# ---
# title: 287. Find the Duplicate Number
# id: problem287
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Array, Two Pointers, Binary Search
# link: <https://leetcode.com/problems/find-the-duplicate-number/description/>
# hidden: true
# ---
# 
# Given an array of integers `nums` containing `n + 1` integers where each
# integer is in the range `[1, n]` inclusive.
# 
# There is only **one duplicate number** in `nums`, return _this  duplicate
# number_.
# 
# **Follow-ups:**
# 
#   1. How can we prove that at least one duplicate number must exist in `nums`? 
#   2. Can you solve the problem **without**  modifying the array `nums`?
#   3. Can you solve the problem using only constant, `O(1)` extra space?
#   4. Can you solve the problem with runtime complexity less than `O(n2)`?
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: nums = [1,3,4,2,2]
#     Output: 2
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: nums = [3,1,3,4,2]
#     Output: 3
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: nums = [1,1]
#     Output: 1
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: nums = [1,1,2]
#     Output: 1
#     
# 
# 
# 
# **Constraints:**
# 
#   * `2 <= n <= 3 * 104`
#   * `nums.length == n + 1`
#   * `1 <= nums[i] <= n`
#   * All the integers in `nums` appear only **once** except for **precisely one integer** which appears **two or more** times.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
