Question

I am having writing an algorithm to generate all possible permutations of an array of this kind:

n = length
k = number of 1’s in array

So this means if we have k 1’s we will have n-k 0’s in the array.

For example:
n = 5;
k = 3;

So obviously there are 5 choose 3 possible permutations for this array because

n!/(k!(n-k)!
5!/(3!2!) = (5*4)/2 = 10
possible values for the array

Here are all the values:
11100
11010
11001
10110
10101
10011
01110
01101
01011
00111

I am guessing i should use a recursive algorithms but i am just not seeing it. I am writing this algorithm in C++.

Any help would be appreciated!

Answer 1

You can split up the combinations into those starting with 1 (n-1, k-1) and those starting with 0 (n-1, k).

This is essentially the recursive formula for the choose function.