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.

Analyse: dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];

Runtime: 32ms.

 1 class Solution {
 2 public:
 3     int minPathSum(vector<vector<int>>& grid) {
 4         if(grid.size() == 0) return 0;
 5         int row = grid.size(); //row size
 6         int col = grid[0].size(); //column size
 7         
 8         vector<vector<int> > dp;
 9         dp = grid;
10         for(int i = 1; i < row; i++) dp[i][0] = dp[i - 1][0] + grid[i][0];
11         for(int j = 1; j < col; j++) dp[0][j] = dp[0][j - 1] + grid[0][j];
12         
13         for(int i = 1; i < row; i++){
14             for(int j = 1; j < col; j++){
15                 dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
16             }
17         }
18         return dp[row - 1][col - 1];
19     }
20 };