Problem 44476. How many unique Pythagorean triples?

Created by Shaul Salomon

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For a given integer</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>n</w:t></w:r><w:r><w:t>, return all</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://en.wikipedia.org/wiki/Pythagorean_triple\"><w:r><w:t>Pythagorean triples</w:t></w:r></w:hyperlink><w:r><w:t> that inlude numbers smaller or equal to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>n</w:t></w:r><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>A Pythagorean triple consist of three positive integers</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>{a, b, c}</w:t></w:r><w:r><w:t> such that:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ a < b < c,\n a^2 + b^2 = c^2]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The triples should be retured in a matrix with tree columns, where each row contains a different triple. Every row needs to be sorted in ascending order (</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>a</w:t></w:r><w:r><w:t> in the first column,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>b</w:t></w:r><w:r><w:t> in the second and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>c</w:t></w:r><w:r><w:t> in the third), and the first column must also be sorted.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Example:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[Input:  n   = 16\nOutput: mat = [3,  4, 5\n               5, 12, 13 \n               6,  8, 10 \n               9, 12, 15]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>n</w:t></w:r><w:r><w:t> is not an integer, or it is smaller than 5, the function should return an empty matrix.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

712 Solutions
133 Solvers

Last Solution submitted on Jun 02, 2022

Last 200 Solutions

Problem Recent Solvers133

Problem Tags

22105 pythagoras

Community Treasure Hunt

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

Start Hunting!

Problem 44476. How many unique Pythagorean triples?

Solution Stats

Last 200 Solutions

Problem Recent Solvers133

Suggested Problems

More from this Author25

Problem Tags

Community Treasure Hunt

Problem 44476. How many unique Pythagorean triples?

Solution Stats

Last 200 Solutions

Problem Recent Solvers133

Suggested Problems

More from this Author25

Problem Tags

Community Treasure Hunt

Players