Minimal Path Sum

Suppose we have a m by n matrix filled with non-negative integers, find a path from top left corner to bottom right corner which minimizes the sum of all numbers along its path.

Note: Movements can only be either down or right at any point in time.

Example:

Input:

1  [
2    [1,3,1],
3    [1,5,1],
4    [4,2,1]
5  ]

Output:

17

Explanation:

Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

Try it yourself