Genrate all combinations of a vector

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Khanh 2011-11-30

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https://ww2.mathworks.cn/matlabcentral/answers/22681-genrate-all-combinations-of-a-vector

I have a vector of size n, whose each element can be an integer in the range from 0 to k. I need to generate all possible variants of such vector, i.e. k^n vectors totally.
The solutions I have found haven't met my need:
- allcomb.m doesn't work with n>=100. I got the following error 
    Maximum variable size allowed by the program is exceeded.
      Error in ndgrid (line 66)
           x = reshape(x(:,ones(1,prod(s))),[length(x) s]); % Expand x
   - perms only generates possible permutations of the n elements of v.
I wonder if there is any function in matlab that does what I need? 
Thanks,

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Walter Roberson 2011-11-30

If you used one byte per element of the vector (e.g., uint8 data type), then you would have n bytes per entry, and (k+1)^n entries, for a total of approximately n*(k+1)^n bytes.

For n=100 and k=3, that would be 100*4^100 which would be about 1.6E62 bytes.

1 gigabyte is approximately 10^9 bytes, so you are asking for approximately 1.6E53 gigabytes.

So how much can you realistically store in (say) 4 gigabytes (the maximum address space for a 32 bit process)? n*4^n = 2^32 solves down to n = (1/2)*LambertW(8589934592*ln(2))/ln(2) which is a little over 14.

Thus, you realistically cannot produce all the combinations for vectors of length greater than 14.

Khanh 2011-11-30