Find duplicate in an array in O(n) and by using O(1) extra space

Given an array arr[] containing n + 1 integers where each integer is between 1 and n (inclusive). There is only one duplicate element, find the duplicate element in O(n) time complexity and O(1) space.

Examples :

Input  : arr[] = {1, 4, 3, 4, 2} 
Output : 4

Input  : arr[] = {1, 3, 2, 1}
Output : 1

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach :
Firstly, the constraints of this problem imply that a cycle must exist. Because each number in an array arr[] is between 1 and n, it will necessarily point to an index that exists. Therefore, the list can be traversed infinitely, which implies that there is a cycle. Additionally, because 0 cannot appear as a value in an array arr[], arr[0] cannot be part of the cycle. Therefore, traversing the array in this manner from arr[0] is equivalent to traversing a cyclic linked list. The problem can be solved just like linked list cycle.

Below is the implementation of above approach:

C++

// CPP code to find the repeated elements 
// in the array where every other is present once 
#include <iostream> 
using namespace std; 
  
// Function to find duplicate 
int findDuplicate(int arr[]) 
{ 
    // Find the intersection point of  
    // the slow and fast. 
    int slow = arr[0]; 
    int fast = arr[0]; 
    do 
    { 
        slow = arr[slow]; 
        fast = arr[arr[fast]]; 
    } while (slow != fast); 
  
    // Find the "entrance" to the cycle. 
    int ptr1 = arr[0]; 
    int ptr2 = slow; 
    while (ptr1 != ptr2)  
    { 
        ptr1 = arr[ptr1]; 
        ptr2 = arr[ptr2]; 
    } 
  
    return ptr1; 
} 
  
// Driver code 
int main() 
{ 
    int arr[] = { 1, 3, 2, 1 }; 
      
    cout << findDuplicate(arr) << endl; 
      
    return 0; 
} 

Java

// Java code to find the repeated  
// elements in the array where  
// every other is present once 
import java.util.*; 
  
class GFG 
{ 
  
// Function to find duplicate 
public static int findDuplicate(int []arr) 
{ 
    // Find the intersection  
    // point of the slow and fast. 
    int slow = arr[0]; 
    int fast = arr[0]; 
    do
    { 
        slow = arr[slow]; 
        fast = arr[arr[fast]]; 
    } while (slow != fast); 
  
    // Find the "entrance" 
    // to the cycle. 
    int ptr1 = arr[0]; 
    int ptr2 = slow; 
    while (ptr1 != ptr2)  
    { 
        ptr1 = arr[ptr1]; 
        ptr2 = arr[ptr2]; 
    } 
  
    return ptr1; 
} 
  
// Driver Code 
public static void main(String[] args) 
{ 
    int []arr = {1, 3, 2, 1}; 
  
    System.out.println("" +  
               findDuplicate(arr)); 
  
    System.exit(0); 
} 
} 
  
// This code is contributed  
// by Harshit Saini  

Python3

# Python code to find the  
# repeated elements in the  
# array where every other 
# is present once 
  
# Function to find duplicate 
def findDuplicate(arr): 
  
    # Find the intersection  
    # point of the slow and fast. 
    slow = arr[0] 
    fast = arr[0] 
    while True: 
        slow = arr[slow] 
        fast = arr[arr[fast]] 
        if slow == fast: 
            break
  
    # Find the "entrance" 
    # to the cycle. 
    ptr1 = arr[0] 
    ptr2 = slow 
    while ptr1 != ptr2: 
        ptr1 = arr[ptr1] 
        ptr2 = arr[ptr2] 
          
    return ptr1 
      
# Driver code 
if __name__ == '__main__': 
      
      
    arr = [ 1, 3, 2, 1 ] 
  
    print(findDuplicate(arr)) 
  
  
# This code is contributed 
# by Harshit Saini  

C#

// C# code to find the repeated  
// elements in the array where  
// every other is present once 
using System; 
  
class GFG 
{ 
  
// Function to find duplicate 
public static int findDuplicate(int []arr) 
{ 
    // Find the intersection  
    // point of the slow and fast. 
    int slow = arr[0]; 
    int fast = arr[0]; 
    do
    { 
        slow = arr[slow]; 
        fast = arr[arr[fast]]; 
    } while (slow != fast); 
  
    // Find the "entrance" 
    // to the cycle. 
    int ptr1 = arr[0]; 
    int ptr2 = slow; 
    while (ptr1 != ptr2)  
    { 
        ptr1 = arr[ptr1]; 
        ptr2 = arr[ptr2]; 
    } 
  
    return ptr1; 
} 
  
// Driver Code 
public static void Main() 
{ 
    int[] arr = {1, 3, 2, 1}; 
  
    Console.WriteLine("" +  
            findDuplicate(arr)); 
  
} 
} 
  
// This code is contributed  
// by Akanksha Rai(Abby_akku)  

PHP

<?php 
// PHP code to find the repeated 
// elements in the array where 
// every other is present once 
  
// Function to find duplicate 
function findDuplicate(&$arr) 
{ 
    $slow = $arr[0]; 
    $fast = $arr[0]; 
    do 
    { 
        $slow = $arr[$slow]; 
        $fast = $arr[$arr[$fast]]; 
    } while ($slow != $fast); 
  
    // Find the "entrance" 
    // to the cycle. 
    $ptr1 = $arr[0]; 
    $ptr2 = $slow; 
    while ($ptr1 != $ptr2)  
    { 
        $ptr1 = $arr[$ptr1]; 
        $ptr2 = $arr[$ptr2]; 
    } 
  
    return $ptr1; 
} 
  
// Driver code 
$arr = array(1, 3, 2, 1); 
echo " " . findDuplicate($arr); 
  
// This code is contributed 
// by Shivi_Aggarwal  
?> 

Output:

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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