C++ Tutorial Index

C++ Tutorial C++ History C++ Installation C++ First Program C++ cin and cout C++ Data type C++ Variable C++ operator C++ Keywords

C++ Control Statements

C++ If C++ Nested if C++ If-else C++ If-else-if C++ Switch C++ Break C++ Continue C++ Goto C++ For loop C++ While loop C++ Do while loop

C++ Functions

C++ Call by Value C++ Call by Reference C++ Recursion Function C++ Inline function C++ Friend function

C++ Arrays

Single dimension array Two dimension array

C++ Strings

C++ Strings

C++ Inheritance

C++ Inheritance Single level Inheritance Multilevel Inheritance Multiple Inheritance Hierarchical Inheritance Hybrid Inheritance

C++ Polymorphism

C++ Polymorphism C++ Overloading C++ Overriding C++ Virtual Function

C++ Pointers

C++ Pointers C++ this pointer

C++ Exception Handling

C++ Exception Handling

C++ Constructors

C++ Constructors Default Constructor Parameterize Constructor Copy constructor Constructor Overloading Destructor

C++ File Handling

C++ File Handling C++ Writing to file C++ Reading file C++ Close file

Miscellaneous

C Vs C++ C++ Comments C++ Data Abstraction C++ Identifier C++ Memory Management C++ Storage Classes C++ Void Pointer C++ Array To Function C++ Expressions C++ Features C++ Interfaces C++ Encapsulation std::min in C++ External merge sort in C++ Remove duplicates from sorted array in C++ Precision of floating point numbers Using these functions floor(), ceil(), trunc(), round() and setprecision() in C++ C++ References C++ Friend Functions C++ Mutable keyword Unary Operators in C++ Initialize Array of objects with parameterized constructors in C++ Differences between #define & const in C/C++ C++ Program to Implement Shell Sort C++ Program to Implement Merge Sort Storage Classes in C Vector resize() in C++ Passing by Reference Vs. Passing by the pointer in C++ Free vs delete() in C++ goto statement in C and C++ C++ program to read string using cin.getline() C++ String Concatenation Heap Sort in C++ Swap numbers in C++ Input Iterators in C++ Fibonacci Series in C++ C ++ Program: Alphabet Triangle and Number Triangle C++ Program: Matrix Multiplication C++ Program to Print Fibonacci Triangle Stack in C++ Maps in C++ Queue in C++ C++ Bitset C++ Algorithms Priority Queue in C++ C++ Multimap C++ Deque Function Pointer in C++ Sizeof() Operators in C++ C++ array of Pointers free() Vs delete in C Timsort Implementation Using C++ CPP Templates C++ Aggregation C++ Enumeration C++ Math Functions C++ Object Class C++ Queue Initialize Vector in C++ Vector in C++ C++ STL Components Function overloading in C++ C++ Maximum Index Problem C++ find missing in the second array C++ Program to find the product array puzzle C++ Program To Find Largest Subarray With 0 Sum C++ Program To Move All Zeros To The End Of The Array C++ Program to find the element that occurs once C++ Program to find the largest number formed from an array Constructor Vs Destructor C++ Namespaces C++ OOPs Concept C++ Static C++ Structs C++ Try-Catch C++ User Defined Exceptions C++ Virtual Destructor C++ vs C# Malloc() and new in C++ Palindrome Number Program in C++ Snake Code in C++ Splitting a string in C++ Structure Vs Class in C++ Virtual Function Vs Pure Virtual Function C++ Bidirectional Iterators C++ Forward Iterators C++ Iterators C++ Output Iterators C++ Range-based For Loop Converting string into integer in C++ LCM Program in C++ Type conversion in C++ Add two numbers using the function in C++ Advantage and disadvantage friend function C++ Armstrong Number Program in C++ ATM machine program in C++ using functions Binary to Decimal in C++ Bit Manipulation in C++ C++ Constructor C++ Dijkstra Algorithm Using the Priority Queue C++ int into String C++ Signal Handling Decimal to Binary in C++ Decimal to Hexadecimal in C++ Decimal to Octal in C++ Factorial Program in C++ Function in C++ Hexadecimal to Decimal in C++ Octal to Decimal in C++ Reverse a Number in C++ Structure Vs Class in C++ C++ Forward Iterators C++ Output Iterators C++ Prime number program Char Array to String in C++ Constructor Overloading in C++ Default arguments in C++ Different Ways to Compare Strings in C++ Dynamic Binding in C++ Program to convert infix to postfix expression in C++ SET Data Structure in C++ Upcasting and Downcasting in C++ Reverse an Array in C++ Fast Input and Output in C++ Delete Operator in C++ Copy elision in C++ C++ Date and Time C++ Bitwise XOR Operator Array of sets in C++ Binary Operator Overloading in C++ Binary Search in C++ Implementing the sets without C++ STL containers Scope Resolution Operator in C++ Smart pointers in C++ Types of polymorphism in C++ Exception Handling in C++ vs Java Const Keyword in C++ Type Casting in C++ Static keyword in C++ vs Java Inheritance in C++ vs Java How to concatenate two strings in C++ Programs to Print Pyramid Patterns in C++ swap() function in C++ Structure of C++ Program Stringstream in C++ and its applications rand() and srand() in C / C++ C++ Ternary Operator C++ Scope of Variables While Loop Examples in C++ Star pattern in C++ using For Loops For Loop Examples in C++ Do-While Loop Examples in C++ Top 5 IDEs for C++ That You Should Try Once Assertions in C/C++ C++ Convert Int to String Continue in C++ While loop Diamond Pattern in C++ using For Loop How to Reverse a String in C++ using Do-While Loop How to Reverse a String in C++ using For Loop How to Reverse a String in C++ using While Loop Infinite loop in C++ Loops in C++ Returning Multiple Values from a Function using Tuple and Pair in C++ wcscpy(), wcslen(), wcscmp() Functions in C++ Auto keyword in C++ C++ 11 vs C++ 14 vs C++ 17 C++ STL (Standard Template Library) Differences Between C Structures and C++ Structures Divide by Zero Exception in C++ Dynamic Constructor in C++ Dynamic Memory Allocation in C++ Find the Size of Array in C/C++ without using sizeof() function Floating Point Operations and Associativity in C, C++ and Java Hello World Program in C++ How to create a table in C++ How to Setup Environment for C++ Programming on Mac Implementation of a Falling Matrix in C++ Message Passing in C++ Pointer to Object in C++ Templates in C++ vs Generics in Java Ways to Copy a Vector in C++ What does Buffer Flush mean in C++ sort() function in C++ Structure Sorting (By Multiple Rules) in C++ Similarities between C++ and Java std::distance in C++

C++ Program to find the element that occurs once

Write a program to find the element in the array that occurs once. Given that all the numbers in the array are present two times and the array is sorted, find the single occurring element.

For example

Input

arr[] = {10, 10, 20, 30, 30, 40, 40, 50, 50} N = 9

Output

20

Explanation

Among all the elements 20 is occurring once.

Input

arr[] = {1, 1,  2,  5, 5} N = 5

Output

2

Explanation

Among all the elements 2 is occurring once.

Naive approach

As we can see the array given is in sorted manner. Run a loop from begin to end and increment the i by 2. Inside the for loop if arr[i] != arr[i+1], store the arr[i] as ans.

C++ Code

#include <bits/stdc++.h>

using namespace std;




void search_single(int arr[], int n) // function to check the single occurring element

{

    int ans = -1; // initially it is -1

    for (int i = 0; i < n; i += 2) { // run for and increment i by 2

        if (arr[i] != arr[i + 1]) { // check the duplicity

            ans = arr[i]; // update ans if found

            break;

        }

    }




    if (arr[n - 2] != arr[n - 1]) // check if last element is unique or not

            ans = arr[n-1];




    cout << "The single occurring element is " << ans << "\n"; // print ans

}




// Driver code

int main()

{

    int arr[] = { 1, 1, 2, 4, 4, 5, 5, 6, 6 };

    int n = sizeof(arr) / sizeof(arr[0]); // find size of the array




    search_single(arr, n);




    return 0;

}

Output

The single occurring element is 2

C code

#include <stdio.h>




void search_single(int arr[], int n) // function to check the single occuring element

{

    int ans = -1; // initially it is -1

    for (int i = 0; i < n; i += 2) { // run for and increment i by 2

        if (arr[i] != arr[i + 1]) { // check the duplicacy

            ans = arr[i]; // update ans if found

            break;

        }

    }




    if (arr[n - 2] != arr[n - 1]) // check if last element is unique or not

            ans = arr[n-1];




    printf( "The single occurring element is %d",ans); // print ans

}




/

int main()

{

    int arr[] = { 1, 1, 2, 4, 4, 5, 5, 6, 6 };

    int n = sizeof(arr) / sizeof(arr[0]); // find size of the array




    search_single(arr, n);




    return 0;

}

Output

The single occurring element is 2

Time complexity - O(n)

Space complexity - O(1)

Using XOR

To find the singly occurring element, we can use the idea of XOR operation.

a^a = 0 and a^0 = a

It means whenever we will encounter two same elements the output will be 0 and if an element and zero goes under XOR operation the result will be a.

For example

arr[]= {1, 1, 2}

Let ans be the output variable

ans = 1^0= 1

ans = 1^1 = 0

ans = 0^2 = 2

Operations at bit level are extremely fast. So, this operation is faster than the naive approach.

Approach

  • Run a loop from 0 to n.
  • Declare a variable ans.
  • Under the loop run ans = ans ^ arr[i]
  • Print ans

C++ code

#include <bits/stdc++.h>

using namespace std;




void search_single(int arr[], int n) // function to check the single occuring element

{

     int ans = 0;

    for (int i = 0; i < n; i++) {

        ans = ans ^ arr[i];

    }




    cout << "The single occurring element is " << ans << "\n"; // print ans

}







int main()

{

    int arr[] = { 1, 1, 2, 4, 4, 5, 5, 6, 6 };

    int n = sizeof(arr) / sizeof(arr[0]); // find size of the array




    search_single(arr, n);




    return 0;

}

Output

The single occurring element is 2

C code

#include <stdio.h>

void search_single(int arr[], int n) // function to check the single occuring element

{

    int ans = 0;

    for (int i = 0; i < n; i++) {

        ans = ans ^ arr[i];

    }




printf( "The single occurring element is %d",ans); // print ans




}




int main()

{

    int arr[] = { 1, 1, 2, 4, 4, 5, 5, 6, 6 };

    int n = sizeof(arr) / sizeof(arr[0]); // find size of the array




    search_single(arr, n);




    return 0;

}

Output

The single occurring element is 2

TIme complexity - O(n)

Space complexity - O(1)

Efficient approach

The use of binary search makes the solution more optimised.

Approach

All elements before the required have the first occurrence at even index (0, 2, ..) and the next occurrence at odd index (1, 3, ...). And all elements after the required elements have the first occurrence at an odd index and the next occurrence at an even index.

1) Find the middle index, say 'mid'.

2) If 'mid' is even, then compare arr[mid] and arr[mid + 1]. If both are the same, then put required element after 'mid' else before mid.

3) If 'mid' is odd, then compare arr[mid] and arr[mid - 1]. If both are the same, then put the required element after 'mid' and else before mid.

C++ code

#include <iostream>

using namespace std;

void search(int arr[], int low, int high) // binary serach implementation

{

          // Base cases

          if (low > high)

                   return;


          if (low == high) {

                   cout << "The element occuring once is  " << arr[low]; // if the element is found that is occuring once

                   return;

          }


          int mid = (low + high) / 2; // find the mid range




          // If mid is even and element next to mid is

          // same as mid, then output element lies on

          // right side, else on left side

          if (mid % 2 == 0) {

                   if (arr[mid] == arr[mid + 1])

                             search(arr, mid + 2, high);

                   else

                             search(arr, low, mid);

          }

          // If mid is odd

          else {

                   if (arr[mid] == arr[mid - 1])

                             search(arr, mid + 1, high);

                   else

                             search(arr, low, mid - 1);

          }

}


int main()

{

          int arr[] = { 1, 1, 2, 4, 4, 5, 5, 6, 6 };

          int len = sizeof(arr) / sizeof(arr[0]);




          search(arr, 0, len - 1);

          return 0;

}

Output

The element occurring once is 2

C code

#include <stdio.h>

void search(int arr[], int low, int high) // binary search implementation

{

          // Base cases

          if (low > high)

                   return;

          if (low == high) {

                   printf( "The element occurring once is  %d", arr[low]); // if the element is found that is occurring once

                   return;

          }

          int mid = (low + high) / 2; // find the mid range

          // If mid is even and element next to mid is

          // same as mid, then output element lies on

          // right side, else on left side

          if (mid % 2 == 0) {

                   if (arr[mid] == arr[mid + 1])

                             search(arr, mid + 2, high);

                   else

                             search(arr, low, mid);

          }


          // If mid is odd

          else {

                   if (arr[mid] == arr[mid - 1])

                             search(arr, mid + 1, high);

                   else

                             search(arr, low, mid - 1);

          }

}


int main()

{

          int arr[] = { 1, 1, 2, 4, 4, 5, 5, 6, 6 };

          int len = sizeof(arr) / sizeof(arr[0]);




          search(arr, 0, len - 1);




          return 0;

}

Output

The element occurring once is 2

Time complexity - (log n)



ADVERTISEMENT
ADVERTISEMENT