Find the Duplicate Number

Problem

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 <= 10:sup:`5`

  • 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?

Pattern

Array, Two Pointers, Binary Search, Bit Manipulation

Approaches

Code

def findDuplicate(nums: list[int]) -> int:
    for i in range(len(nums)):
        n = abs(nums[i])
        if nums[n] < 0:
            return n
        else:
            nums[n] = -nums[n]

    return -1

Test

>>> from find_the_duplicate_number__negation_marking import findDuplicate
>>> findDuplicate([1, 3, 4, 2, 2])
2
>>> findDuplicate([3, 1, 3, 4, 2])
3
>>> findDuplicate([3, 3, 3, 3, 3])
3
find_the_duplicate_number__negation_marking.findDuplicate(nums: list[int]) → int