Unique Paths
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 7 x 3 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
Example 1:
Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:
Input: m = 7, n = 3
Output: 28
class Solution{ public: int uniquePaths(int m, int n){ if(m == 1 || n == 1) return 1; vector<vector<int>> memo(m,vector<int>(n)); for(int i = 0; i < m; i++) memo[i][0] = 1; for(int j = 0; j < n; j++) memo[0][j] = 1; for(int i = 1; i < m; i++){ for(int j = 1; j < n; j++){ memo[i][j] = memo[i-1][j] + memo[i][j-1]; } } return memo[m-1][n-1]; } };
参考:
怕什么真理无穷,进一寸有一寸的欢喜。---胡适