19.2.9 [LeetCode 62] 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

 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 };

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不记忆递归的话会TLE，用空间换时间