Count subsequences with same values of Bitwise AND, OR and XOR
Last Updated :
28 Nov, 2022
We are given an array arr of n element. We need to count number of non-empty subsequences such that these individual subsequences have same values of bitwise AND, OR and XOR. For example, we need to count a subsequence (x, y, z) if (x | y | z) is equal to (x & y & z) and (x ^ y ^ z). For a single element subsequence, we consider the element itself as result of XOR, AND and OR. Therefore all single-element subsequences are always counted as part of result.
Examples:
Input : a = [1, 3, 7]
Output : 3
Explanation:
There are 7 non empty subsequence .
subsequence OR AND XOR
{1} 1 1 1
{3} 3 3 3
{7} 7 7 7
{1, 3} 3 1 2
{1, 7} 7 1 6
{3, 7} 7 3 4
{1, 3, 7} 7 1 5
Out of 7, there are 3 subsequences {1}
{3} {7} which have same values of AND,
OR and XOR.
Input : a[] = [0, 0, 0]
Output : 7
Explanation: All 7 non empty subsequences
have same values of AND, OR and XOR.
Input : a[] = [2, 2, 2, 3, 4]
Output : 6
Explanation: subsequence {2}, {2}, {2},
{2, 2, 2}, {3}, {4} have same values of
AND, OR and XOR.
1) If there are n occurrences of zeroes in the given array, then will be 2n - 1 subsequences contributed by these zeroes.
2) If there are n occurrences of a non-zero element x, then there will be 2n-1 subsequences contributed by occurrences of this element. Please note that, in case of non-zero elements, only odd number of occurrences can cause same results for bitwise operators.
Find count of each element in the array then apply the above formulas.
C++
#include <bits/stdc++.h>
using namespace std;
// function for finding count of possible subsequence
int countSubseq(int arr[], int n)
{
int count = 0;
// creating a map to count the frequency of each element
unordered_map<int, int> mp;
// store frequency of each element
for (int i = 0; i < n; i++)
mp[arr[i]]++;
// iterate through the map
for (auto i : mp) {
// add all possible combination for key equal zero
if (i.first == 0)
count += pow(2, i.second) - 1;
// add all (odd number of elements) possible
// combination for key other than zero
else
count += pow(2, i.second - 1);
}
return count;
}
// driver function
int main()
{
int arr[] = { 2, 2, 2, 5, 6 };
int n = sizeof(arr) / sizeof(arr[0]);
cout << countSubseq(arr, n);
return 0;
}
import java .io.*;
import java.util.*;
class GFG {
// function for finding count of possible subsequence
static int countSubseq(int arr[], int n)
{
int count = 0;
// creating a map to count the frequency of each element
HashMap<Integer,Integer>mp=new HashMap<Integer,Integer>();
// store frequency of each element
for (int i = 0; i < n; i++)
if (mp.containsKey(arr[i]))
mp.put(arr[i],mp.get(arr[i])+1);
else
mp.put(arr[i],1);
// iterate through the map
for (Map.Entry<Integer,Integer>entry:mp.entrySet()) {
// add all possible combination for key equal zero
if (entry.getKey() == 0)
count += Math.pow(2, entry.getValue()) - 1;
// add all (odd number of elements) possible
// combination for key other than zero
else
count += Math.pow(2, entry.getValue()- 1);
}
return count;
}
// driver function
public static void main(String[] args)
{
int arr[] = { 2, 2, 2, 5, 6 };
int n=arr.length;
System.out.println(countSubseq(arr, n));
}
}
// This code is contributed by apurva raj
using System;
using System.Collections.Generic;
class GFG{
// function for finding count of possible subsequence
static int countSubseq(int []arr, int n)
{
int count = 0;
// creating a map to count the frequency of each element
Dictionary<int, int> mp = new Dictionary<int,int>();
// store frequency of each element
for (int i = 0; i < n; i++)
{
if (mp.ContainsKey(arr[i]))
{
var val = mp[arr[i]];
mp.Remove(arr[i]);
mp.Add(arr[i], val + 1);
}
else
{
mp.Add(arr[i], 1);
}
}
// iterate through the map
foreach(KeyValuePair<int, int> entry in mp) {
// add all possible combination for key equal zero
if (entry.Key == 0)
count += (int)(Math.Pow(2, entry.Value - 1));
// add all (odd number of elements) possible
// combination for key other than zero
else
count += (int)(Math.Pow(2, entry.Value - 1));
}
return count;
}
// Driver function
public static void Main(String []args)
{
int []arr = { 2, 2, 2, 5, 6 };
int n = arr.Length;
Console.WriteLine(countSubseq(arr, n));
}
}
// This code is contributed by shivanisinghss2110
# function for finding count of possible subsequence
def countSubseq(arr, n):
count = 0
# creating a map to count the frequency of each element
mp = {}
# store frequency of each element
for x in arr:
if x in mp.keys():
mp[x]+=1
else:
mp[x]=1
# iterate through the map
for i in mp.keys():
# add all possible combination for key equal zero
if (i == 0):
count += pow(2, mp[i]) - 1
# add all (odd number of elements) possible
# combination for key other than zero
else:
count += pow(2, mp[i] - 1)
return count
# Driver function
arr= [2, 2, 2, 5, 6 ]
n = len(arr)
print(countSubseq(arr, n))
# This code is contributed by apurva raj
<script>
// function for finding count of possible subsequence
function countSubseq(arr, n)
{
let count = 0;
// creating a map to count the frequency of each element
let mp = new Map();
// store frequency of each element
for (let i = 0; i < n; i++){
mp[arr[i]]++;
if(mp.has(arr[i])){
mp.set(arr[i], mp.get(arr[i]) + 1)
}else{
mp.set(arr[i], 1)
}
}
// iterate through the map
for (let i of mp) {
// add all possible combination for key equal zero
if (i[0] == 0)
count += Math.pow(2, i[1]) - 1;
// add all (odd number of elements) possible
// combination for key other than zero
else
count += Math.pow(2, i[1] - 1);
}
return count;
}
// driver function
let arr = [ 2, 2, 2, 5, 6 ];
let n = arr.length;
document.write(countSubseq(arr, n));
// This code is contributed by _saurabh_jaiswal
</script>
Time complexity: O(N)
Auxiliary Space: O(N)
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