Skip to content

287. Find the Duplicate Number

Difficulty Topics

Description

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?

Solution

find-the-duplicate-number.py
class Solution:
    def findDuplicate(self, nums: List[int]) -> int:
        n = len(nums)
        left, right = 1, len(nums) - 1

        while left <= right:
            mid = left + (right - left) // 2

            count = 0

            for x in nums:
                if x <= mid:
                    count += 1

            if count <= mid:
                left = mid + 1
            else:
                right = mid - 1

        return left