Related Articles

# Bitwise OR of all unordered pairs from a given array

• Difficulty Level : Easy
• Last Updated : 23 Apr, 2021

Given an array arr[] of size N, the task is to find the Bitwise XOR of all possible unordered pairs from the given array.

Examples:

Input: arr[] = {1, 5, 3, 7}
Output:
Explanation:
All possible unordered pairs are (1, 5), (1, 3), (1, 7), (5, 3), (5, 7), (3, 7)
Bitwise OR of all possible pairs are = { ( 1 | 5 ) | ( 1 | 3 ) | ( 1 | 7 ) | ( 5 | 3 ) | ( 5 | 7 ) | ( 3 | 7 ) }
Therefore, the required output is 7.

Input: arr[] = {4, 5, 12, 15}
Output: 15

Approach: The simplest approach to solve this problem is to traverse the array and generate all possible pairs of the given array. Finally, print the Bitwise OR of each element of all possible pairs of the given array. Follow the steps below to solve the problem:

• Initialize a variable, say totalOR, to store Bit-wise OR of each element of all possible pairs.
• Traverse the given array and generate all possible pairs(arr[i], arr[j]) from the given array and for each pair (arr[i], arr[j]), update the value of totalOR = (totalOR | arr[i] | arr[j]).
• Finally, print the value of totalOR.

Below is the implementation of the above approach:

## C++

 `// C++ program to implement``// the above approach` `#include ``using` `namespace` `std;` `// Function to find the Bitwise OR of``// all possible pairs from the array``int` `TotalBitwiseORPair(``int` `arr[], ``int` `N)``{` `    ``// Stores bitwise OR of all``    ``// possible pairs from arr[]``    ``int` `totalOR = 0;` `    ``// Traverse the array and calculate``    ``// bitwise OR of all possible pairs``    ``for` `(``int` `i = 0; i < N; i++) {``        ``for` `(``int` `j = i + 1; j < N;``             ``j++) {` `            ``// Update totalOR``            ``totalOR |= (arr[i] | arr[j]);``        ``}``    ``}` `    ``// Return Bitwise OR of all``    ``// possible pairs from arr[]``    ``return` `totalOR;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 4, 5, 12, 15 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);``    ``cout << TotalBitwiseORPair(arr, N);``}`

## Java

 `// Java program to implement``// the above approach``import` `java.util.*;``class` `GFG{``  ` `// Function to find the Bitwise OR of``// all possible pairs from the array``static` `int` `TotalBitwiseORPair(``int` `arr[],``                              ``int` `N)``{``  ``// Stores bitwise OR of all``  ``// possible pairs from arr[]``  ``int` `totalOR = ``0``;` `  ``// Traverse the array and``  ``// calculate bitwise OR of``  ``// all possible pairs``  ``for` `(``int` `i = ``0``; i < N; i++)``  ``{``    ``for` `(``int` `j = i + ``1``; j < N;``         ``j++)``    ``{``      ``// Update totalOR``      ``totalOR |= (arr[i] |``                  ``arr[j]);``    ``}``  ``}` `  ``// Return Bitwise OR of all``  ``// possible pairs from arr[]``  ``return` `totalOR;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``  ``int` `arr[] = {``4``, ``5``, ``12``, ``15``};``  ``int` `N = arr.length;``  ``System.out.print(TotalBitwiseORPair(arr, N));``}``}` `// This code is contributed by sanjoy_62`

## Python3

 `# Python3 program to implement``# the above approach` `# Function to find the Bitwise``# OR of all possible pairs``# from the array``def` `TotalBitwiseORPair(arr, N):` `    ``# Stores bitwise OR of all``    ``# possible pairs from arr[]``    ``totalOR ``=` `0` `    ``# Traverse the array and``    ``# calculate bitwise OR of``    ``# all possible pairs``    ``for` `i ``in` `range``(N):``        ``for` `j ``in` `range``(i ``+` `1``, N):` `            ``# Update totalOR``            ``totalOR |``=` `(arr[i] | arr[j])` `    ``# Return Bitwise OR of all``    ``# possible pairs from arr[]``    ``return` `totalOR` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``  ` `    ``arr ``=` `[``4``, ``5``, ``12``, ``15``]``    ``N ``=` `len``(arr)``    ``print``(TotalBitwiseORPair(arr, N))` `# This code is contributed by Mohit Kumar 29`

## C#

 `// C# program to implement``// the above approach ``using` `System;``  ` `class` `GFG{``  ` `// Function to find the Bitwise OR of``// all possible pairs from the array``static` `int` `TotalBitwiseORPair(``int``[] arr,``                              ``int` `N)``{``    ` `  ``// Stores bitwise OR of all``  ``// possible pairs from arr[]``  ``int` `totalOR = 0;`` ` `  ``// Traverse the array and``  ``// calculate bitwise OR of``  ``// all possible pairs``  ``for``(``int` `i = 0; i < N; i++)``  ``{``    ``for``(``int` `j = i + 1; j < N; j++)``    ``{``        ` `      ``// Update totalOR``      ``totalOR |= (arr[i] | arr[j]);``    ``}``  ``}`` ` `  ``// Return Bitwise OR of all``  ``// possible pairs from arr[]``  ``return` `totalOR;``}`` ` `// Driver Code``public` `static` `void` `Main()``{``    ``int``[] arr = { 4, 5, 12, 15 };``    ``int` `N = arr.Length;``    ` `    ``Console.WriteLine(TotalBitwiseORPair(arr, N));``}``}` `// This code is contributed by susmitakundugoaldanga`

## Javascript

 ``
Output:
`15`

Time Complexity: O(N2)
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach the idea is based on the following observations:

1 | 1 | 1 | …..(n times) = 1
0 | 0 | 0 | …..(n times) = 0
Therefore, (a | a | a | …. (n times)) = a

Follow the steps below to solve the problem:

• Initialize a variable, say totalOR to store the bitwise OR of all possible unordered pairs of the array.
• Traverse the array and update the value of totalOR = (totalOR | arr[i]).
• Finally, print the value of totalOR.

Below is the implementation of the above approach

## C++

 `// C++ program to implement``// the above approach` `#include ``using` `namespace` `std;` `// Function to find the bitwise OR of``// all possible pairs of the array``int` `TotalBitwiseORPair(``int` `arr[], ``int` `N)``{` `    ``// Stores bitwise OR of all``    ``// possible pairs of arr[]``    ``int` `totalOR = 0;` `    ``// Traverse the array arr[]``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``// Update totalOR``        ``totalOR |= arr[i];``    ``}` `    ``// Return bitwise OR of all``    ``// possible pairs of arr[]``    ``return` `totalOR;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 4, 5, 12, 15 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);``    ``cout << TotalBitwiseORPair(arr, N);``}`

## Java

 `// Java program to implement``// the above approach``import` `java.util.*;` `class` `GFG{` `// Function to find the bitwise OR of``// all possible pairs of the array``static` `int` `TotalBitwiseORPair(``int` `arr[],``                              ``int` `N)``{``    ` `    ``// Stores bitwise OR of all``    ``// possible pairs of arr[]``    ``int` `totalOR = ``0``;` `    ``// Traverse the array arr[]``    ``for``(``int` `i = ``0``; i < N; i++)``    ``{``        ` `        ``// Update totalOR``        ``totalOR |= arr[i];``    ``}` `    ``// Return bitwise OR of all``    ``// possible pairs of arr[]``    ``return` `totalOR;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``4``, ``5``, ``12``, ``15` `};``    ``int` `N = arr.length;``    ` `    ``System.out.print(TotalBitwiseORPair(arr, N));``}``}` `// This code is contributed by gauravrajput1`

## Python3

 `# Python program to implement``# the above approach` `# Function to find the bitwise OR of``# all possible pairs of the array``def` `TotalBitwiseORPair(arr, N):``  ` `    ``# Stores bitwise OR of all``    ``# possible pairs of arr``    ``totalOR ``=` `0``;` `    ``# Traverse the array arr``    ``for` `i ``in` `range``(N):``      ` `        ``# Update totalOR``        ``totalOR |``=` `arr[i];` `    ``# Return bitwise OR of all``    ``# possible pairs of arr``    ``return` `totalOR;` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``arr ``=` `[``4``, ``5``, ``12``, ``15``];``    ``N ``=` `len``(arr);` `    ``print``(TotalBitwiseORPair(arr, N));` `    ``# This code is contributed by shikhasingrajput`

## C#

 `// C# program to implement``// the above approach``using` `System;` `class` `GFG{` `// Function to find the bitwise OR of``// all possible pairs of the array``static` `int` `TotalBitwiseORPair(``int` `[]arr,``                              ``int` `N)``{``    ` `    ``// Stores bitwise OR of all``    ``// possible pairs of []arr``    ``int` `totalOR = 0;` `    ``// Traverse the array []arr``    ``for``(``int` `i = 0; i < N; i++)``    ``{``        ` `        ``// Update totalOR``        ``totalOR |= arr[i];``    ``}` `    ``// Return bitwise OR of all``    ``// possible pairs of []arr``    ``return` `totalOR;``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 4, 5, 12, 15 };``    ``int` `N = arr.Length;``    ` `    ``Console.Write(TotalBitwiseORPair(arr, N));``}``}` `// This code is contributed by Princi Singh`

## Javascript

 ``
Output:
`15`

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

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.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up