how can I make the code generating all the possible combinations of integer numbers more efficient

Question

Hugo 2022-1-27

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https://ww2.mathworks.cn/matlabcentral/answers/1637650-how-can-i-make-the-code-generating-all-the-possible-combinations-of-integer-numbers-more-efficient

回答： Benjamin Thompson 2022-1-27

Hi,

I would like to know how I can modify the following code, as to make it more efficient. This code writes the matrix total, which has all the possible combinations of 4 and 5 numbers, considering all the integer numbers from 1 to 10. I thank you in advance.

v = 1:1:10;
sens5 = nchoosek(v,5)
sens5(:,6)=0
sens5(:,7)=0
sens5(:,8)=0
sens5(:,9)=0
sens5(:,10)=
sens4 = nchoosek(v,4)
sens4(:,5)=0
sens4(:,6)=0
sens4(:,7)=0
sens4(:,8)=0
sens4(:,9)=0
sens4(:,10)=0
total=[sens4; sens5] 

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Answer 1

Benjamin Thompson 2022-1-27

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https://ww2.mathworks.cn/matlabcentral/answers/1637650-how-can-i-make-the-code-generating-all-the-possible-combinations-of-integer-numbers-more-efficient#answer_883245

This runs very fast. But if you are scaling up to a bigger problem, you can probably precompute the value of the factorial operation, just look at the mathematical definition of nchoosek. Then if you are sequentially calculating nchoosek with increasing n, the math of calculating it for n+1 can be done using the previous nchoosek.

There is also parfor, or see if nchoosek can be run on a GPU with a gpuArray input if you have a good GPU.