64-Minimum Path Sum

题目

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.

分析

和Dungeon Game 的方法类似，比那个问题还要简单，自己在草纸上画一下会更清晰。

但是空间复杂度比较高，好像有空间复杂度为O(n) 的算法，可以再深入研究一下

实现

/*Author:FancyDate:2017-03-20Algorithm:64-Minimum Path SumSpace Complexity:O(M*N)*/class Solution {public:    int minPathSum(vector<vector<int>>& grid) {        int rows = grid.size(), cols = grid[0].size();        vector<vector<int>> sumMat(rows + 1, vector<int>(cols + 1, INT_MAX));        sumMat[rows][cols - 1] = 0;        sumMat[rows - 1][cols] = 0;        for (int i = rows-1; i >= 0; i--)            for (int j = cols-1; j >= 0; j--)                sumMat[i][j] = min(sumMat[i][j + 1], sumMat[i + 1][j]) + grid[i][j];        return sumMat[0][0];    }};