You are given 4 parameters

• a string that is only 0 and 1’s
• n which is the length of the string
• k which is the number of items you can insert and
• m which is the position that is taken at the end

The problem is that you have to insert 1’s into the string (from 0 to k) and in the end you take the m-th positions. The algorithm has to find the best places to insert in order to get the lowest sum on the m-th positions.

Example:
n = 35 k = 6 m = 8 string = 11011001000011010101010101110010111

You can insert 6 ones into the string and after you insert each 8-th number will be taken and summed.

Solution:
sum = 0 index of insertion = 7 31

I tried a recursive solution which would try each possible combination of insertions, but the problem is that with larger examples it takes too long.