# 0287. Find the Duplicate Number

<https://leetcode.com/problems/find-the-duplicate-number>

## Description

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 = [1,1]
**Output:** 1
```

**Example 4:**

```
**Input:** nums = [1,1,2]
**Output:** 1
```

**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?

## ac

```java
class Solution {
    public int findDuplicate(int[] nums) {
        // fast/slow pointers
        int fast = nums[0], slow = nums[0];
        do {
            slow = nums[slow];
            fast = nums[nums[fast]];
        }while (fast != slow);

        int i = nums[0];
        while (i != slow) {
            i = nums[i];
            slow = nums[slow];
        } 

        return i;
    }
}
```