Problem 57646. Easy Sequences 93: Recursive Polynomial Function

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For a natural number </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:t> and a polynomial function </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>P(x)</w:t></w:r></w:customXml><w:r><w:t>, we define a recursive function </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>R(x)</w:t></w:r></w:customXml><w:r><w:t>, as follows:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>R(0)=P(0)</w:t></w:r></w:customXml><w:r><w:t>, and</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>R(x) = x\\cdot R(x-1) + P(x)</w:t></w:r></w:customXml><w:r><w:t>, for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x&gt;0</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>P(x) = x^2+2x+1</w:t></w:r></w:customXml><w:r><w:t> (or in Matlab array form, </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>P = [1 2 1]</w:t></w:r><w:r><w:t>):</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>R(0) = P(0)=0^2+2\\cdot 0 + 1=1</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>R(1) = 1\\cdot R(0)+P(1)=1\\cdot 1+1^2+2\\cdot 1 + 1=5</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>R(2) = 2\\cdot R(1)+P(2)=2\\cdot 5+2^2+2\\cdot 2 + 1=19</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>R(3) = 3\\cdot R(2)+P(3)=3\\cdot 19+3^2+2\\cdot 3 + 1=73</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> ...</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>R(10) = 49320491</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> and so on...</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>We can see that </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>R(x)</w:t></w:r></w:customXml><w:r><w:t> can grow very quickly. Therefore, we will instead calculate:</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>T(x) = \\text{log}|R(x)|</w:t></w:r></w:customXml><w:r><w:t>, that is, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>T(x)</w:t></w:r></w:customXml><w:r><w:t>is equal to the logarithm (base-</w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>e</w:t></w:r></w:customXml><w:r><w:t>) of the absolute value of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>R(x)</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given a polynomial array </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>P</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, and an integer </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, find the value of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>T(x)</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, rounded-off to 4 decimal places.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>----------------------</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>NOTE: </w:t></w:r><w:r><w:t>To encourage vectorization , </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>FOR and WHILE loops are disabled</w:t></w:r><w:r><w:t>. If you know the </w:t></w:r><w:hyperlink w:docLocation=\"https://www.cs.mtsu.edu/~xyang/3080/recurrenceRelations.html\"><w:r><w:rPr><w:b/><w:u/></w:rPr><w:t>math</w:t></w:r></w:hyperlink><w:r><w:t>, this problem can be solved in less than </w:t></w:r><w:r><w:rPr><w:u/></w:rPr><w:t>15</w:t></w:r><w:r><w:t> lines of code. However, </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>solutions up to </w:t></w:r><w:r><w:rPr><w:b/><w:u/></w:rPr><w:t>50</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> lines of code will still be accepted</w:t></w:r><w:r><w:t>. The semicolon (</w:t></w:r><w:r><w:rPr><w:b/><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>;</w:t></w:r><w:r><w:t>), shall be considered as an end-of-line character. </w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 505px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 252.5px; transform-origin: 407px 252.5px; vertical-align: baseline; "><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 69px 8px; transform-origin: 69px 8px; unicode-bidi: normal; ">For a natural number x<span 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: 84.5px 8px; transform-origin: 84.5px 8px; unicode-bidi: normal; "> and a polynomial function <img src="data:image/png;base64,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" style="width: 31.5px; height: 18.5px;" width="31.5" height="18.5"><span 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: 100px 8px; transform-origin: 100px 8px; unicode-bidi: normal; ">, we define a recursive function <img src="data:image/png;base64,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" style="width: 32px; height: 18.5px;" width="32" height="18.5"><span 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: 36.5px 8px; transform-origin: 36.5px 8px; unicode-bidi: normal; ">, as follows:</div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 79px; height: 18.5px;" width="79" height="18.5"><span 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: 18px 8px; transform-origin: 18px 8px; unicode-bidi: normal; ">, and</div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 167.5px; height: 18.5px;" width="167.5" height="18.5"><span 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: 16.5px 8px; transform-origin: 16.5px 8px; unicode-bidi: normal; ">, for <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEkAAAAkCAYAAADFGRdYAAADS0lEQVRoQ+2YOasVMRTH3/sEbp2VuNRaKDZaaKGCraBiKbg0VuIOFi7gWrqA1j5RW3EBLbRQFNHKwuUbuOEH0P/vkcC5uZlMJs69V7gZ+PPumyRzzvxycnIyszP1aiUw29qjdpipkDKCoEKqkDIIZHSpkVQhNRJYrpalrvVlG6dpi6RdAnJWeiu9k5ZJ3Dsu3Ze+xYBNE6RrAnBQOi+dNDD26/cN6bG0JwZqWiB5EF8EYX0ExCPd2xoBOM9yEpDIB1/b8kCP7Uv0rE/SoiYIbsndcTbX6O8Ha38SkP44Z2+PCZaPIt57u/QwMgFMHFHGFS7HiUTSdzer3qFRw3ojQ2sdgBWJifF+AWtlSST5LfOjBoc7wAbd+x2GaGK5EP57pWMG1nX9vtnhGYnHDzURuVw/pMWJgT4v0WUAZmq5rVZnQnWLGxSGIu0PXBsOMFtdck0MFjvM0R5h4eP7AkgDyzIFiej5JRE5nx0Mvzss0P/UGkTATjdDqVlKzfwoYRHlLwogHdAYInv+yk3cR9T3ghtDKN6Vrkhzqbfv2DYKWBYSPlM4Nl32HYsgWWNE0BPJFmQdeSS79wnL+s1S3pawfE5tJ1x7ESTG5ibAvoB5WPv0QKKXiwk6LcW28ZjdsS43HPDZH0fX9UWi5TnkxcMSxwl/UcdclaLnrMjzcifX7m4DBWVuTsI2+YckzU62qoOTJTxDONjkEPpU6rKDYttvOrklwNBOnQvJVq0YbqpcS4DYMb7s8JHj4TSe0DMM+oMtXYeOHGa8j7ihlZIDydca5IXG0j3D2VQXcscpiUMmVx9wvD2bl3a7FRH6YuupgaRNxzZIJM/X0iGJZBnLS8zU5YJlgP0QDpNwSfqXyIlNhve7aYfzO1v0K0EMEkuL65V0S7onXXT3wnqJpMqsdy0HQjiEeN91l4VFjsMGXwLCJWe/EmxU+9CXyhCSDU2MhAWYDctYe2wWw3t2Fxk1HGsb35+7G5v0l88hwOMdOVI15tkQElTPuMHPTARZY0TTZqmpvQ0UCXKccKw/vN8OCUgLpZ8OXHLXbMtJbS9c0s7RoM/jTIkPncZMAlInB/+HzhVSxixUSBVSBoGMLjWSKqQMAhldaiRVSBkEMrr8BSuWwSV1VFtVAAAAAElFTkSuQmCC" style="width: 36.5px; height: 18px;" width="36.5" height="18"><span 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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</div><div style="block-size: 21.5px; 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; perspective-origin: 384px 10.75px; text-align: left; transform-origin: 384px 10.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 48.5px 8px; transform-origin: 48.5px 8px; unicode-bidi: normal; ">For example, if <img src="data:image/png;base64,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" style="width: 118.5px; height: 19.5px;" width="118.5" height="19.5"><span 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: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; "> (or in Matlab array form, <span 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: 44px 8px; transform-origin: 44px 8px; unicode-bidi: normal; ">P = [1 2 1]<span 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: 4.5px 8px; transform-origin: 4.5px 8px; unicode-bidi: normal; ">):</div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 203.5px; height: 19.5px;" width="203.5" height="19.5"></div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 311px; height: 19.5px;" width="311" height="19.5"></div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 318.5px; height: 19.5px;" width="318.5" height="19.5"></div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 326px; height: 19.5px;" width="326" height="19.5"></div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; "> ...</div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 32px 8px; transform-origin: 32px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 118px; height: 18.5px;" width="118" height="18.5"></div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 69.5px 8px; transform-origin: 69.5px 8px; unicode-bidi: normal; "> and so on...</div><div 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; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 53.5px 8px; transform-origin: 53.5px 8px; unicode-bidi: normal; ">We can see that <img src="data:image/png;base64,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" style="width: 32px; height: 18.5px;" width="32" height="18.5"><span 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: 185px 8px; transform-origin: 185px 8px; unicode-bidi: normal; "> can grow very quickly. Therefore, we will instead calculate:<span 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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; "> <img src="data:image/png;base64,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" style="width: 108.5px; height: 18.5px;" width="108.5" height="18.5"><span 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: 27px 8px; transform-origin: 27px 8px; unicode-bidi: normal; ">, that is, <img src="data:image/png;base64,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" style="width: 32px; height: 18.5px;" width="32" height="18.5"><span 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: 26.5px 8px; transform-origin: 26.5px 8px; unicode-bidi: normal; ">is equal to the logarithm (base-e<span 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: 80.5px 8px; transform-origin: 80.5px 8px; unicode-bidi: normal; ">) of the absolute value of <img src="data:image/png;base64,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" style="width: 32px; height: 18.5px;" width="32" height="18.5"><span 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: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; ">.</div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 88px 8px; transform-origin: 88px 8px; unicode-bidi: normal; ">Given a polynomial array P<span 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: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; ">, and an integer x<span 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: 63.5px 8px; transform-origin: 63.5px 8px; unicode-bidi: normal; ">, find the value of <img src="data:image/png;base64,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" style="width: 32px; height: 18.5px;" width="32" height="18.5"><span 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: 117px 8px; transform-origin: 117px 8px; unicode-bidi: normal; ">, rounded-off to 4 decimal places.</div><div 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; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 55px 8px; transform-origin: 55px 8px; unicode-bidi: normal; ">----------------------</div><div style="block-size: 63.5px; 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; perspective-origin: 384px 31.75px; text-align: left; transform-origin: 384px 31.75px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span 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: 23px 8px; transform-origin: 23px 8px; unicode-bidi: normal; ">NOTE: <span 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: 91px 8px; transform-origin: 91px 8px; unicode-bidi: normal; ">To encourage vectorization , <span 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: 121px 8px; transform-origin: 121px 8px; unicode-bidi: normal; ">FOR and WHILE loops are disabled<span 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: 53px 8px; transform-origin: 53px 8px; unicode-bidi: normal; ">. If you know the <a target='_blank' href = "https://www.cs.mtsu.edu/~xyang/3080/recurrenceRelations.html">math</a><span 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: 68px 8px; transform-origin: 68px 8px; unicode-bidi: normal; ">, this problem can be solved in less than <span 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: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; ">15<span 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: 76.5px 8px; transform-origin: 76.5px 8px; unicode-bidi: normal; "> lines of code. However, <span 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: 54.5px 8px; transform-origin: 54.5px 8px; unicode-bidi: normal; ">solutions up to <span 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: 8px 8px; transform-origin: 8px 8px; unicode-bidi: normal; ">50<span 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: 121px 8px; transform-origin: 121px 8px; unicode-bidi: normal; "> lines of code will still be accepted<span 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: 52px 8px; transform-origin: 52px 8px; unicode-bidi: normal; ">. The semicolon (<span 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: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; ">;<span 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: 159px 8px; transform-origin: 159px 8px; unicode-bidi: normal; ">), shall be considered as an end-of-line character. </div></div></div>

Solve

Solution Stats

3 Solutions
2 Solvers

Last Solution submitted on Apr 29, 2023

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Ramon Villamangca on 7 Feb 2023

Update:
1. Up to 50 lines of code is acceptable solution.
2. Link to a website explaining recursive closed form is added.

Solution Comments

Show comments

Problem Recent Solvers2

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 57646. Easy Sequences 93: Recursive Polynomial Function

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers2

Suggested Problems

More from this Author116

Problem Tags

Community Treasure Hunt

Problem 57646. Easy Sequences 93: Recursive Polynomial Function

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers2

Suggested Problems

More from this Author116

Problem Tags

Community Treasure Hunt

Players