64. Minimum Path Sum

难度: Medium

题目描述

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 1:

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
Output: 7
Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

Example 2:

Input: grid = [[1,2,3],[4,5,6]]
Output: 12

 

Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 200
• 0 <= grid[i][j] <= 200

解题思路

代码实现

解决方案

java

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

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

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

        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                int target = 0;
                if (i == 0 && j==0) {
                    target = 0;
                } else if (i == 0) {
                    target = dp[i][j - 1];
                } else if (j== 0) {
                    target = dp[i - 1][j];
                }else{
                    target = Math.min(dp[i - 1][j], dp[i][j - 1]);
                }
                dp[i][j] = grid[i][j] + target;// Math.min(dp[i - 1][j], dp[i][j - 1]);
            }
        }

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

    }
}