62. Unique Paths

Let dp[i][j] is the maximum path at grid[i][j], so the transition statement is quite easy to achieve:
dp[i][j] = dp[i-1][j] + dp[i][j-1]. For the initial state, the first row and first column are initialized to all 1s.

1:  class Solution {  
2:  public:  
3:    int uniquePaths(int m, int n) {  
4:      vector<vector<int>> grid(m, vector<int>(n, 1));  
5:      for (int i = 1; i < m; i++) {  
6:        for (int j = 1; j < n; j++) {  
7:          grid[i][j] = grid[i-1][j] + grid[i][j-1];  
8:        }  
9:      }  
10:      return grid[m-1][n-1];  
11:    }  
12:  };