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.
Recursion, memoization.
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| class Solution { | |
| public: | |
| int uniquePaths(int m, int n) { | |
| vector<vector<int>> dp(m+1,vector<int>(n+1,0)); | |
| dp[0][1] = 1; | |
| for(int i = 1 ; i <= m ; ++i) | |
| for(int j = 1 ; j <= n ; ++j) | |
| dp[i][j] = dp[i-1][j]+dp[i][j-1]; | |
| return dp[m][n]; | |
| } | |
| }; |
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