Unique Paths

IF
AlgoAxiomStaff Engineers
JSTS
Medium20 mins

There is a robot on an m x n grid. The robot is initially located at the top-left corner (i.e., grid[0][0]). The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner (i.e., grid[m-1][n-1]).

Return the number of possible unique paths that the robot can take to reach the bottom-right corner.

Examples

Example 1:

Input: m = 3, n = 7

Output: 28

Explanation: From the top-left corner, there are 28 unique paths to reach the bottom-right corner.

Example 2:

Input: m = 3, n = 2

Output: 3

Explanation: There are three paths: Right → Down → Down, Down → Down → Right, Down → Right → Down.

Example 3:

Input: m = 1, n = 1

Output: 1

Explanation: The robot is already at the destination.

Constraints

  • 1 <= m, n <= 100
Source: Dynamic Programming pattern — AlgoAxiom
JavaScript
Test Case 1
root = [1, 2, 3]
Test Case 2
root = [1, 2, 3, 4, 5]
Idle