find_duplicate_integer.py

"""
https://leetcode.com/problems/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 using 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?
"""

from typing import List

def find_duplicate(nums: List[int]) -> int:
    i = 0

    while True:
        if nums[i] == -1:
            break
        
        tmp = nums[i]
        nums[i] = -1
        i = tmp

    return i