# 287.Find-the-Duplicate-Number

## 287. Find the Duplicate Number

## 题目地址

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

## 题目描述

```
Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.

Example 1:
Input: [1,3,4,2,2]
Output: 2

Example 2:
Input: [3,1,3,4,2]
Output: 3

Note:
You must not modify the array (assume the array is read only).
You must use only constant, O(1) extra space.
Your runtime complexity should be less than O(n2).
There is only one duplicate number in the array, but it could be repeated more than once.
```

## 代码

### Approach #1 Sorting

```java
class Solution {
  public int findDuplicate(int[] nums) {
        Arrays.sort(nums);
    for (int i = 1; i < nums.length; i++) {
      if (nums[i] == nums[i - 1]) {
        return nums[i];
      }
    }

    return -1;
  }
}
```

### Approach #2 Set

```java
class Solution {
  public int findDuplicate(int[] nums) {
    Set<Integer> seen = new HashSet<Integer>();
    for (int num: nums) {
      if (seen.contains(num)) {
        return num;
      }
      seen.add(num);
    }
    return -1;
  }
}
```

### Approach #3 Floyd's Tortoise and Hare (Cycle Detection)

```java
class Solution {
    public int findDuplicate(int[] nums) {
        // Find the intersection point of the two runners.
        int tortoise = nums[0];
        int hare = nums[0];
        do {
            tortoise = nums[tortoise];
            hare = nums[nums[hare]];
        } while (tortoise != hare);

        // Find the "entrance" to the cycle.
        int ptr1 = nums[0];
        int ptr2 = tortoise;
        while (ptr1 != ptr2) {
            ptr1 = nums[ptr1];
            ptr2 = nums[ptr2];
        }

        return ptr1;
    }
}
```


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