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.
动态规划
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 };