# 62. Unique Paths (Medium)

https://leetcode.com/problems/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```

## Solutions

``````class Solution {
public int uniquePaths(int m, int n) {
int[][] arr = new int[m][n];
return getCount(arr, m, n);
}

private int getCount(int[][] arr, int m, int n) {
for (int i=0; i<arr.length; i++) {
for (int j=0; j<arr.length; j++) {
if (i == 0 || j ==0) {
arr[i][j] = 1;
}
else {
arr[i][j] = arr[i-1][j] + arr[i][j-1];
}
}
}

return arr[m-1][n-1];
}
}
``````