Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Sum of XOR of all possible subsets in C++
In this problem, we are given an array aar[] of n numbers. Our task is to create a program to find the Sum of XOR of all possible subsets.
Here, we will find all subsets of the array. Then for each subset, we will find the XOR of elements of the subset and add them to the sum variable.
Let’s take an example to understand the problem,
Input: arr[] = {5, 1, 4}
Output: 20
Explanation: XOR of all subsets:
{5} = 5
{1} = 1
{4} = 4
{5, 1} = 4
{5, 4} = 1
{1, 4} = 5
{5, 1, 4} = 0
Sum of XOR = 5 + 1 + 4 + 4 + 1 + 5 = 20A simple solution to the problem, is using loop and find all possible subsets of the array and then for each subset find XOR of all the elements and update the sum. Return sum at the end.
This is not an effective approach, for the large value, the time complexity will grow exponentially.
An efficient approach is using the properties of XOR. Here, we will find the OR of all elements of the array and check the bits. If the ith is set, then update sum with (2^(n-1+i)).
Example
Program to illustrate the working of our solution,
#include <iostream>
#include <math.h>
using namespace std;
int subSetXORSum(int arr[], int n) {
int bitOR = 0;
for (int i=0; i < n; ++i)
bitOR |= arr[i];
return (bitOR * pow(2, n-1));
}
int main() {
int arr[] = {1, 5, 4};
int size = sizeof(arr) / sizeof(arr[0]);
cout<<"Sum of XOR of all possible subsets is "<<subSetXORSum(arr, size);
}Output
Sum of XOR of all possible subsets is 20
312 Views
