LeetCode-in-All

62. Unique Paths

Medium

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 tries to move to the bottom-right corner (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.

Given the two integers m and n, return the number of possible unique paths that the robot can take to reach the bottom-right corner.

The test cases are generated so that the answer will be less than or equal to 2 * 109.

Example 1:

Input: m = 3, n = 7

Output: 28

Example 2:

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 -> Down -> Down

  2. Down -> Down -> Right

  3. Down -> Right -> Down

Constraints:

Solution

defmodule Solution do
  @spec unique_paths(m :: integer, n :: integer) :: integer
  def unique_paths(m, n) do
    ncr(m + n - 2, min(m, n) - 1)
  end

  defp ncr(n, r) do
    Enum.reduce(1..r#1, 1, fn i, acc ->
      div(acc * (i + n - r), i)
    end)
  end
end