287. Find the Duplicate Number

Problem Link

Description

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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?

Solution

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Python3

class Solution:
    def findDuplicate(self, nums: List[int]) -> int:
        slow, fast = nums[0], nums[nums[0]]
 
        while slow != fast:
            slow = nums[slow]
            fast = nums[nums[fast]]
        
        slow = 0
        while slow != fast:
            slow = nums[slow]
            fast = nums[fast]
        
        return slow