LeetCode--minimum-path-sum

题目描述

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：可以很容易想到用dfs方法或dp方法求解，思路比较简单。dfs递归的方法容易超时，可以用dp方法维护一个二维数组，代码如下：

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