64. Minimum Path Sum

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LeetCode

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Problem

Given a m x n grid filled with non-negative numbers, 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.

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.

Code

class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;

        // initial row
        for(int j = 1; j < n; j++){
            grid[0][j] += grid[0][j - 1];
        }

        // initial col
        for(int i = 1; i < m; i++){
            grid[i][0] += grid[i - 1][0];
        }

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

        return grid[m - 1][n - 1];
    }
}