Problem 1517. Put m balls into n boxes (again)

Created by Binbin Qi

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>According to</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/1516-put-m-balls-into-n-boxes\"><w:r><w:t>Cody Problem 1516</w:t></w:r></w:hyperlink><w:r><w:t>, if I put 3 balls into 2 boxes then</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 1 1 1\n 1 1 2\n 1 2 2\n 2 2 2]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>The columns stand for a ball, the number stands for a box, and the row stands for a case.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Now we count the number of balls in each boxes.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>so we get</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 3 0\n 2 1\n 1 2\n 0 3]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>the 1-th row stand for the 1-th case,3 balls are put into the first boxes,the others is empty the 2-th row stand for the 2-th case,2 balls are put into the first boxes,1 balls is put into the second boxes</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You should write a function, input m and n, m stand for the number of balls ,n stand for the number of boxes,output all the cases.</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=\"text\"/></w:pPr><w:r><w:t>If m = 3,n = 4, you should output</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ 3 0 0 0\n 2 1 0 0\n 2 0 1 0\n 2 0 0 1\n 1 2 0 0\n 1 1 1 0\n 1 1 0 1\n 1 0 2 0\n 1 0 1 1\n 1 0 0 2\n 0 3 0 0\n 0 2 1 0\n 0 2 0 1\n 0 1 2 0\n 0 1 1 1\n 0 1 0 2\n 0 0 3 0\n 0 0 2 1\n 0 0 1 2\n 0 0 0 3]]></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>"}]}

According to <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1516-put-m-balls-into-n-boxes">Cody Problem 1516</a>, if I put 3 balls into 2 boxes then<pre> 1 1 1
 1 1 2
 1 2 2
 2 2 2</pre>The columns stand for a ball, the number stands for a box, and the row stands for a case.Now we count the number of balls in each boxes.so we get<pre> 3 0
 2 1
 1 2
 0 3</pre>the 1-th row stand for the 1-th case,3 balls are put into the first boxes,the others is empty
the 2-th row stand for the 2-th case,2 balls are put into the first boxes,1 balls is put into the second boxesYou should write a function, input m and n, m stand for the number of balls ,n stand for the number of boxes,output all the cases.ExampleIf m = 3,n = 4, you should output<pre> 3 0 0 0
 2 1 0 0
 2 0 1 0
 2 0 0 1
 1 2 0 0
 1 1 1 0
 1 1 0 1
 1 0 2 0
 1 0 1 1
 1 0 0 2
 0 3 0 0
 0 2 1 0
 0 2 0 1
 0 1 2 0
 0 1 1 1
 0 1 0 2
 0 0 3 0
 0 0 2 1
 0 0 1 2
 0 0 0 3</pre>

According to <http://www.mathworks.com/matlabcentral/cody/problems/1516-put-m-balls-into-n-boxes Cody Problem 1516>, if I put 3 balls into 2 boxes then

1     1     1
     1     1     2
     1     2     2
     2     2     2

The columns stand for a ball, the number stands for a box, and the row stands for a case.

*Now we count the number of balls in each boxes.*

so we get

3     0
     2     1
     1     2
     0     3

the 1-th row stand for the 1-th case,3 balls are put into the first boxes,the others is empty
the 2-th row stand for the 2-th case,2 balls are put into the first boxes,1 balls is put into the second boxes

You should write a function, input m and n, m stand for the number of balls ,n stand for the number of boxes,output all the cases.

Example

If m = 3,n = 4, you should output

3     0     0     0
     2     1     0     0
     2     0     1     0
     2     0     0     1
     1     2     0     0
     1     1     1     0
     1     1     0     1
     1     0     2     0
     1     0     1     1
     1     0     0     2
     0     3     0     0
     0     2     1     0
     0     2     0     1
     0     1     2     0
     0     1     1     1
     0     1     0     2
     0     0     3     0
     0     0     2     1
     0     0     1     2
     0     0     0     3

Solve

Solution Stats

84 Solutions
36 Solvers

Last Solution submitted on Jun 14, 2021

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Piotr Lesniewski on 12 Jul 2019

I'm not sure what is the point of eliminating 'ifs'? At any rate they can be easily replaced by e.g. 'while' loops, so in my opinion you should either eliminate both of them or none.

Rafael S.T. Vieira on 17 Jul 2020

Again, the best way to generate such a sequence is using depth-first search or recursion. By prohibiting the usage of IFs, all solutions are inefficient (because we can't cut the tree, and are forced to follow all branches).

Problem Recent Solvers36

Problem Tags

nchoosek

Community Treasure Hunt

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

Start Hunting!