Dynamic Programming: 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 in C++

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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.