Problem 42790. Full combinations

Created by Peng Liu

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{"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>Given n input vectors x1, x2, …, xn, generate a p*n matrix y whose rows contain all element-wise combinations of the vectors x1, x2, …, xn, where p = numel(x1)*numel(x2)*…* numel(xn). The rows of y are organized in an \"increasing\" ordering; see examples below.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Example 1 (character array, n = 2): Input: x1 = 'ab'; x2 = 'cde'; Output:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ y = ['ac'\n 'ad'\n 'ae'\n 'bc'\n 'bd'\n 'be']]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>Example 2 (numeric array, n = 3): Input: x1 = [0 1], x2 = [0 1]; x3 = [0 1]; Output:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ y = [0 0 0\n 0 0 1\n 0 1 0\n 0 1 1\n 1 0 0\n 1 0 1\n 1 1 0\n 1 1 1]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You may assume that all inputs are valid vectors whose lengths are at least 1.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Note: The Statistics and Machine Learning toolbox provides two useful functions for full factorial design, namely</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>ff2n</w:t></w:r><w:r><w:t> (for binary case) and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>fullfact</w:t></w:r><w:r><w:t> (for general cases). However, they do not directly accomplish the task in Example 1. The purpose of this problem is to create a toolbox independent function to achieve our goal. Have fun!</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>"}]}

Given n input vectors x1, x2, …, xn, generate a p*n matrix y whose rows contain all element-wise combinations of the vectors x1, x2, …, xn, where p = numel(x1)*numel(x2)*…* numel(xn). The rows of y are organized in an "increasing" ordering; see examples below.<ul><li>Example 1 (character array, n = 2): Input: x1 = 'ab'; x2 = 'cde'; Output:</li></ul><pre> y = ['ac'
 'ad'
 'ae'
 'bc'
 'bd'
 'be'] </pre><ul><li>Example 2 (numeric array, n = 3): Input: x1 = [0 1], x2 = [0 1]; x3 = [0 1]; Output:</li></ul><pre> y = [0 0 0
 0 0 1
 0 1 0
 0 1 1
 1 0 0
 1 0 1
 1 1 0
 1 1 1]</pre>You may assume that all inputs are valid vectors whose lengths are at least 1.Note: The Statistics and Machine Learning toolbox provides two useful functions for full factorial design, namely ff2n (for binary case) and fullfact (for general cases). However, they do not directly accomplish the task in Example 1. The purpose of this problem is to create a toolbox independent function to achieve our goal. Have fun!

Given n input vectors x1, x2, …, xn, generate a p*n matrix y whose rows contain all element-wise combinations of the vectors x1, x2, …, xn, where p = numel(x1)*numel(x2)*…* numel(xn). The rows of y are organized in an "increasing" ordering; see examples below.

* Example 1 (character array, n = 2): Input: x1 = 'ab'; x2 = 'cde'; Output:

y = ['ac'
         'ad'
         'ae'
         'bc'
         'bd'
         'be']

* Example 2 (numeric array, n = 3): Input: x1 = [0 1], x2 = [0 1]; x3 = [0 1]; Output:

y = [0 0 0
         0 0 1
         0 1 0
         0 1 1
         1 0 0
         1 0 1
         1 1 0
         1 1 1]

You may assume that all inputs are valid vectors whose lengths are at least 1.

Note: The Statistics and Machine Learning toolbox provides two useful functions for full factorial design, namely *ff2n* (for binary case) and *fullfact* (for general cases). However, they do not directly accomplish the task in Example 1. The purpose of this problem is to create a toolbox independent function to achieve our goal. Have fun!

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Last Solution submitted on Feb 22, 2023

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Guillaume on 30 Mar 2016

It would be better if the test suite did not rely on a particular ordering of the rows. You could use isempty(setxor(myfullfact(...), y_correct, 'rows')) instead of isequal(...)

Peng Liu on 30 Mar 2016

Thanks for your suggestion. But I prefer an "increasing" ordering of the rows because that could be more useful in some applications. I have made it clear in the problem description that ordering is required.

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Problem 42790. Full combinations

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