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:

• 1 <= m, n <= 100

Solution

-spec unique_paths(M :: integer(), N :: integer()) -> integer().
unique_paths(M, N) ->
    Ncr = fun(N, R) ->
        lists:foldl(
          fun(I, Acc) -> 
              (Acc * (I + N - R)) div I
          end, 
          1, 
          lists:seq(1, R)
        )
    end,
    Ncr(M + N - 2, erlang:min(M, N) - 1).

This site is open source. Improve this page.