# ---
# title: 62. Unique Paths
# id: problem62
# author: AquaIndigo
# date: 2020-12-09
# difficulty: Medium
# categories: Array, Dynamic Programming
# link: <https://leetcode.com/problems/unique-paths/description/>
# hidden: true
# ---
# 
# 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?
# 
# 
# 
# **Example 1:**
# 
# ![](https://assets.leetcode.com/uploads/2018/10/22/robot_maze.png)
# 
#     
#     
#     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
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: m = 7, n = 3
#     Output: 28
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: m = 3, n = 3
#     Output: 6
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= m, n <= 100`
#   * It's guaranteed that the answer will be less than or equal to `2 * 109`.
# 
# 
## @lc code=start
using LeetCode

unique_paths(m::Int, n::Int) = binomial(m + n - 2, n - 1)
## @lc code=end
