Question

I need to compute all possible combinations of n things selected r at a time where 0<=r<=n, One method to do so is generating the numbers up to 0 to 2^n-1. But I need to generate these numbers such that the numbers should be sorted on the basis of the number of bits set in that number. for n=3:

0         // numbers with 0 bits set

1 2 4     // numbers with 1 bits set

3 5 6     // numbers with 2 bits set

7         // numbers with 3 bits set

I need to know how to generate the numbers such that they are sorted in increasing/decreasing order of bits set?

Answer 1

Implement regular algorithm to generate the combinations, but also hold an additional array where you store the numbers sorted accoding to the 1-bits set. Then for each combination generated replace the numbers with the numbers sitting in the corresponding position minus one in the array sorted as I described.