## Description

https://leetcode.com/problems/unique-paths/description/

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 3 x 7 grid. How many possible unique paths are there?

**Note:** *m* and *n* will be at most 100.

## Explanation

We can use a two-dimensional array to show the number of unique paths to each square on the grid.

The number of unique paths to each square on the left border would be 1.

The number of unique paths to each square on the top border would be 1.

The number of unique paths to other squares on the left border would be the sum of the number of unique paths to its previous left square and top square.

## Video Tutorial

## Java Solution

class Solution { public int uniquePaths(int m, int n) { if (m == 0 || n == 0) { return 0; } int[][] numberOfPaths = new int[m][n]; for (int i = 0; i < m; i++) { numberOfPaths[i][0] = 1; } for (int j = 0; j < n; j++) { numberOfPaths[0][j] = 1; } for (int i = 1; i < m; i++) { for (int j = 1; j < n; j++) { numberOfPaths[i][j] = numberOfPaths[i - 1][j] + numberOfPaths[i][j - 1]; } } return numberOfPaths[m - 1][n - 1]; // Time Complexity: O(m * n) // Space Complexity: O(m * n) } }

Thank you for the tutorial!

Thank you 🙂