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
x = [1 2 2 3 2 3 3 6 1 3 1 1 6 3 2 5 2 2 4 2]
Histogram
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]
where the r-th (r=1,...,S) row of h is the histogram bin counts for number r along every column of x.
HoH
f = [1 0 3 5 2 1 1 0 0 1 0 0]
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:
h = histc(x,1:max(x(:)),1); f = histc(h,1:max(h(:)),1);
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.
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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Solution 773068
This is nearly 30% slower than Solution 772002(size 35) on my PC(win 10 pro x64,i7 4700mq)