[LeetCode] Minimum Path Sum

问题：

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：

一道简单的dp问题。建立一个m*n的table，记录每一个点到右下角的点的最短距离。关系是：a[i][j] = val[i][j] + min(a[i+1][j], a[i][j+1])。即，站在一个位置上，要么选择向右走，要么选择向左走。然后我们从右下角开始逐渐向左上角填充这个table。

代码：（O(mn)）

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