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*(*n*^{2}). - There is only one duplicate number in the array, but it could be repeated more than once.

## Solution

public class Solution { public int FindDuplicate(int[] nums) { //Find the intersection point of two runners int tortoise = nums[0]; int hare = nums[0]; do{ tortoise = nums[tortoise]; hare = nums[nums[hare]]; }while(tortoise != hare); //Find the starting point of the cycle int ptr1 = nums[0]; int ptr2 = tortoise; while(ptr1 != ptr2) { ptr1 = nums[ptr1]; ptr2 = nums[ptr2]; } return ptr1; } }

Time Complexity: O(n)

Space Complexity: O(1)