62. Unique Paths，62uniquepaths

62. Unique Paths，62uniquepaths

A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

動態規劃

dp[i][j] = dp[i-1][j]+dp[i][j-1];

 1 class Solution {
 2 public:
 3     int uniquePaths(int m, int n) {
 4         int dp[m][n];
 5         
 6         for(int i = 0; i < m; i++){
 7             dp[i][0] = 1;
 8         }
 9         for(int j = 0; j < n; j++){
10             dp[0][j] = 1;
11         }
12         
13         for(int i=1;i<m;i++){
14             for(int j=1;j<n;j++){
15                 dp[i][j] = dp[i-1][j]+dp[i][j-1];
16             }
17         }
18         return dp[m-1][n-1];
19     }
20 };