[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.

解题思路:

动态规划，算出所有位置到起点的最小距离

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