Problem 42676. Histogram of histogram

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>Histogram of histogram (HoH) is a useful measure concerning the distribution of random data, which has diverse applications in data science, statistics, information theory, etc.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>In this problem, given an n-by-m array x of integer numbers {1,2,...,S}, return the HoH along every column of x: f = HoH(x). An example for n = 5, m = 4, and S = 6 follows.</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>Input</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ x = [1 2 2 3\n 2 3 3 6\n 1 3 1 1\n 6 3 2 5\n 2 2 4 2]]]></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>Histogram</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ h = [2 0 1 1\n 2 2 2 1\n 0 3 1 1\n 0 0 1 0\n 0 0 0 1\n 1 0 0 1]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>where the r-th (r=1,...,S) row of h is the histogram bin counts for number r along every column of x.</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>HoH</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ f = [1 0 3 5\n 2 1 1 0\n 0 1 0 0]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>where f is a max(h(:))-by-m matrix, with the p-th row representing the histogram of number p along every column of h.</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>Hint</w:t></w:r><w:r><w:t> : A straightforward reference scheme to obtain f could be:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ h = histc(x,1:max(x(:)),1); \n f = histc(h,1:max(h(:)),1);]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This is simple but inefficient in terms of both performance and memory (It will crash for the last test case). Note that the ultimate goal is to find f (HoH); thus, it is not necessary to go through exactly the same h as described above. Try your best to improve your code in terms of both</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>speed</w:t></w:r><w:r><w:t> and</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>memory</w:t></w:r><w:r><w:t>. Your score will be based on the</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>speed</w:t></w:r><w:r><w:t> of your code.</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>"}]}

Histogram of histogram (HoH) is a useful measure concerning the distribution of random data, which has diverse applications in data science, statistics, information theory, etc.In this problem, given an n-by-m array x of integer numbers {1,2,...,S}, return the HoH along every column of x: f = HoH(x). An example for n = 5, m = 4, and S = 6 follows.Input<pre> x = [1 2 2 3
 2 3 3 6
 1 3 1 1
 6 3 2 5
 2 2 4 2]</pre>Histogram<pre> h = [2 0 1 1
 2 2 2 1
 0 3 1 1
 0 0 1 0
 0 0 0 1
 1 0 0 1]</pre>where the r-th (r=1,...,S) row of h is the histogram bin counts for number r along every column of x.HoH<pre> f = [1 0 3 5
 2 1 1 0
 0 1 0 0]</pre>where f is a max(h(:))-by-m matrix, with the p-th row representing the histogram of number p along every column of h.Hint : A straightforward reference scheme to obtain f could be:<pre> h = histc(x,1:max(x(:)),1); 
 f = histc(h,1:max(h(:)),1);</pre>This is simple but inefficient in terms of both performance and memory (It will crash for the last test case). Note that the ultimate goal is to find f (HoH); thus, it is not necessary to go through exactly the same h as described above. Try your best to improve your code in terms of both speed and memory. Your score will be based on the speed of your code.

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Last Solution submitted on Jul 27, 2020

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Solution 773068

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LY Cao on 7 Nov 2015

This is nearly 30% slower than Solution 772002(size 35) on my PC(win 10 pro x64,i7 4700mq)

Solution 771853

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Peng Liu on 6 Nov 2015

Hi Alfonso, I noticed that a faster solution is often beat by a slower solution (according to my own computer) when running on Cody. Could you share your knowledge or some guess on this issue? Thanks.

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histogram matrix manipulation

Problem 42676. Histogram of histogram

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