# 287    Find the Duplicate Number

## 287. [Find the Duplicate Number](https://leetcode.com/problems/find-the-duplicate-number/description/)

## 1. Question

Given an arraynumscontainingn+ 1 integers where each integer is between 1 andn(inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.

**Note:**

1. You **must not** modify the array (assume the array is read only).
2. You must use only constant, O(1) extra space.
3. Your runtime complexity should be less than`O(n^2)`.
4. There is only one duplicate number in the array, but it could be repeated more than once.

## 2. Implementation

**(1) Binary Search**

```java
class Solution {
    public int findDuplicate(int[] nums) {
        int start = 0, end = nums.length - 1, mid = 0;

        while (start + 1 < end) {
            mid = start + (end - start) / 2;

            int count = countNum(nums, mid);

            if (count <= mid) {
                start = mid + 1;
            }
            else {
                end = mid;
            }
        }

        return countNum(nums, start) > start ? start : end;
    }

    public int countNum(int[] nums, int target) {
        int count = 0;

        for (int num : nums) {
            if (num <= target) {
                ++count;
            }
        }
        return count;
    }
}
```

**(2) Two Pointers**

```java
public class Solution {
    public int findDuplicate(int[] nums) {
        // Similar to Linked List Cycle II 
        // Use Two Pointers to find the begnning of loop
        // This is where the duplicate occur
        int fast = 0, slow = 0;

        do {
            fast = nums[nums[fast]];
            slow = nums[slow];
        } while (fast != slow);

        slow = 0;

        while (fast != slow) {
            fast = nums[fast];
            slow = nums[slow];
        }
        return slow;
    }
}
```

## 3. Time & Space Complexity

**Binary Search**: 时间复杂度O(nlogn), 空间复杂度O(1)

**Two Pointers:** 时间复杂度O(n), 空间复杂度O(1)


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://protegejj.gitbook.io/algorithm-practice/leetcode/binary-search/287-find-the-duplicate-number.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.