Brian Yang
Brian Yang
algorithm designer
Mar 18, 2020 1 min read

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?

 

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

 

Constraints:

  • 1 <= m, n <= 100
  • It's guaranteed that the answer will be less than or equal to 2 * 10 ^ 9.

Solution

var uniquePaths = function (m, n) {
  if (m == 0 && n == 0) return 1
  if (m < 0 || n < 0) return 0
  return uniquePaths(m - 1, n) + uniquePaths(m, n - 1)
};
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