- Related Questions & Answers
- Largest set with bitwise OR equal to n in C++
- Find N distinct numbers whose bitwise Or is equal to K in C++
- Find N distinct numbers whose bitwise Or is equal to K in Python
- Find subsequences with maximum Bitwise AND and Bitwise OR in Python
- Triples with Bitwise AND Equal To Zero in C++
- Maximum elements that can be made equal with k updates in C++
- Print triplets with sum less than or equal to k in C Program
- Partition Equal Subset Sum in C++
- Maximum size subset with given sum in C++
- Subset with maximum sum in JavaScript
- Maximum of four numbers without using conditional or bitwise operator in C++
- Maximum steps to transform 0 to X with bitwise AND in C++
- Maximum Equal Frequency in C++
- Largest number smaller than or equal to N divisible by K in C++
- Maximum length subarray with LCM equal to product in C++

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

Given an array of non-negative integers and an integer k, find the subset of maximum length with bitwise OR equal to k.

If given input array is = [1, 4, 2] and k = 3 then output is: [1, 2] The bitwise OR of 1 and 2 equals 3. It is not possible to obtain a subset of length greater than 2.

Below are the properties of bitwise OR −

0 OR 0 = 0 1 OR 0 = 1 1 OR 1 = 1

for all the positions in the binary representation of k with the bit equal to 0, the corresponding position in the binary representations of all the elements in the resulting subset should necessarily be 0

On the other hand, for positions in k with the bit equal to 1, there has to be at least one element with a 1 in the corresponding position. Rest of the elements can have either 0 or 1 in that position, it does not matter.

Therefore, to obtain the resulting subset, traverse the initial array. While deciding if the element should be in the resulting subset or not, check whether there is any position in the binary representation of k which is 0 and the corresponding position in that element is 1. If there exists such a position, then ignore that element, else include it in the resulting subset.

How to determine if there exists a position in the binary representation of k which is 0 and the corresponding position in an element is 1? Simply take bitwise OR of k and that element. If it does not equal to k, then there exists such a position and the element has to be ignored. If their bitwise OR equals to k, then include the current element in the resulting subset.

The final step is to determine if there is at least one element with a 1 in a position with 1 in the corresponding position in k.

Simply compute the bitwise OR of the resulting subset. If it equals to k, then this is the final answer. Else no subset exists which satisfies the condition

#include <bits/stdc++.h> using namespace std; void getSubSet(int *arr, int n, int k){ vector<int> v; for (int i = 0; i < n; i++) { if ((arr[i] | k) == k) v.push_back(arr[i]); } int ans = 0; for (int i = 0; i < v.size(); i++) { ans |= v[i]; } if (ans != k) { cout << "Subset does not exist" << endl; return; } cout << "Result = "; for (int i = 0; i < v.size(); i++) { cout << v[i] << " "; } cout << endl; } int main(){ int arr[] = { 1, 4, 2 }; int k = 3; int n = sizeof(arr) / sizeof(arr[0]); getSubSet(arr, n, k); return 0; }

When you compile and execute above program. It generates following output −

Result = 1 2

Advertisements