What’s the best algorithm to find all binary strings of length n that contain k bits set? For example, if n=4 and k=3, there are…
0111 1011 1101 1110
I need a good way to generate these given any n and any k so I’d prefer it to be done with strings.
Practice As Follows
This method will generate all integers with exactly N ‘1’ bits.
Compute the lexicographically next bit permutation
Suppose we have a pattern of N bits set to 1 in an integer and we want
the next permutation of N 1 bits in a lexicographical sense. For
example, if N is 3 and the bit pattern is
00010011, the next patterns
and so forth. The following is a fast way to compute the next
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));
__builtin_ctz(v)GNU C compiler intrinsic for x86 CPUs returns the number of trailing zeros. If you are using Microsoft compilers for
x86, the intrinsic is
_BitScanForward. These both emit a
instruction, but equivalents may be available for other architectures.
If not, then consider using one of the methods for counting the
consecutive zero bits mentioned earlier. Here is another version that
tends to be slower because of its division operator, but it does not
require counting the trailing zeros.
unsigned int t = (v | (v - 1)) + 1; w = t | ((((t & -t) / (v & -v)) >> 1) - 1);
Thanks to Dario Sneidermanis of Argentina, who provided this on November 28, 2009.