# Leetcode 62 - Unique paths

`Note`

:

- The DP formula is
`DP[i][j] = DP[i-1][j] + DP[i][j-1]`

; - Every element in this 2D array means how many paths there are from
`[0][0]`

to`[i][j]`

. - To initialize our array, we just need to fill the
`first row`

and`col`

with`1`

because there is only`1`

way from`(0,0)`

to those places.

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 | Input: m = 3, n = 7 |

1 | /** |