Find the two repeating elements in a given array

You are given an array of n+2 elements. All elements of the array are in range 1 to n. And all elements occur once except two numbers which occur twice. Find the two repeating numbers.

For example, array = {4, 2, 4, 5, 2, 3, 1} and n = 5

The above array has n + 2 = 7 elements with all elements occurring once except 2 and 4 which occur twice. So the output should be 4 2.

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Method 1 (Basic)
Use two loops. In the outer loop, pick elements one by one and count the number of occurrences of the picked element in the inner loop.

This method doesn’t use the other useful data provided in questions like range of numbers is between 1 to n and there are only two repeating elements.

C++

// C++ program to Find the two repeating  
// elements in a given array 
#include<bits/stdc++.h> 
using namespace std; 
  
void printRepeating(int arr[], int size) 
{ 
    int i, j; 
    printf(" Repeating elements are "); 
    for(i = 0; i < size; i++) 
        for(j = i + 1; j < size; j++) 
        if(arr[i] == arr[j]) 
            cout << arr[i] << " "; 
}  
  
// Driver Code 
int main() 
{ 
    int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
    int arr_size = sizeof(arr)/sizeof(arr[0]);  
    printRepeating(arr, arr_size); 
} 
  
// This code is contributed by Shivi_Aggarwal 

C

#include<stdio.h> 
#include<stdlib.h> 
void printRepeating(int arr[], int size) 
{ 
  int i, j; 
  printf(" Repeating elements are "); 
  for(i = 0; i < size; i++) 
    for(j = i+1; j < size; j++) 
      if(arr[i] == arr[j]) 
        printf(" %d ", arr[i]); 
}      
  
int main() 
{ 
  int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
  int arr_size = sizeof(arr)/sizeof(arr[0]);   
  printRepeating(arr, arr_size); 
  getchar(); 
  return 0; 
} 

Java

class RepeatElement  
{ 
    void printRepeating(int arr[], int size)  
    { 
        int i, j; 
        System.out.println("Repeated Elements are :"); 
        for (i = 0; i < size; i++)  
        { 
            for (j = i + 1; j < size; j++)  
            { 
                if (arr[i] == arr[j])  
                    System.out.print(arr[i] + " "); 
            } 
        } 
    } 
  
    public static void main(String[] args)  
    { 
        RepeatElement repeat = new RepeatElement(); 
        int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
        int arr_size = arr.length; 
        repeat.printRepeating(arr, arr_size); 
    } 
} 

Python3

# Python3 program to Find the two 
# repeating elements in a given array 
  
def printRepeating(arr, size): 
  
    print("Repeating elements are ", 
                         end = '') 
    for i in range (0, size): 
        for j in range (i + 1, size): 
            if arr[i] == arr[j]: 
                print(arr[i], end = ' ') 
      
# Driver code 
arr = [4, 2, 4, 5, 2, 3, 1] 
arr_size = len(arr) 
printRepeating(arr, arr_size) 
  
# This code is contributed by Smitha Dinesh Semwal 

C#

using System; 
  
class GFG 
{ 
          
    static void printRepeating(int []arr, int size)  
    { 
        int i, j; 
          
        Console.Write("Repeated Elements are :"); 
        for (i = 0; i < size; i++)  
        { 
            for (j = i + 1; j < size; j++)  
            { 
                if (arr[i] == arr[j])  
                    Console.Write(arr[i] + " "); 
            } 
        } 
    } 
    // driver code 
    public static void Main()  
    { 
        int []arr = {4, 2, 4, 5, 2, 3, 1}; 
        int arr_size = arr.Length; 
          
        printRepeating(arr, arr_size); 
    } 
} 
  
// This code is contributed by Sam007 

PHP

<?php 
// PHP program to Find the two  
// repeating elements in  
// a given array 
  
function printRepeating($arr, $size) 
{ 
    $i; 
    $j; 
    echo " Repeating elements are "; 
  
    for($i = 0; $i < $size; $i++) 
        for($j = $i + 1; $j < $size; $j++) 
            if($arr[$i] == $arr[$j]) 
                echo $arr[$i], " "; 
}  
  
// Driver Code 
$arr = array(4, 2, 4, 5, 2, 3, 1); 
$arr_size = sizeof($arr, 0); 
printRepeating($arr, $arr_size); 
  
// This code is contributed by Ajit 
?> 

Output :

Repeating elements are 4 2

Time Complexity: O(n*n)
Auxiliary Space: O(1)

Method 2 (Use Count array)
Traverse the array once. While traversing, keep track of count of all elements in the array using a temp array count[] of size n, when you see an element whose count is already set, print it as duplicate.

This method uses the range given in the question to restrict the size of count[], but doesn’t use the data that there are only two repeating elements.

C++

// C++ implementation of above approach 
#include <bits/stdc++.h> 
using namespace std; 
  
void printRepeating(int arr[], int size)  
{  
    int *count = new int[sizeof(int)*(size - 2)];  
    int i;  
          
    cout << " Repeating elements are ";  
    for(i = 0; i < size; i++)  
    {  
        if(count[arr[i]] == 1)  
            cout << arr[i] << " ";  
        else
            count[arr[i]]++;  
    }  
}  
  
// Driver code 
int main()  
{  
    int arr[] = {4, 2, 4, 5, 2, 3, 1};  
    int arr_size = sizeof(arr)/sizeof(arr[0]);  
    printRepeating(arr, arr_size);  
    return 0;  
}  
  
// This is code is contributed by rathbhupendra 

C

#include<stdio.h> 
#include<stdlib.h> 
  
void printRepeating(int arr[], int size) 
{ 
  int *count = (int *)calloc(sizeof(int), (size - 2)); 
  int i; 
    
  printf(" Repeating elements are "); 
  for(i = 0; i < size; i++) 
  {   
    if(count[arr[i]] == 1) 
      printf(" %d ", arr[i]); 
    else
     count[arr[i]]++; 
  }     
}      
  
int main() 
{ 
  int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
  int arr_size = sizeof(arr)/sizeof(arr[0]);   
  printRepeating(arr, arr_size); 
  getchar(); 
  return 0; 
} 

Java

class RepeatElement 
{ 
    void printRepeating(int arr[], int size)  
    { 
        int count[] = new int[size]; 
        int i; 
  
        System.out.println("Repeated elements are : "); 
        for (i = 0; i < size; i++)  
        { 
            if (count[arr[i]] == 1) 
                System.out.print(arr[i] + " "); 
            else
                count[arr[i]]++; 
        } 
    } 
  
    public static void main(String[] args) 
    { 
        RepeatElement repeat = new RepeatElement(); 
        int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
        int arr_size = arr.length; 
        repeat.printRepeating(arr, arr_size); 
    } 
} 

Python3

# Python3 code for Find the two repeating  
# elements in a given array 
  
  
def printRepeating(arr,size) : 
    count = [0] * size 
    print(" Repeating elements are ",end = "") 
    for i in range(0, size) : 
        if(count[arr[i]] == 1) : 
            print(arr[i], end = " ") 
        else : 
            count[arr[i]] = count[arr[i]] + 1
  
  
# Driver code 
arr = [4, 2, 4, 5, 2, 3, 1] 
arr_size = len(arr) 
printRepeating(arr, arr_size) 
  
  
          
# This code is contributed by Nikita Tiwari. 

C#

// C# program to Find the two 
// repeating elements in a given array 
using System; 
  
class GFG 
{ 
          
    static void printRepeating(int []arr, 
                                    int size)  
    { 
        int []count = new int[size]; 
        int i; 
  
        Console.Write("Repeated elements are: "); 
        for (i = 0; i < size; i++)  
        { 
            if (count[arr[i]] == 1) 
                Console.Write(arr[i] + " "); 
            else
                count[arr[i]]++; 
        } 
    } 
  
    // driver code 
    public static void Main() 
    { 
        int []arr = {4, 2, 4, 5, 2, 3, 1}; 
        int arr_size = arr.Length; 
          
        printRepeating(arr, arr_size); 
    } 
} 
  
//This code is contributed by Sam007 

PHP

<?php 
// PHP program to Find the two 
// repeating elements in a given array 
function printRepeating($arr, $size)  
{  
    $count = array_fill(0, $size, 0); 
    echo "Repeated elements are "; 
    for ($i = 0; $i < $size; $i++)  
    { 
        if ($count[$arr[$i]] == 1) 
            echo $arr[$i]." "; 
        else
            $count[$arr[$i]]++; 
    } 
} 
  
// Driver code 
$arr = array(4, 2, 4, 5, 2, 3, 1); 
$arr_size = count($arr); 
  
printRepeating($arr, $arr_size); 
          
// This code is contributed by mits 
?> 

Output :

Repeating elements are 4 2

Time Complexity: O(n)
Auxiliary Space: O(n)

Method 3 (Make two equations)
Let the numbers which are being repeated are X and Y. We make two equations for X and Y and the simple task left is to solve the two equations.
We know the sum of integers from 1 to n is n(n+1)/2 and product is n!. We calculate the sum of input array, when this sum is subtracted from n(n+1)/2, we get X + Y because X and Y are the two numbers missing from set [1..n]. Similarly calculate product of input array, when this product is divided from n!, we get X*Y. Given sum and product of X and Y, we can find easily out X and Y.

Let summation of all numbers in array be S and product be P

X + Y = S – n(n+1)/2
XY = P/n!

Using above two equations, we can find out X and Y. For array = 4 2 4 5 2 3 1, we get S = 21 and P as 960.

X + Y = 21 – 15 = 6

XY = 960/5! = 8

X – Y = sqrt((X+Y)^2 – 4*XY) = sqrt(4) = 2

Using below two equations, we easily get X = (6 + 2)/2 and Y = (6-2)/2
X + Y = 6
X – Y = 2

Thanks to geek4u for suggesting this method. As pointed by Beginer , there can be addition and multiplication overflow problem with this approach.
The methods 3 and 4 use all useful information given in the question 🙂

C++

#include <bits/stdc++.h> 
using namespace std;  
  
/* function to get factorial of n */
int fact(int n);  
  
void printRepeating(int arr[], int size)  
{  
    int S = 0; /* S is for sum of elements in arr[] */
    int P = 1; /* P is for product of elements in arr[] */
    int x, y; /* x and y are two repeating elements */
    int D; /* D is for difference of x and y, i.e., x-y*/
    int n = size - 2, i;  
      
    /* Calculate Sum and Product of all elements in arr[] */
    for(i = 0; i < size; i++)  
    {  
        S = S + arr[i];  
        P = P*arr[i];  
    }      
          
    S = S - n*(n+1)/2; /* S is x + y now */
    P = P/fact(n);     /* P is x*y now */
          
    D = sqrt(S*S - 4*P); /* D is x - y now */
          
    x = (D + S)/2;  
    y = (S - D)/2;  
          
    cout<<"The two Repeating elements are "<<x<<" & "<<y;  
}  
  
int fact(int n)  
{  
    return (n == 0)? 1 : n*fact(n-1);  
}  
  
// Driver code 
int main()  
{  
    int arr[] = {4, 2, 4, 5, 2, 3, 1};  
    int arr_size = sizeof(arr)/sizeof(arr[0]);  
    printRepeating(arr, arr_size);  
    return 0;  
}  
  
// This code is contributed by rathbhupendra 

C

#include<stdio.h> 
#include<stdlib.h> 
#include<math.h> 
  
/* function to get factorial of n */
int fact(int n); 
  
void printRepeating(int arr[], int size) 
{ 
  int S = 0;  /* S is for sum of elements in arr[] */
  int P = 1;  /* P is for product of elements in arr[] */  
  int x,  y;   /* x and y are two repeating elements */
  int D;      /* D is for difference of x and y, i.e., x-y*/
  int n = size - 2,  i; 
  
  /* Calculate Sum and Product of all elements in arr[] */
  for(i = 0; i < size; i++) 
  { 
    S = S + arr[i]; 
    P = P*arr[i]; 
  }         
    
  S = S - n*(n+1)/2;  /* S is x + y now */
  P = P/fact(n);         /* P is x*y now */
    
  D = sqrt(S*S - 4*P); /* D is x - y now */
    
  x = (D + S)/2; 
  y = (S - D)/2; 
    
  printf("The two Repeating elements are %d & %d", x, y); 
}      
  
int fact(int n) 
{ 
   return (n == 0)? 1 : n*fact(n-1); 
}     
  
int main() 
{ 
  int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
  int arr_size = sizeof(arr)/sizeof(arr[0]);   
  printRepeating(arr, arr_size); 
  getchar(); 
  return 0; 
} 

Java

class RepeatElement 
{ 
    void printRepeating(int arr[], int size)  
    { 
        /* S is for sum of elements in arr[] */
        int S = 0; 
          
        /* P is for product of elements in arr[] */
        int P = 1; 
          
        /* x and y are two repeating elements */
        int x, y; 
          
        /* D is for difference of x and y, i.e., x-y*/
        int D; 
          
        int n = size - 2, i; 
  
        /* Calculate Sum and Product of all elements in arr[] */
        for (i = 0; i < size; i++)  
        { 
            S = S + arr[i]; 
            P = P * arr[i]; 
        } 
  
        /* S is x + y now */
        S = S - n * (n + 1) / 2; 
          
        /* P is x*y now */
        P = P / fact(n); 
         
        /* D is x - y now */
        D = (int) Math.sqrt(S * S - 4 * P); 
          
  
        x = (D + S) / 2; 
        y = (S - D) / 2; 
  
        System.out.println("The two repeating elements are :"); 
        System.out.print(x + " " + y); 
    } 
  
    int fact(int n)  
    { 
        return (n == 0) ? 1 : n * fact(n - 1); 
    } 
  
    public static void main(String[] args) { 
        RepeatElement repeat = new RepeatElement(); 
        int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
        int arr_size = arr.length; 
        repeat.printRepeating(arr, arr_size); 
    } 
} 
  
// This code has been contributed by Mayank Jaiswal 

Python3

# Python3 code for Find the two repeating  
# elements in a given array 
import math 
  
def printRepeating(arr, size) : 
      
    # S is for sum of elements in arr[]  
    S = 0;  
      
    # P is for product of elements in arr[]  
    P = 1; 
      
    n = size - 2
  
    # Calculate Sum and Product  
    # of all elements in arr[]  
    for i in range(0, size) : 
        S = S + arr[i] 
        P = P * arr[i] 
      
    # S is x + y now  
    S = S - n * (n + 1) // 2 
      
     # P is x*y now  
    P = P // fact(n)     
      
    # D is x - y now  
    D = math.sqrt(S * S - 4 * P)  
      
    x = (D + S) // 2
    y = (S - D) // 2
      
    print("The two Repeating elements are ",  
          (int)(x)," & " ,(int)(y)) 
      
  
def fact(n) : 
    if(n == 0) : 
        return 1
    else : 
        return(n * fact(n - 1)) 
  
# Driver code 
arr = [4, 2, 4, 5, 2, 3, 1] 
arr_size = len(arr)  
printRepeating(arr, arr_size) 
  
          
# This code is contributed by Nikita Tiwari. 

C#

using System; 
  
class GFG 
{ 
          
    static void printRepeating(int []arr, int size)  
    { 
        /* S is for sum of elements in arr[] */
        int S = 0; 
          
        /* P is for product of elements in arr[] */
        int P = 1; 
          
        /* x and y are two repeating elements */
        int x, y; 
          
        /* D is for difference of x and y, i.e., x-y*/
        int D; 
          
        int n = size - 2, i; 
  
        /* Calculate Sum and Product  
         of all elements in arr[] */
        for (i = 0; i < size; i++)  
        { 
            S = S + arr[i]; 
            P = P * arr[i]; 
        } 
  
        /* S is x + y now */
        S = S - n * (n + 1) / 2; 
          
        /* P is x*y now */
        P = P / fact(n); 
          
        /* D is x - y now */
        D = (int) Math.Sqrt(S * S - 4 * P); 
          
  
        x = (D + S) / 2; 
        y = (S - D) / 2; 
  
        Console.WriteLine("The two" +  
                " repeating elements are :"); 
        Console.Write(x + " " + y); 
    } 
  
    static int fact(int n)  
    { 
        return (n == 0) ? 1 : n * fact(n - 1); 
    } 
  
    // driver code 
    public static void Main() { 
        int []arr = {4, 2, 4, 5, 2, 3, 1}; 
        int arr_size = arr.Length; 
          
        printRepeating(arr, arr_size); 
    } 
} 
// This code is contributed by Sam007  

PHP

<?php 
  
/* function to get factorial of n */
function fact($n){ 
    
return ($n == 0)? 1 : $n*fact($n-1); 
} 
  
function printRepeating($arr, $size) 
{ 
 $S = 0; /* S is for sum of elements in arr[] */
 $P = 1; /* P is for product of elements in arr[] */
 $x; $y; /* x and y are two repeating elements */
 $D;     /* D is for difference of x and y, i.e., x-y*/
 $n = $size - 2; 
   
  
/* Calculate Sum and Product of all elements in arr[] */
for($i = 0; $i < $size; $i++) 
{ 
    $S = $S + $arr[$i]; 
    $P = $P*$arr[$i]; 
}      
  
$S = $S - $n*($n+1)/2; /* S is x + y now */
$P = $P/fact($n);         /* P is x*y now */
  
$D = sqrt($S*$S - 4*$P); /* D is x - y now */
  
$x = ($D + $S)/2; 
$y = ($S - $D)/2; 
  
echo "The two Repeating elements are ".$x." & ".$y; 
}      
  
  
  
$arr = array(4, 2, 4, 5, 2, 3, 1); 
$arr_size = count($arr);  
printRepeating($arr, $arr_size); 
?> 

Output :

Repeating elements are 4 2

Time Complexity: O(n)
Auxiliary Space: O(1)

Method 4 (Use XOR)
Thanks to neophyte for suggesting this method.
The approach used here is similar to method 2 of this post.
Let the repeating numbers be X and Y, if we xor all the elements in the array and all integers from 1 to n, then the result is X xor Y.
The 1’s in binary representation of X xor Y is corresponding to the different bits between X and Y. Suppose that the kth bit of X xor Y is 1, we can xor all the elements in the array and all integers from 1 to n, whose kth bits are 1. The result will be one of X and Y.

C++

#include <bits/stdc++.h> 
using namespace std; 
  
void printRepeating(int arr[], int size)  
{  
    int Xor = arr[0]; /* Will hold Xor of all elements */
    int set_bit_no; /* Will have only single set bit of Xor */
    int i;  
    int n = size - 2;  
    int x = 0, y = 0;  
          
    /* Get the Xor of all elements in arr[] and {1, 2 .. n} */
    for(i = 1; i < size; i++)  
        Xor ^= arr[i];  
    for(i = 1; i <= n; i++)  
        Xor ^= i;  
      
    /* Get the rightmost set bit in set_bit_no */
    set_bit_no = Xor & ~(Xor-1);  
      
    /* Now divide elements in two sets by comparing rightmost set  
    bit of Xor with bit at same position in each element. */
    for(i = 0; i < size; i++)  
    {  
        if(arr[i] & set_bit_no)  
        x = x ^ arr[i]; /*Xor of first set in arr[] */
        else
        y = y ^ arr[i]; /*Xor of second set in arr[] */
    }  
    for(i = 1; i <= n; i++)  
    {  
        if(i & set_bit_no)  
        x = x ^ i; /*Xor of first set in arr[] and {1, 2, ...n }*/
        else
        y = y ^ i; /*Xor of second set in arr[] and {1, 2, ...n } */
    }  
          
    cout<<"The two repeating elements are "<<y<<" "<<x;  
}  
  
// Driver code 
int main()  
{  
    int arr[] = {4, 2, 4, 5, 2, 3, 1};  
    int arr_size = sizeof(arr)/sizeof(arr[0]);  
    printRepeating(arr, arr_size);  
    return 0;  
}  
  
// This code is contributed by rathbhupendra 

C

void printRepeating(int arr[], int size) 
{ 
  int xor = arr[0]; /* Will hold xor of all elements */
  int set_bit_no;  /* Will have only single set bit of xor */
  int i; 
  int n = size - 2; 
  int x = 0, y = 0; 
    
  /* Get the xor of all elements in arr[] and {1, 2 .. n} */
  for(i = 1; i < size; i++) 
    xor ^= arr[i];   
  for(i = 1; i <= n; i++) 
    xor ^= i;    
  
  /* Get the rightmost set bit in set_bit_no */
  set_bit_no = xor & ~(xor-1); 
  
  /* Now divide elements in two sets by comparing rightmost set 
   bit of xor with bit at same position in each element. */
  for(i = 0; i < size; i++) 
  { 
    if(arr[i] & set_bit_no) 
      x = x ^ arr[i]; /*XOR of first set in arr[] */
    else
      y = y ^ arr[i]; /*XOR of second set in arr[] */
  } 
  for(i = 1; i <= n; i++) 
  { 
    if(i & set_bit_no) 
      x = x ^ i; /*XOR of first set in arr[] and {1, 2, ...n }*/
    else
      y = y ^ i; /*XOR of second set in arr[] and {1, 2, ...n } */
  } 
    
  printf("n The two repeating elements are %d & %d ", x, y); 
}      
  
  
int main() 
{ 
  int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
  int arr_size = sizeof(arr)/sizeof(arr[0]);   
  printRepeating(arr, arr_size); 
  getchar(); 
  return 0; 
} 

Java

class RepeatElement 
{ 
    void printRepeating(int arr[], int size)  
    { 
        /* Will hold xor of all elements */
        int xor = arr[0]; 
          
        /* Will have only single set bit of xor */
        int set_bit_no; 
          
        int i; 
        int n = size - 2; 
        int x = 0, y = 0; 
  
        /* Get the xor of all elements in arr[] and {1, 2 .. n} */
        for (i = 1; i < size; i++) 
            xor ^= arr[i]; 
        for (i = 1; i <= n; i++) 
            xor ^= i; 
  
        /* Get the rightmost set bit in set_bit_no */
        set_bit_no = (xor & ~(xor - 1)); 
  
        /* Now divide elements in two sets by comparing rightmost set 
           bit of xor with bit at same position in each element. */
        for (i = 0; i < size; i++) { 
            int a = arr[i] & set_bit_no; 
            if (a != 0) 
                x = x ^ arr[i]; /*XOR of first set in arr[] */
            else
                y = y ^ arr[i]; /*XOR of second set in arr[] */
        } 
        for (i = 1; i <= n; i++)  
        { 
            int a = i & set_bit_no; 
            if (a != 0) 
                x = x ^ i; /*XOR of first set in arr[] and {1, 2, ...n }*/
            else
                y = y ^ i; /*XOR of second set in arr[] and {1, 2, ...n } */
        } 
  
        System.out.println("The two reppeated elements are :"); 
        System.out.println(x + " " + y); 
    } 
  
    /* Driver program to test the above function */
    public static void main(String[] args)  
    { 
        RepeatElement repeat = new RepeatElement(); 
        int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
        int arr_size = arr.length; 
        repeat.printRepeating(arr, arr_size); 
    } 
} 
  
// This code has been contributed by Mayank Jaiswal 

Python3

# Python3 code to Find the  
# two repeating elements  
# in a given array 
def printRepeating(arr, size): 
      
    # Will hold xor  
    # of all elements  
    xor = arr[0]  
    n = size - 2
    x = 0
    y = 0
      
    # Get the xor of all  
    # elements in arr[]  
    # and 1, 2 .. n  
    for i in range(1 , size): 
        xor ^= arr[i]  
    for i in range(1 , n + 1): 
        xor ^= i  
      
    # Get the rightmost set 
    # bit in set_bit_no  
    set_bit_no = xor & ~(xor-1) 
      
    # Now divide elements in two 
    # sets by comparing rightmost  
    # set bit of xor with bit at 
    # same position in each element.  
    for i in range(0, size): 
          
        if(arr[i] & set_bit_no): 
              
            # XOR of first  
            # set in arr[]  
            x = x ^ arr[i]  
        else: 
              
            # XOR of second 
            # set in arr[]  
            y = y ^ arr[i]  
              
    for i in range(1 , n + 1): 
  
        if(i & set_bit_no): 
              
            # XOR of first set 
            # in arr[] and  
            # 1, 2, ...n  
            x = x ^ i  
        else: 
              
             # XOR of second set  
             # in arr[] and 
             # 1, 2, ...n  
            y = y ^ i 
              
    print("The two repeating", 
         "elements are", y, x) 
  
# Driver code     
arr = [4, 2, 4,  
       5, 2, 3, 1] 
arr_size = len(arr)  
printRepeating(arr, arr_size) 
  
# This code is contributed  
# by Smitha 

C#

using System; 
  
class GFG 
{ 
    static void printRepeating(int []arr, int size)  
    { 
        /* Will hold xor of all elements */
        int xor = arr[0]; 
          
        /* Will have only single set bit of xor */
        int set_bit_no; 
          
        int i; 
        int n = size - 2; 
        int x = 0, y = 0; 
  
        /* Get the xor of all elements 
         in arr[] and {1, 2 .. n} */
        for (i = 1; i < size; i++) 
            xor ^= arr[i]; 
          
        for (i = 1; i <= n; i++) 
            xor ^= i; 
  
        /* Get the rightmost set bit in set_bit_no */
        set_bit_no = (xor & ~(xor - 1)); 
  
        /* Now divide elements in two sets by  
         comparing rightmost set bit of xor with bit 
         at same position in each element. */
        for (i = 0; i < size; i++) { 
            int a = arr[i] & set_bit_no; 
          
            if (a != 0) 
                /* XOR of first set in arr[] */
                x = x ^ arr[i];  
            else
                /* XOR of second set in arr[] */
                y = y ^ arr[i];  
        } 
        for (i = 1; i <= n; i++)  
        { 
            int a = i & set_bit_no; 
              
            if (a != 0) 
              
                /* XOR of first set in 
                 arr[] and {1, 2, ...n }*/
                x = x ^ i;  
            else
              
                /* XOR of second set in  
                 arr[] and {1, 2, ...n } */
                y = y ^ i;  
        } 
  
        Console.WriteLine("The two" +  
            " reppeated elements are :"); 
        Console.Write(x + " " + y); 
    } 
  
    /* Driver program to test the above function */
    public static void Main()  
    { 
        int []arr = {4, 2, 4, 5, 2, 3, 1}; 
        int arr_size = arr.Length; 
          
        printRepeating(arr, arr_size); 
    } 
} 
  
// This code is contributed by Sam007 

PHP

<?php  
// PHP code to Find the  
// two repeating elements  
// in a given array 
function printRepeating( $arr, $size)  
{  
    $xor = $arr[0]; /* Will hold xor of all elements */
    $set_bit_no; /* Will have only single set bit of xor */
    $i;  
    $n = $size - 2;  
    $x = 0; $y = 0;  
      
    /* Get the xor of all elements in arr[] and {1, 2 .. n} */
    for($i = 1; $i < $size; $i++)  
    $xor ^= $arr[$i];  
    for($i = 1; $i <= $n; $i++)  
    $xor ^= $i;  
      
    /* Get the rightmost set bit in set_bit_no */
    $set_bit_no = $xor & ~($xor-1);  
      
    /* Now divide elements in two sets by  
    comparing rightmost set bit of xor with  
    bit at same position in each element. */
    for($i = 0; $i < $size; $i++)  
    {  
        if($arr[$i] & $set_bit_no)  
        $x = $x ^ $arr[$i]; /*XOR of first set in arr[] */
        else
        $y = $y ^ $arr[$i]; /*XOR of second set in arr[] */
          
    }  
    for($i = 1; $i <= $n; $i++)  
    {  
        if($i & $set_bit_no)  
        /*XOR of first set in arr[] and {1, 2, ...n }*/
        $x = $x ^ $i;  
        else
        /*XOR of second set in arr[] and {1, 2, ...n } */
        $y = $y ^ $i; 
          
    }  
    echo "n The two repeating elements are "; 
    echo $y. " ".$x; 
      
}  
  
$arr = array(4, 2, 4, 5, 2, 3, 1);  
$arr_size = count($arr);  
printRepeating($arr, $arr_size);  
  
// This code has been contributed by Rajput-Ji 
?> 

Output :

The two repeating elements are 4 2

Method 5 (Use array elements as index)
Thanks to Manish K. Aasawat for suggesting this method.

Traverse the array. Do following for every index i of A[].
{
check for sign of A[abs(A[i])] ;
if positive then
   make it negative by   A[abs(A[i])]=-A[abs(A[i])];
else  // i.e., A[abs(A[i])] is negative
   this   element (ith element of list) is a repetition
}

Example: A[] =  {1, 1, 2, 3, 2}
i=0; 
Check sign of A[abs(A[0])] which is A[1].  A[1] is positive, so make it negative. 
Array now becomes {1, -1, 2, 3, 2}

i=1; 
Check sign of A[abs(A[1])] which is A[1].  A[1] is negative, so A[1] is a repetition.

i=2; 
Check sign of A[abs(A[2])] which is A[2].  A[2] is  positive, so make it negative. '
Array now becomes {1, -1, -2, 3, 2}

i=3; 
Check sign of A[abs(A[3])] which is A[3].  A[3] is  positive, so make it negative. 
Array now becomes {1, -1, -2, -3, 2}

i=4; 
Check sign of A[abs(A[4])] which is A[2].  A[2] is negative, so A[4] is a repetition.

Note that this method modifies the original array and may not be a recommended method if we are not allowed to modify the array.

C++

#include <bits/stdc++.h> 
using namespace std;  
  
void printRepeating(int arr[], int size)  
{  
    int i;  
      
    cout << "The repeating elements are";  
          
    for(i = 0; i < size; i++)  
    {  
        if(arr[abs(arr[i])] > 0)  
            arr[abs(arr[i])] = -arr[abs(arr[i])];  
        else
            cout<<" " << abs(arr[i]) <<" ";  
    }      
}  
  
// Driver code 
int main()  
{  
    int arr[] = {4, 2, 4, 5, 2, 3, 1};  
    int arr_size = sizeof(arr)/sizeof(arr[0]);  
    printRepeating(arr, arr_size);  
    return 0;  
}  
  
// This code is contributed by rathbhupendra 

C

#include <stdio.h> 
#include <stdlib.h> 
  
void printRepeating(int arr[], int size) 
{ 
  int i;   
   
  printf("n The repeating elements are"); 
    
  for(i = 0; i < size; i++) 
  { 
    if(arr[abs(arr[i])] > 0) 
      arr[abs(arr[i])] = -arr[abs(arr[i])]; 
    else
      printf(" %d ", abs(arr[i])); 
  }          
}      
  
int main() 
{ 
  int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
  int arr_size = sizeof(arr)/sizeof(arr[0]); 
  printRepeating(arr, arr_size); 
  getchar(); 
  return 0; 
} 

Java

class RepeatElement 
{ 
    void printRepeating(int arr[], int size) 
    { 
        int i;   
        System.out.println("The repeating elements are : "); 
     
        for(i = 0; i < size; i++) 
        { 
            if(arr[Math.abs(arr[i])] > 0) 
                arr[Math.abs(arr[i])] = -arr[Math.abs(arr[i])]; 
            else
                System.out.print(Math.abs(arr[i]) + " "); 
        }          
    }  
  
    /* Driver program to test the above function */
    public static void main(String[] args)  
    { 
        RepeatElement repeat = new RepeatElement(); 
        int arr[] = {4, 2, 4, 5, 2, 3, 1}; 
        int arr_size = arr.length; 
        repeat.printRepeating(arr, arr_size); 
    } 
} 
  
// This code has been contributed by Mayank Jaiswal 

Python3

# Python3 code for Find the two repeating  
# elements in a given array 
  
  
def printRepeating(arr, size) : 
      
    print(" The repeating elements are",end=" ") 
      
    for i in range(0,size) : 
          
        if(arr[abs(arr[i])] > 0) : 
            arr[abs(arr[i])] = (-1) * arr[abs(arr[i])] 
        else : 
            print(abs(arr[i]),end = " ") 
  
# Driver code 
arr = [4, 2, 4, 5, 2, 3, 1] 
arr_size = len(arr)  
printRepeating(arr, arr_size) 
  
  
# This code is contributed by Nikita Tiwari. 

C#

// C# code for Find the two repeating  
// elements in a given array 
 using System; 
  
class GFG 
{ 
    static void printRepeating(int []arr, int size) 
    { 
        int i;  
        Console.Write("The repeating elements are : "); 
      
        for(i = 0; i < size; i++) 
        { 
            if(arr[Math.Abs(arr[i])] > 0) 
                arr[Math.Abs(arr[i])] = -arr[Math.Abs(arr[i])]; 
            else
                Console.Write(Math.Abs(arr[i]) + " "); 
        }          
    }  
  
    /* Driver program to test the above function */
    public static void Main()  
    { 
        int []arr = {4, 2, 4, 5, 2, 3, 1}; 
        int arr_size = arr.Length; 
          
        printRepeating(arr, arr_size); 
    } 
} 
  
// This code is contributed by Sam007 

PHP

<?php 
  
  
function  printRepeating($arr, $size) 
{ 
    $i;  
  
 echo "The repeating elements are"," "; 
  
for($i = 0; $i < $size; $i++) 
{ 
    if($arr[abs($arr[$i])] > 0) 
    $arr[abs($arr[$i])] = -$arr[abs($arr[$i])]; 
    else
    echo  abs($arr[$i])," "; 
}          
}      
  
  
    $arr = array (4, 2, 4, 5, 2, 3, 1); 
    $arr_size = sizeof($arr); 
    printRepeating($arr, $arr_size); 
      
      
#This code is contributed by aj_36 
?> 

Output :

The repeating elements are 4 2

Please write comments if you find the above codes/algorithms incorrect, or find better ways to solve the same problem.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

C++

C

Java

Python3

C#

PHP

C++

C

Java

Python3

C#

PHP

C++

C

Java

Python3

C#

PHP

C++

C

Java

Python3

C#

PHP

C++

C

Java

Python3

C#

PHP

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