【Leetcode】【Medium】Minimum Path Sum

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.

解题思路：

和Unique Paths题目非常类似，区别在于本题为有权值路径；

解题方法基本一致，还是通过数组迭代方法，使用n个额外空间的动态规划思路，区别在于迭代前需要计算数组初始值。

代码：

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        vector<int> col(grid.back());
        
        for (int i = n - 2; i >= 0; --i) 
            col[i] += col[i+1];
        
        for (int i = m - 2; i >= 0; --i) {
            col[n-1] += grid[i][n-1];
            for (int j = n - 2; j >= 0; --j) {
                col[j] = grid[i][j] + min(col[j], col[j+1]);
            }
        }
        
        return col[0];
    }
};