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:
-
Right -> Down -> Down
-
Down -> Down -> Right
-
Down -> Right -> Down
Constraints:
1 <= m, n <= 100
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