64. Minimum Path Sum

Let dp[i][j] to be the minimum path sum at (i, j), then the transition state is dp[i][j] = grid[i][j] + min(dp[i-1][j], dp[i][j-1]).

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