Posts Min Sum Path in Matrix
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Min Sum Path in Matrix

Problem Description

Given a M x N grid A of integers, find a path from top left to bottom right which minimizes the sum of all numbers along its path. Return the minimum sum of the path.
NOTE: You can only move either down or right at any point in time.

Solution

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public class Solution {
    
    public int minPathSum(int[][] A) {

        int n = A.length;
        int m = A[0].length;

        int[][] dp = new int[n][m];

        dp[0][0] = A[0][0];

        for(int i=1; i<n; i++){
            dp[i][0] = A[i][0] + dp[i-1][0];
        }

        for(int i=1; i<m; i++){
            dp[0][i] = A[0][i] + dp[0][i-1];
        }

        for(int i=1; i<n; i++){
            for(int j=1; j<m; j++){
                dp[i][j] = A[i][j] + Math.min(dp[i-1][j], dp[i][j-1]);
            }
        }

        return dp[n-1][m-1];

    }
}
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