leetcode - Minimum Path Sum

leetcode - Minimum Path Sum

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.

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

动态规划问题，注意初始的一些值，最左上角的值，以及最上和最右的两条边。