What is the fastest algorithm to computer all permutations of a binary number with same hamming weight?

Question

I want an algorithm to compute all permutations of a fixed size binary number with a given hamming weight. For example, if the hamming weight is 2 and the binary size is 4 t

Answer 1

You can implement the "lexicographically next bit-permutation" using Gosper's Hack:

unsigned int v; // current permutation of bits 
unsigned int w; // next permutation of bits

unsigned int t = v | (v - 1); // t gets v's least significant 0 bits set to 1
// Next set to 1 the most significant bit to change, 
// set to 0 the least significant ones, and add the necessary 1 bits.
w = (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(v) + 1));

Or if you don't have ctz (_BitScanForward on MSVC),

unsigned int t = (v | (v - 1)) + 1;  
w = t | ((((t & -t) / (v & -v)) >> 1) - 1);