Leetcode: 64. Minimum Path Sum

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于 2017-12-13 14:18:47 发布

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分类专栏： c++ Algorithms 文章标签： leetcode

本文链接：https://blog.youkuaiyun.com/csdn_cinderella/article/details/78791249

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本文介绍了一个经典的动态规划问题——给定一个二维网格，寻找从左上角到右下角的路径，使得路径上的数字之和最小。文章详细阐述了解决这一问题的动态规划方法，并给出了具体的实现代码。

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Description

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:
[[1,3,1],
[1,5,1],
[4,2,1]]
Given the above grid map, return 7. Because the path 1→3→1→1→1 minimizes the sum.

解题思路

动态规划，动态方程为
res[i][j] = min(res[i-1][j],res[i][j-1])+grid[i][j];

返回结果 res[m-1][n-1]
实现代码如下

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        vector<vector<int>> res(m,vector<int>(n,grid[0][0]));
        for (int i = 1; i< m; i++) {
            res[i][0] = res[i-1][0] + grid[i][0];
        }
        for (int j = 1; j < n; j++) {
            res[0][j] = res[0][j-1]+grid[0][j];
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                res[i][j] = min(res[i-1][j],res[i][j-1])+grid[i][j];
            }
        }
        return res[m-1][n-1];
    }
};