[Leetcode] 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.

思路：DP，对于某个位置，只可能是由上或者由左到达，因此选取这两个路径中较小的那个。

class Solution {public:    int minPathSum(vector<vector<int> > &grid) {        if (grid.size() <= 0) return 0;        int width = (int)grid.size();        int length = (int)grid[0].size();        vector<vector<int>> dist(width, vector<int>(length, 0));        dist[0][0] = grid[0][0];        for (int i = 1; i < width; ++i) {            dist[i][0] = dist[i-1][0] + grid[i][0];        }        for (int j = 1; j < length; ++j) {            dist[0][j] = dist[0][j-1] + grid[0][j];        }        for (int i = 1; i < width; ++i) {            for (int j = 1; j < length; ++j) {                dist[i][j] = (dist[i-1][j] < dist[i][j-1] ? dist[i-1][j] : dist[i][j-1]) + grid[i][j];            }        }        return dist[width-1][length-1];    }};

总结：复杂度为O(mn).