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Min Sum Path in Matrix


Problem Description

Given a 2D integer array A of size M x N, you need to find a path from top left to bottom right which minimizes the sum of all numbers along its path.

NOTE: You can only move either down or right at any point in time.



Input Format

First and only argument is an 2D integer array A of size M x N.



Output Format

Return a single integer denoting the minimum sum of a path from cell (1, 1) to cell (M, N).



Example Input

Input 1:

 A = [  [1, 3, 2]
        [4, 3, 1]
        [5, 6, 1]
     ]


Example Output

Output 1:

 9


Example Explanation

Explanation 1:

 The path is 1 -> 3 -> 2 -> 1 -> 1
 So ( 1 + 3 + 2 + 1 + 1) = 8


NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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