LeetCode [62] Unique Paths

 62. Unique Paths

Medium

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?

 

Example 1:

Input: m = 3, n = 7
Output: 28

Example 2:

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 -> Down -> Down
2. Down -> Down -> Right
3. Down -> Right -> Down

Example 3:

Input: m = 7, n = 3
Output: 28

Example 4:

Input: m = 3, n = 3
Output: 6

 

Constraints:

• 1 <= m, n <= 100
• It's guaranteed that the answer will be less than or equal to 2 * 109.

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