# Unique Paths Problem

## Description

LeetCode Problem 62.

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:

1
2

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

Example 2:

1
2
3
4
5
6
7

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:

1
2

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

Example 4:

1
2

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 * 10^9.

## Sample C++ Code

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

class Solution {
public:
int uniquePaths(int m, int n) {
vector<vector<int>> dp(m+1, vector<int>(n+1, 0));
for (int i = 1; i <= m; i ++) {
for (int j = 1; j <= n; j ++) {
if ((i == 1) || (j == 1))
dp[i][j] = 1;
else
dp[i][j] = dp[i-1][j] + dp[i][j-1];
}
}
return dp[m][n];
}
};