Leetcode:64. Minimum Path Sum

Description

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

• 动态规划，用一个二维数组记录状态,dp[i][j]表示从(0,0)到(i,j)的最小路径长度
• dp[i][j] = min(dp[i][j-1], dp[i-1][j]) + grid[i][j]

代码

• 二维数组

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