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
1 class Solution { 2 public: 3 int caluniquePaths(vector<vector<int>>&mark,int m, int n) { 4 int down = 0, right = 0; 5 if (mark[m][n] != -1)return mark[m][n]; 6 if (m > 1) 7 down = caluniquePaths(mark, m - 1, n); 8 if (n > 1) 9 right = caluniquePaths(mark, m, n - 1); 10 mark[m][n] = down + right; 11 return mark[m][n]; 12 } 13 int uniquePaths(int m, int n) { 14 vector<vector<int>>mark(m+1, vector<int>(n+1, -1)); 15 mark[1][1] = 1; 16 return caluniquePaths(mark, m, n); 17 } 18 };
不记忆递归的话会TLE，用空间换时间