise linear function constituted by two branches:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eone branch stands for the parent polynomial \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eand another branch stands for the perpendicular line, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, to \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ep\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e that passes by the point \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eP \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e(see figure below).\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(P, p)\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, find\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 40.875px; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 391px 20.4375px; transform-origin: 391px 20.4375px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003eR,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the breaking point;\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4375px; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2125px; text-align: left; transform-origin: 363px 10.2188px; white-space-collapse: preserve; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er,\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e1\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e×\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e2\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e array that represents the perpendicular line. If \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e violates the definition of a function, return \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003er = ''\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003einput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(P, p)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-family: Menlo, Monaco, Consolas, \u0026quot;Courier New\u0026quot;, monospace; \"\u003eoutput: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-style: italic; \"\u003e(R, r)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 213.8px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 384px 106.9px; text-align: left; transform-origin: 384px 106.9px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cimg class=\"imageNode\" width=\"251\" height=\"208\" style=\"vertical-align: baseline;width: 251px;height: 208px\" src=\"data:image/png;base64,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\" alt=\"Break line\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [R, r] = breaking(P,p)\r\n  R = x;\r\n  r = x;\r\nend","test_suite":"%%\r\nP = [1 1];\r\np = [2 1];\r\nR_correct = [0.2 1.4];\r\nr_correct = [-0.5 1.5];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.5 1];\r\nR_correct = [0.8 0.6];\r\nr_correct = [2 -1];\r\n[R, r] = breaking(P,p);\r\nassert(all(isapprox(R,R_correct), 'all'))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.5 1.5];\r\nR_correct = [1 1];\r\nr_correct = [2 -1];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [1 -1];\r\nR_correct = [1.5 0.5];\r\nr_correct = [-1 2];\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nfiletext = fileread('breaking.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'regexp') || ...\r\n          contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nP = [1 1];\r\np = [0 2];\r\nR_correct = [1 2];\r\nr_correct = '';\r\n[R, r] = breaking(P,p);\r\nassert(isequal(R,R_correct))\r\nassert(isequal(r,r_correct))\r\n\r\n%%\r\nP = [1 1];\r\np = [-0.2 2];  \r\nR_correct = [15/13 23/13];\r\nr_correct = [5 -4];\r\n[R, r] = breaking(P,p);\r\nassert(all(isapprox(R,R_correct), 'all'))\r\nassert(isequal(r,r_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":4,"created_by":4993982,"edited_by":4993982,"edited_at":"2026-01-29T17:18:34.000Z","deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":"2026-01-29T17:18:34.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-01-15T15:30:33.000Z","updated_at":"2026-04-09T10:19:31.000Z","published_at":"2026-01-26T14:18:09.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a point in \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOxy\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e plane and let \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e be a \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array representing an one-degree or zero-degree polynomials, if its first entry is a non-zero constant or a zero constant, respectively.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBreak the given line by building a piecewise linear function constituted by two branches:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eone branch stands for the parent polynomial \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand another branch stands for the perpendicular line, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, to \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ep\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that passes by the point \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e(see figure below).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(P, p)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, find\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eR,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the breaking point;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e×\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e array that represents the perpendicular line. If \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e violates the definition of a function, return \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003er = ''\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003einput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(P, p)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eoutput: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(R, r)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"208\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"251\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"baseline\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"Break line\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"target\":\"/media/image1.png\",\"relationshipId\":\"rId1\"}]},{\"partUri\":\"/media/image1.png\",\"contentType\":\"image/png\",\"content\":\"data:image/png;base64,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\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"if-then-else\"","current_player_id":null,"fields":[{"name":"page","type":"integer","callback":null,"default":1,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"per_page","type":"integer","callback":null,"default":50,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"sort","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":null,"prepend":true},{"name":"body","type":"text","callback":null,"default":"*:*","directive":null,"facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":false},{"name":"group","type":"string","callback":null,"default":null,"directive":"group","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"difficulty_rating_bin","type":"string","callback":null,"default":null,"directive":"difficulty_rating_bin","facet":true,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"id","type":"integer","callback":null,"default":null,"directive":"id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"tag","type":"string","callback":null,"default":null,"directive":"tag","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"product","type":"string","callback":null,"default":null,"directive":"product","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_at","type":"timeframe","callback":{},"default":null,"directive":"created_at","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"profile_id","type":"integer","callback":null,"default":null,"directive":"author_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"created_by","type":"string","callback":null,"default":null,"directive":"author","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player_id","type":"integer","callback":null,"default":null,"directive":"solver_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"player","type":"string","callback":null,"default":null,"directive":"solver","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"solvers_count","type":"integer","callback":null,"default":null,"directive":"solvers_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"comments_count","type":"integer","callback":null,"default":null,"directive":"comments_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"likes_count","type":"integer","callback":null,"default":null,"directive":"likes_count","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leader_id","type":"integer","callback":null,"default":null,"directive":"leader_id","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true},{"name":"leading_solution","type":"integer","callback":null,"default":null,"directive":"leading_solution","facet":null,"facet_method":"and","operator":null,"param":"term","static":null,"prepend":true}],"filters":[{"name":"asset_type","type":"string","callback":null,"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":null,"static":"\"cody:problem\"","prepend":true},{"name":"profile_id","type":"integer","callback":{},"default":null,"directive":null,"facet":null,"facet_method":"and","operator":null,"param":"author_id","static":null,"prepend":true}],"query":{"params":{"per_page":50,"term":"tag:\"if-then-else\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"if-then-else\"","","\"","if-then-else","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f64b6ab4380\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f64b6ab42e0\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f64b6ab3a20\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f64b6ab4600\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f64b6ab4560\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f64b6ab44c0\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f64b6ab4420\u003e":"tag:\"if-then-else\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f64b6ab4420\u003e":"tag:\"if-then-else\""},"queried_facets":{}},"query_backend":{"connection":{"configuration":{"index_url":"http://index-op-v2/solr/","query_url":"http://search-op-v2/solr/","direct_access_index_urls":["http://index-op-v2/solr/"],"direct_access_query_urls":["http://search-op-v2/solr/"],"timeout":10,"vhost":"search","exchange":"search.topic","heartbeat":30,"pre_index_mode":false,"host":"rabbitmq-eks","port":5672,"username":"cody-search","password":"78X075ddcV44","virtual_host":"search","indexer":"amqp","http_logging":"true","core":"cody"},"query_connection":{"uri":"http://search-op-v2/solr/cody/","proxy":null,"connection":{"parallel_manager":null,"headers":{"User-Agent":"Faraday v1.0.1"},"params":{},"options":{"params_encoder":"Faraday::FlatParamsEncoder","proxy":null,"bind":null,"timeout":null,"open_timeout":null,"read_timeout":null,"write_timeout":null,"boundary":null,"oauth":null,"context":null,"on_data":null},"ssl":{"verify":true,"ca_file":null,"ca_path":null,"verify_mode":null,"cert_store":null,"client_cert":null,"client_key":null,"certificate":null,"private_key":null,"verify_depth":null,"version":null,"min_version":null,"max_version":null},"default_parallel_manager":null,"builder":{"adapter":{"name":"Faraday::Adapter::NetHttp","args":[],"block":null},"handlers":[{"name":"Faraday::Response::RaiseError","args":[],"block":null}],"app":{"app":{"ssl_cert_store":{"verify_callback":null,"error":null,"error_string":null,"chain":null,"time":null},"app":{},"connection_options":{},"config_block":null}}},"url_prefix":"http://search-op-v2/solr/cody/","manual_proxy":false,"proxy":null},"update_format":"RSolr::JSON::Generator","update_path":"update","options":{"url":"http://search-op-v2/solr/cody"}}},"query":{"params":{"per_page":50,"term":"tag:\"if-then-else\"","current_player":null,"sort":"map(difficulty_value,0,0,999) asc"},"parser":"MathWorks::Search::Solr::QueryParser","directives":{"term":{"directives":{"tag":[["tag:\"if-then-else\"","","\"","if-then-else","\""]]}}},"facets":{"#\u003cMathWorks::Search::Field:0x00007f64b6ab4380\u003e":null,"#\u003cMathWorks::Search::Field:0x00007f64b6ab42e0\u003e":null},"filters":{"#\u003cMathWorks::Search::Field:0x00007f64b6ab3a20\u003e":"\"cody:problem\""},"fields":{"#\u003cMathWorks::Search::Field:0x00007f64b6ab4600\u003e":1,"#\u003cMathWorks::Search::Field:0x00007f64b6ab4560\u003e":50,"#\u003cMathWorks::Search::Field:0x00007f64b6ab44c0\u003e":"map(difficulty_value,0,0,999) asc","#\u003cMathWorks::Search::Field:0x00007f64b6ab4420\u003e":"tag:\"if-then-else\""},"user_query":{"#\u003cMathWorks::Search::Field:0x00007f64b6ab4420\u003e":"tag:\"if-then-else\""},"queried_facets":{}},"options":{"fields":["id","difficulty_rating"]},"join":" "},"results":[{"id":61151,"difficulty_rating":"easy"},{"id":61165,"difficulty_rating":"easy-medium"}]}}