【LeetCode】127.Minimum Path Sum

题目描述(Medium)

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.

题目链接

https://leetcode.com/problems/minimum-path-sum/description/

Example 1:

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

算法分析

对每一行有路径转移方程path[j] = min(path[j], path[j - 1]) + grid[i][j]，path[j]代表当前行每一列的最小到达路径。

提交代码：

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