# Bitwise OR of sum of all subsequences of an array

• Last Updated : 23 Apr, 2021

Given an array arr[] of length N, the task is to find the Bitwise OR of the sum of all possible subsequences from the given array.

Examples:

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Input: arr[] = {4, 2, 5}
Output: 15
Explanation: All subsequences from the given array and their corresponding sums:
{4} – 4
{2} – 2
{5} – 5
{4, 2} – 6
{4, 5} – 9
{2, 5} – 7
{4, 2, 5} -11
Therefore, the Bitwise OR of all sums = 4 | 2 | 5 | 6 | 9 | 7 | 11 = 15.

Input: arr[] = {1, 9, 8}
Output: 27
Explanation: All subsequences from the given array and their corresponding sums:
{1} – 1
{9} – 9
{8} – 8
{1, 9} – 10
{9, 8} – 17
{1, 8} – 9
{1, 9, 8} – 18
Therefore, Bitwise OR of all sums = 1 | 9 | 8 | 10 | 17 | 9 | 18 = 27.

Naive Approach: The simplest approach is to generate all possible subsequences from the given array and find their respective sums. Now, after calculating their sums, print the Bitwise OR of all the sums obtained.

Time Complexity: O(2N)
Auxiliary Space: O(1)

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

• All the set bits in the array elements are also set in the final result.
• All the bits set in the prefix sum array of the given array are also set in the final result.

Follow the steps below to solve the above problem:

• Initialize a variable result with 0 that stores the Bitwise OR of the sum of each subsequence of the given array arr[].
• Initialize a variable prefixSum with 0 that stores the prefix sum of arr[] at any instant.
• Iterate over the array elements in the range [0, N] using variable i.
• Update prefixSumas prefixSum+= arr[i].
• Update result as result | = arr[i] | prefixSum.
• After the above steps, print the value of the result as the answer.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to calculate Bitwise OR of``// sums of all subsequences``int` `findOR(``int` `nums[], ``int` `N)``{``    ``// Stores the prefix sum of nums[]``    ``int` `prefix_sum = 0;` `    ``// Stores the bitwise OR of``    ``// sum of each subsequence``    ``int` `result = 0;` `    ``// Iterate through array nums[]``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``// Bits set in nums[i] are``        ``// also set in result``        ``result |= nums[i];` `        ``// Calculate prefix_sum``        ``prefix_sum += nums[i];` `        ``// Bits set in prefix_sum``        ``// are also set in result``        ``result |= prefix_sum;``    ``}` `    ``// Return the result``    ``return` `result;``}` `// Driver Code``int` `main()``{``    ``// Given array arr[]``    ``int` `arr[] = { 4, 2, 5 };` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``// Function Call``    ``cout << findOR(arr, N);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.util.*;` `class` `GFG{``  ` `// Function to calculate Bitwise OR of``// sums of all subsequences``static` `int` `findOR(``int` `nums[], ``int` `N)``{``    ``// Stores the prefix sum of nums[]``    ``int` `prefix_sum = ``0``;` `    ``// Stores the bitwise OR of``    ``// sum of each subsequence``    ``int` `result = ``0``;` `    ``// Iterate through array nums[]``    ``for` `(``int` `i = ``0``; i < N; i++) {` `        ``// Bits set in nums[i] are``        ``// also set in result``        ``result |= nums[i];` `        ``// Calculate prefix_sum``        ``prefix_sum += nums[i];` `        ``// Bits set in prefix_sum``        ``// are also set in result``        ``result |= prefix_sum;``    ``}` `    ``// Return the result``    ``return` `result;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``// Given array arr[]``    ``int` `arr[] = { ``4``, ``2``, ``5` `};``    ``int` `N = arr.length;``    ``System.out.print(findOR(arr, N));``}``}`

## Python3

 `# Python3 program for the``# above approach` `# Function to calculate``# Bitwise OR of sums of``# all subsequences``def` `findOR(nums,  N):` `    ``# Stores the prefix``    ``# sum of nums[]``    ``prefix_sum ``=` `0` `    ``# Stores the bitwise OR of``    ``# sum of each subsequence``    ``result ``=` `0` `    ``# Iterate through array nums[]``    ``for` `i ``in` `range``(N):` `        ``# Bits set in nums[i] are``        ``# also set in result``        ``result |``=` `nums[i]` `        ``# Calculate prefix_sum``        ``prefix_sum ``+``=` `nums[i]` `        ``# Bits set in prefix_sum``        ``# are also set in result``        ``result |``=` `prefix_sum` `    ``# Return the result``    ``return` `result` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:` `    ``# Given array arr[]``    ``arr ``=` `[``4``, ``2``, ``5``]` `    ``N ``=` `len``(arr)` `    ``# Function Call``    ``print``(findOR(arr, N))` `# This code is contributed by Chitranayal`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{` `// Function to calculate Bitwise OR of``// sums of all subsequences``static` `int` `findOR(``int``[] nums, ``int` `N)``{``    ` `    ``// Stores the prefix sum of nums[]``    ``int` `prefix_sum = 0;` `    ``// Stores the bitwise OR of``    ``// sum of each subsequence``    ``int` `result = 0;` `    ``// Iterate through array nums[]``    ``for``(``int` `i = 0; i < N; i++)``    ``{``        ` `        ``// Bits set in nums[i] are``        ``// also set in result``        ``result |= nums[i];` `        ``// Calculate prefix_sum``        ``prefix_sum += nums[i];` `        ``// Bits set in prefix_sum``        ``// are also set in result``        ``result |= prefix_sum;``    ``}` `    ``// Return the result``    ``return` `result;``}` `// Driver Code``public` `static` `void` `Main()``{``    ` `    ``// Given array arr[]``    ``int``[] arr = { 4, 2, 5 };``    ` `    ``// Size of array``    ``int` `N = arr.Length;``    ` `    ``// Function call``    ``Console.Write(findOR(arr, N));``}``}` `// This code is contributed by code_hunt`

## Javascript

 ``
Output:
`15`

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

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