title

problem link

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 = 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

solution

DP

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