find-the-duplicate-number

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

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?