Maximum subset with bitwise OR equal to k
Last Updated :
06 Apr, 2023
Given an array of non-negative integers and an integer k, find the subset of maximum length with bitwise OR equal to k.
Examples:
Input : arr[] = [1, 4, 2]
k = 3
Output : [1, 2]
Explanation: The bitwise OR of
1 and 2 equals 3. It is not possible to obtain
a subset of length greater than 2.
Input : arr[] = [1, 2, 5]
k = 4
Output : []
No subset's bitwise OR equals 4.
Method 1(Simple):
The naive method would be to consider all the subsets. While considering a subset, compute its bitwise OR. If it equals k, compare the subset’s length with the maximum length so far and update the maximum length if required.
Method 2(Efficient):
0 OR 0 = 0
1 OR 0 = 1
1 OR 1 = 1
Hence, 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. The 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 the 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 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 k, then this is the final answer. Else no subset exists which satisfies the condition.
Steps to solve this problem:
1. declare a vector v of integers.
2. iterate through i=0 till n:
*check if arr[i] bitwise or k is equal to k than push arr[i] in v.
3. declare a variable ans=0.
4. iterate through i=0 till size of v:
*update ans to ans bitwise or v[i].
5. check if ans is not equal to k than subset doesn’t exist.
6. iterate through i=0 till size of v:
*print v[i].
C++
#include <bits/stdc++.h>
using namespace std;
void subsetBitwiseORk( 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 ;
}
for ( int i = 0; i < v.size(); i++)
cout << v[i] << ' ' ;
}
int main()
{
int k = 3;
int arr[] = { 1, 4, 2 };
int n = sizeof (arr) / sizeof (arr[0]);
subsetBitwiseORk(arr, n, k);
return 0;
}
|
Java
import java.util.*;
class GFG {
static void subsetBitwiseORk( int arr[],
int n, int k)
{
ArrayList<Integer> v =
new ArrayList<Integer>();
for ( int i = 0 ; i < n; i++) {
if ((arr[i] | k) == k){
v.add(arr[i]);
}
}
int ans = 0 ;
for ( int i = 0 ; i < v.size(); i++)
ans = ans|v.get(i);
if (ans != k) {
System.out.println( "Subset does"
+ " not exist" );
return ;
}
for ( int i = 0 ; i < v.size(); i++)
System.out.print(v.get(i) + " " );
}
public static void main(String[] args)
{
int k = 3 ;
int arr[] = { 1 , 4 , 2 };
int n = arr.length;
subsetBitwiseORk(arr, n, k);
}
}
|
Python3
def subsetBitwiseORk(arr, n, k) :
v = []
for i in range ( 0 , n) :
if ((arr[i] | k) = = k) :
v.append(arr[i])
ans = 0
for i in range ( 0 , len (v)) :
ans | = v[i]
if (ans ! = k) :
print ( "Subset does not exist\n" )
return
for i in range ( 0 , len (v)) :
print ( "{} " . format (v[i]), end = "")
k = 3
arr = [ 1 , 4 , 2 ]
n = len (arr)
subsetBitwiseORk(arr, n, k)
|
C#
using System;
using System.Collections;
class GFG {
static void subsetBitwiseORk( int []arr,
int n, int k)
{
ArrayList v = new ArrayList();
for ( int i = 0; i < n; i++) {
if ((arr[i] | k) == k){
v.Add(arr[i]);
}
}
int ans = 0;
for ( int i = 0; i < v.Count; i++)
ans = ans|( int )v[i];
if (ans != k) {
Console.WriteLine( "Subset does"
+ " not exist" );
return ;
}
for ( int i = 0; i < v.Count; i++)
Console.Write(( int )v[i] + " " );
}
static public void Main(String []args)
{
int k = 3;
int []arr = { 1, 4, 2 };
int n = arr.Length;
subsetBitwiseORk(arr, n, k);
}
}
|
PHP
<?php
function subsetBitwiseORk( $arr , $n , $k )
{
$v = array ();
for ( $i = 0; $i < $n ; $i ++)
{
if (( $arr [ $i ] | $k ) == $k )
array_push ( $v , $arr [ $i ]);
}
$ans = 0;
for ( $i = 0; $i < count ( $v ); $i ++)
$ans |= $v [ $i ];
if ( $ans != $k )
{
echo ( "Subset does not exist\n" );
return ;
}
for ( $i = 0; $i < count ( $v ); $i ++)
echo ( $v [ $i ]. " " );
}
$k = 3;
$arr = array (1, 4, 2);
$n = count ( $arr );
subsetBitwiseORk( $arr , $n , $k );
?>
|
Javascript
<script>
function subsetBitwiseORk(arr, n, k)
{
var v = [];
for ( var i = 0; i < n; i++) {
if ((arr[i] | k) == k)
v.push(arr[i]);
}
var ans = 0;
for ( var i = 0; i < v.length; i++)
ans |= v[i];
if (ans != k) {
document.write( "Subset does not exist" );
return ;
}
for ( var i = 0; i < v.length; i++)
document.write( v[i] + ' ');
}
var k = 3;
var arr = [1, 4, 2];
var n = arr.length;
subsetBitwiseORk(arr, n, k);
</script>
|
Output :
1 2
Time complexity: O(N), where N is the size of the array.
Auxiliary Space : O(N)
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