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Find Duplicate Number in Array

Certification: Intermediate Level Accuracy: 100% Submissions: 1 Points: 10

Write a JavaScript program to find the duplicate number in an array containing n+1 integers where each integer is between 1 and n (inclusive). There is only one repeated number but it could be repeated more than once. You must solve this without modifying the array and using only constant extra space.

Example 1
    
      
  • Input: nums = [1,3,4,2,2]
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  • Output: 2
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  • Explanation: 
    • The array contains numbers from 1 to 4, but has 5 elements. 
    • Number 2 appears twice in the array at indices 3 and 4. 
    • Therefore, 2 is the duplicate number.
    •
Example 2
    
      
  • Input: nums = [3,1,3,4,2]
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  • Output: 3
    • 
      
  • Explanation: 
    • The array contains numbers from 1 to 4, but has 5 elements. 
    • Number 3 appears twice in the array at indices 0 and 2. 
    • Therefore, 3 is the duplicate number.
    •
Constraints
    
      
  • 1 ≤ n ≤ 10^5
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  • nums.length == n + 1
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  • 1 ≤ nums[i] ≤ n
    • 
      
  • All the integers in nums appear only once except for precisely one integer which appears two or more times
    • 
      
  • You must not modify the array
    • 
      
  • You must use only constant extra space
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  • Time Complexity: O(n)
    • 
      
  • Space Complexity: O(1)
    •
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Hint
Solution

Solution Hints

    
      
  • Treat the array indices and values as a linked list where nums[i] points to nums[nums[i]]
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  • Use two pointers (slow and fast) to detect the cycle
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  • Once a cycle is detected, find the entrance point of the cycle
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  • The entrance point will be the duplicate number
    •

Steps to solve by this approach:

 Step 1: Initialize two pointers (slow and fast) both pointing to the first element of the array.

 Step 2: Move slow pointer one step at a time and fast pointer two steps at a time until they meet.

 Step 3: This meeting point indicates there's a cycle in the "linked list" representation of the array.

 Step 4: Reset the slow pointer to the beginning of the array.

 Step 5: Move both pointers one step at a time until they meet again.

 Step 6: The meeting point is the entrance to the cycle, which is our duplicate number.

 Step 7: Return the duplicate number found.

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