Find the Duplicate Number
Difficulty: Medium
Category: DSA
Topics: Array, Two Pointers, Binary Search, Bit Manipulation
Asked at: Microsoft, Amazon, Apple, Google, Bloomberg, Paypal, Goldman Sachs
Given an array of integers `nums` containing `n + 1` integers where each integer is in the range `[1, n]` inclusive.
There is only **one repeated number** in `nums`, return _this repeated number_.
You must solve the problem **without** modifying the array `nums` and using only constant extra space.
**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 = [3,3,3,3,3]
**Output:** 3
```
**Constraints:**
- `1 <= n <= 105`
- `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.
Follow up:
- How can we prove that at least one duplicate number must exist in `nums`?
- Can you solve the problem in linear runtime complexity?