【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[].size();
         vector<int> col(grid.back());

         for (int i = n - ; i >= ; --i)
             col[i] += col[i+];

         for (int i = m - ; i >= ; --i) {
             col[n-] += grid[i][n-];
             for (int j = n - ; j >= ; --j) {
                 col[j] = grid[i][j] + min(col[j], col[j+]);
             }
         }

         return col[];
     }
 };