Problem 1888. Get ranking of a combination

Created by Doug Hull

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>I have the numbers pulled without replacement from the set [1 2 3 4 5 6 7 8 9 10 11 12 13]; They are then ordered from least to greatest.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>So a selection of [3 2 9], [9 2 3] are both considered to be [2 3 9].</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>There are 286 unique selections possible. These can be ordered in lexicographic order:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[Element 1 = [ 1 2 3]\nElement 2 = [ 1 2 4]\nElement 3 = [ 1 2 5]\nElement 4 = [ 1 2 6]\nElement 5 = [ 1 2 7]\nElement 6 = [ 1 2 8]\nElement 7 = [ 1 2 9]\nElement 8 = [ 1 2 10]\nElement 9 = [ 1 2 11]\nElement 10 = [ 1 2 12]\nElement 11 = [ 1 2 13]\nElement 12 = [ 1 3 4]\nElement 13 = [ 1 3 5]\nElement 14 = [ 1 3 6]\nElement 15 = [ 1 3 7]\n...\nElement 285 = [10 12 13]\nElement 286 = [11 12 13]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given the three ordered values as a row vector, return the element number.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Do this with an eye for speed, though it is not tested for here.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Looking for a way to do this WITHOUT generating the nchoosek 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>"}]}

I have the numbers pulled without replacement from the set [1 2 3 4 5 6 7 8 9 10 11 12 13]; They are then ordered from least to greatest.So a selection of [3 2 9], [9 2 3] are both considered to be [2 3 9].There are 286 unique selections possible. These can be ordered in lexicographic order:<pre class="language-matlab">Element 1 = [ 1 2 3]
Element 2 = [ 1 2 4]
Element 3 = [ 1 2 5]
Element 4 = [ 1 2 6]
Element 5 = [ 1 2 7]
Element 6 = [ 1 2 8]
Element 7 = [ 1 2 9]
Element 8 = [ 1 2 10]
Element 9 = [ 1 2 11]
Element 10 = [ 1 2 12]
Element 11 = [ 1 2 13]
Element 12 = [ 1 3 4]
Element 13 = [ 1 3 5]
Element 14 = [ 1 3 6]
Element 15 = [ 1 3 7]
...
Element 285 = [10 12 13]
Element 286 = [11 12 13]
</pre>Given the three ordered values as a row vector, return the element number.Do this with an eye for speed, though it is not tested for here.Looking for a way to do this WITHOUT generating the nchoosek matrix.

Solve

Solution Stats

111 Solutions
43 Solvers

Last Solution submitted on Jan 11, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers43

Problem Tags

Community Treasure Hunt

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

Start Hunting!

Problem 1888. Get ranking of a combination

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers43

Suggested Problems

More from this Author52

Problem Tags

Community Treasure Hunt

Problem 1888. Get ranking of a combination

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers43

Suggested Problems

More from this Author52

Problem Tags

Community Treasure Hunt

Players