# Find the Duplicate Number

## Problem

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 uses 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?

## Solution

I thought this was a XOR question, but it turns out that I misunderstood the prompt.

This is similar to the linked list cycle question.

```
class Solution {
public int findDuplicate(int[] nums) {
var slow = 0;
var fast = 0;
do {
slow = nums[slow];
fast = nums[nums[fast]];
} while (slow != fast);
fast = 0;
while (slow != fast) {
slow = nums[slow];
fast = nums[fast];
}
return slow;
}
}
```