Count all binary numbers with equal 1 and 0

Question

I am implementing a binary representation of a two-way equalization algorithm, and I am wondering what is the best way to iterate through all combinations of N bits having equal (N / 2) 1 and 0. I am trying to find the fastest way and not the simplest code. Thank.

Answer 1

It is simple (N choose N/2); you choose which bits are 0s, the remaining 1s.

If you have 10 bits and you want 5 zeros and 5 units, there are (10 choose 5) = 252possibilities.

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See also:

• Algorithm for returning all combinations of k elements from n

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, (n k). k n/2, ; , , , .

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