Given an arraynumscontainingn + 1integers where each integer is between1andn(inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.

Notice

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.

Have you met this question in a real interview?

Yes

Example

Givennums=[5,5,4,3,2,1]return5
Givennums=[5,4,4,3,2,1]return4

class Solution {

public:

/\*\*

 \* @param nums an array containing n + 1 integers which is between 1 and n

 \* @return the duplicate one

 \*/

int findDuplicate\(vector<int>& nums\) {

    // Write your code here

    if \(nums.empty\(\)\) {

        return -1;

    }

    int slow = 0, fast = 0;

    slow = nums\[slow\];

    fast = nums\[nums\[fast\]\];



    while \(slow != fast\) {

        slow = nums\[slow\];

        fast = nums\[nums\[fast\]\];

    }



    fast = 0;

    while \(slow != fast\) {

        slow = nums\[slow\];

        fast = nums\[fast\];

    }



    return slow;

}

};