Find the Duplicate Number

Problem

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

Example 3:

Input: nums = [3,3,3,3,3]
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?

Solution

I thought this was a XOR question, but it turns out that I misunderstood the prompt.

This is similar to the linked list cycle question.

class Solution {
    public int findDuplicate(int[] nums) {
        var slow = 0;
        var fast = 0;

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

        fast = 0;
        while (slow != fast) {
            slow = nums[slow];
            fast = nums[fast];
        }

        return slow;
    }
}