[Leetcode] 63. 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.

解题之法

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        int m = grid.size(), n = grid[0].size();
        int dp[m][n];
        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];
    }
};

分析

这道题跟Dungeon Game 地牢游戏 没有什么太大的区别，都需要用动态规划Dynamic Programming来做，这应该算是DP问题中比较简单的一类，我们维护一个二维的dp数组，其中dp[i][j]表示当前位置的最小路径和，递推式也容易写出来 dp[i][j] = grid[i][j] + min(min(dp[i - 1][j], dp[i][j - 1]）。