LeetCode 64. 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.

【题解】

这是一道典型的动态规划题目，令sum[i][j]为走到第i行第j列的格子时沿路上所有数字和最小的值，其动态转移方程为

sum[i][j]=min(sum[i-1][j], sum[i][j-1])+grid[i][j]

其中grid[i][j]为第i行第j列的格子上的数字,最后返回的结果为sum[m-1][n-1]，m为行数，n为列数

【代码】

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