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:

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

Output: 7

Explanation:

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

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