Algorithm to split an array into P subarrays of balanced sum

Question

I have an big array of length N, let\'s say something like:

2 4 6 7 6 3 3 3 4 3 4 4 4 3 3 1

I need to split this array into P subarrays (in

Answer 1

If I am not mistaken here, one more approach is dynamic programming.

You can define P[ pos, n ] as the smallest possible "penalty" accumulated up to position pos if n subarrays were created. Obviously there is some position pos' such that

P[pos', n-1] + penalty(pos', pos) = P[pos, n]

You can just minimize over pos' = 1..pos.

The naive implementation will run in O(N^2 * M), where N - size of the original array and M - number of divisions.