# XOR of K largest prime and composite numbers from the given array

• Last Updated : 14 Apr, 2021

Given an array arr[] of N non-zero positive integers and an integer K, the task is to find the XOR of the K largest prime and composite numbers.
Examples:

Input: arr[] = {4, 2, 12, 13, 5, 19}, K = 3
Output:
Prime XOR = 27
Composite XOR = 8
5, 13 and 19 are the three maximum primes
from the given array and 5 ^ 13 ^ 19 = 27.
There are only 2 composites in the array i.e. 4 and 12.
And 4 ^ 12 = 8
Input: arr[] = {1, 2, 3, 4, 5, 6, 7}, K = 1
Output:
Prime XOR = 7
Composite XOR = 6

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

Approach: Using Sieve of Eratosthenes generate a boolean vector upto the size of the maximum element from the array which can be used to check whether a number is prime or not.
Now traverse the array and insert all the numbers which are prime in a max heap maxHeapPrime and all the composite numbers in max heap maxHeapNonPrime
Now, pop out the top K elements from both the max heaps and take the xor of these elements.
Below is the implementation of the above approach:

## C++

 // C++ implementation of the approach#include using namespace std; // Function for Sieve of Eratosthenesvector SieveOfEratosthenes(int max_val){    // Create a boolean vector "prime[0..n]". A    // value in prime[i] will finally be false    // if i is Not a prime, else true.    vector prime(max_val + 1, true);     // Set 0 and 1 as non-primes as    // they don't need to be    // counted as prime numbers    prime[0] = false;    prime[1] = false;     for (int p = 2; p * p <= max_val; p++) {         // If prime[p] is not changed, then        // it is a prime        if (prime[p] == true) {             // Update all multiples of p            for (int i = p * 2; i <= max_val; i += p)                prime[i] = false;        }    }    return prime;} // Function that calculates the xor// of k smallest and k// largest prime numbers in an arrayvoid kMaxXOR(int arr[], int n, int k){    // Find maximum value in the array    int max_val = *max_element(arr, arr + n);     // Use sieve to find all prime numbers    // less than or equal to max_val    vector prime = SieveOfEratosthenes(max_val);     // Min Heaps to store the max K prime    // and composite numbers    priority_queue, greater >        minHeapPrime, minHeapNonPrime;     for (int i = 0; i < n; i++) {         // If current element is prime        if (prime[arr[i]]) {             // Min heap will only store k elements            if (minHeapPrime.size() < k)                minHeapPrime.push(arr[i]);             // If the size of min heap is K and the            // top element is smaller than the current            // element than it needs to be replaced            // by the current element as only            // max k elements are required            else if (minHeapPrime.top() < arr[i]) {                minHeapPrime.pop();                minHeapPrime.push(arr[i]);            }        }         // If current element is composite        else if (arr[i] != 1) {             // Heap will only store k elements            if (minHeapNonPrime.size() < k)                minHeapNonPrime.push(arr[i]);             // If the size of min heap is K and the            // top element is smaller than the current            // element than it needs to be replaced            // by the current element as only            // max k elements are required            else if (minHeapNonPrime.top() < arr[i]) {                minHeapNonPrime.pop();                minHeapNonPrime.push(arr[i]);            }        }    }     long long int primeXOR = 0, nonPrimeXor = 0;    while (k--) {         // Calculate the xor        if (minHeapPrime.size() > 0) {            primeXOR ^= minHeapPrime.top();            minHeapPrime.pop();        }         if (minHeapNonPrime.size() > 0) {            nonPrimeXor ^= minHeapNonPrime.top();            minHeapNonPrime.pop();        }    }     cout << "Prime XOR = " << primeXOR << "\n";    cout << "Composite XOR = " << nonPrimeXor << "\n";} // Driver codeint main(){     int arr[] = { 4, 2, 12, 13, 5, 19 };    int n = sizeof(arr) / sizeof(arr[0]);    int k = 3;     kMaxXOR(arr, n, k);     return 0;}

## Java

 // Java implementation of the approachimport java.util.*; class GFG{     // Function for Sieve of Eratosthenes    static boolean[] SieveOfEratosThenes(int max_val)    {         // Create a boolean vector "prime[0..n]". A        // value in prime[i] will finally be false        // if i is Not a prime, else true.        boolean[] prime = new boolean[max_val + 1];        Arrays.fill(prime, true);         // Set 0 and 1 as non-primes as        // they don't need to be        // counted as prime numbers        prime[0] = false;        prime[1] = false;         for (int p = 2; p * p <= max_val; p++)        {             // If prime[p] is not changed, then            // it is a prime            if (prime[p])            {                 // Update all multiples of p                for (int i = p * 2; i <= max_val; i += p)                    prime[i] = false;            }        }        return prime;    }     // Function that calculates the xor    // of k smallest and k    // largest prime numbers in an array    static void kMinXOR(Integer[] arr, int n, int k)    {         // Find maximum value in the array        int max_val = Collections.max(Arrays.asList(arr));         // Use sieve to find all prime numbers        // less than or equal to max_val        boolean[] prime = SieveOfEratosThenes(max_val);         // Min Heaps to store the max K prime        // and composite numbers        PriorityQueue minHeapPrime = new PriorityQueue<>();        PriorityQueue minHeapNonPrime = new PriorityQueue<>();         for (int i = 0; i < n; i++)        {             // If current element is prime            if (prime[arr[i]])            {                 // Min heap will only store k elements                if (minHeapPrime.size() < k)                    minHeapPrime.add(arr[i]);                 // If the size of min heap is K and the                // top element is smaller than the current                // element than it needs to be replaced                // by the current element as only                // max k elements are required                else if (minHeapPrime.peek() < arr[i])                {                    minHeapPrime.poll();                    minHeapPrime.add(arr[i]);                }            }             // If current element is composite            else if (arr[i] != -1)            {                 // Heap will only store k elements                if (minHeapNonPrime.size() < k)                    minHeapNonPrime.add(arr[i]);                 // If the size of min heap is K and the                // top element is smaller than the current                // element than it needs to be replaced                // by the current element as only                // max k elements are required                else if (minHeapNonPrime.peek() < arr[i])                {                    minHeapNonPrime.poll();                    minHeapNonPrime.add(arr[i]);                }            }        }         long primeXOR = 0, nonPrimeXor = 0;         while (k-- > 0)        {             // Calculate the xor            if (minHeapPrime.size() > 0)            {                primeXOR ^= minHeapPrime.peek();                minHeapPrime.poll();            }             if (minHeapNonPrime.size() > 0)            {                nonPrimeXor ^= minHeapNonPrime.peek();                minHeapNonPrime.poll();            }        }         System.out.println("Prime XOR = " + primeXOR);        System.out.println("Composite XOR = " + nonPrimeXor);    }     // Driver Code    public static void main(String[] args)    {        Integer[] arr = { 4, 2, 12, 13, 5, 19 };        int n = arr.length;        int k = 3;         kMinXOR(arr, n, k);    }} // This code is contributed by// sanjeev2552

## Python3

 # Python implimentation of above approach import heapq  # Function for Sieve of Eratosthenesdef SieveOfEratosthenes(max_val: int) -> list:     # Create a boolean vector "prime[0..n]". A    # value in prime[i] will finally be false    # if i is Not a prime, else true.    prime = [True] * (max_val + 1)     # Set 0 and 1 as non-primes as    # they don't need to be    # counted as prime numbers    prime[0] = False    prime[1] = False     p = 2    while p * p <= max_val:         # If prime[p] is not changed, then        # it is a prime        if prime[p]:             # Update all multiples of p            for i in range(p * 2, max_val + 1, p):                prime[i] = False        p += 1    return prime  # Function that calculates the xor# of k smallest and k# largest prime numbers in an arraydef kMaxXOR(arr: list, n: int, k: int):     # Find maximum value in the array    max_val = max(arr)     # Use sieve to find all prime numbers    # less than or equal to max_val    prime = SieveOfEratosthenes(max_val)     # Min Heaps to store the max K prime    # and composite numbers    minHeapPrime, minHeapNonPrime = [], []    heapq.heapify(minHeapPrime)    heapq.heapify(minHeapNonPrime)     for i in range(n):         # If current element is prime        if prime[arr[i]]:             # Min heap will only store k elements            if len(minHeapPrime) < k:                heapq.heappush(minHeapPrime, arr[i])             # If the size of min heap is K and the            # top element is smaller than the current            # element than it needs to be replaced            # by the current element as only            # max k elements are required            elif heapq.nsmallest(1, minHeapPrime)[0] < arr[i]:                heapq.heappop(minHeapPrime)                heapq.heappush(minHeapPrime, arr[i])         # If current element is composite        elif arr[i] != 1:             # Heap will only store k elements            if len(minHeapNonPrime) < k:                heapq.heappush(minHeapNonPrime, arr[i])             # If the size of min heap is K and the            # top element is smaller than the current            # element than it needs to be replaced            # by the current element as only            # max k elements are required            elif heapq.nsmallest(1, minHeapNonPrime)[0] < arr[i]:                heapq.heappop(minHeapNonPrime)                heapq.heappush(minHeapNonPrime, arr[i])     primeXOR = 0    nonPrimeXor = 0     while k > 0:         # Calculate the xor        if len(minHeapPrime) > 0:            primeXOR ^= heapq.nsmallest(1, minHeapPrime)[0]            heapq.heappop(minHeapPrime)         if len(minHeapNonPrime) > 0:            nonPrimeXor ^= heapq.nsmallest(1, minHeapNonPrime)[0]            heapq.heappop(minHeapNonPrime)        k -= 1     print("Prime XOR =", primeXOR)    print("Composite XOR =", nonPrimeXor)  # Driver Codeif __name__ == "__main__":     arr = [4, 2, 12, 13, 5, 19]    n = len(arr)    k = 3    kMaxXOR(arr, n, k) # This code is contributed by# sanjeev2552

## C#

 // C# implementation of the approach using System;using System.Collections.Generic;class GFG {   // Function for Sieve of Eratosthenes  static bool[] SieveOfEratosThenes(int max_val)  {     // Create a boolean vector "prime[0..n]". A    // value in prime[i] will finally be false    // if i is Not a prime, else true.    bool[] prime = new bool[max_val + 1];    for(int i = 0; i < max_val + 1; i++)    {      prime[i] = true;    }     // Set 0 and 1 as non-primes as    // they don't need to be    // counted as prime numbers    prime[0] = false;    prime[1] = false;     for (int p = 2; p * p <= max_val; p++)    {       // If prime[p] is not changed, then      // it is a prime      if (prime[p])       {         // Update all multiples of p        for (int i = p * 2; i <= max_val; i += p)          prime[i] = false;      }    }    return prime;  }   // Function that calculates the xor  // of k smallest and k  // largest prime numbers in an array  static void kMinXOR(int[] arr, int n, int k)   {     // Find maximum value in the array    int max_val = Int32.MinValue;    for(int i = 0; i < arr.Length; i++)    {      max_val = Math.Max(max_val,arr[i]);    }     // Use sieve to find all prime numbers    // less than or equal to max_val    bool[] prime = SieveOfEratosThenes(max_val);     // Min Heaps to store the max K prime    // and composite numbers    List minHeapPrime = new List();    List minHeapNonPrime = new List();     for (int i = 0; i < n; i++)    {       // If current element is prime      if (prime[arr[i]])       {         // Min heap will only store k elements        if (minHeapPrime.Count < k)        {          minHeapPrime.Add(arr[i]);        }         // If the size of min heap is K and the        // top element is smaller than the current        // element than it needs to be replaced        // by the current element as only        // max k elements are required        else if (minHeapPrime[0] < arr[i])        {          minHeapPrime.RemoveAt(0);          minHeapPrime.Add(arr[i]);        }        minHeapPrime.Sort();      }       // If current element is composite      else if (arr[i] != -1)      {         // Heap will only store k elements        if (minHeapNonPrime.Count < k)          minHeapNonPrime.Add(arr[i]);         // If the size of min heap is K and the        // top element is smaller than the current        // element than it needs to be replaced        // by the current element as only        // max k elements are required        else if (minHeapNonPrime[0] < arr[i])         {          minHeapNonPrime.RemoveAt(0);          minHeapNonPrime.Add(arr[i]);        }        minHeapNonPrime.Sort();      }    }     long primeXOR = 0, nonPrimeXor = 0;     while (k-- > 0)     {       // Calculate the xor      if (minHeapPrime.Count > 0)      {        primeXOR ^= minHeapPrime[0];        minHeapPrime.RemoveAt(0);      }       if (minHeapNonPrime.Count > 0)       {        nonPrimeXor ^= minHeapNonPrime[0];        minHeapNonPrime.RemoveAt(0);      }    }     Console.WriteLine("Prime XOR = " + primeXOR);    Console.WriteLine("Composite XOR = " + nonPrimeXor);  }   // Driver code  static void Main()  {    int[] arr = { 4, 2, 12, 13, 5, 19 };    int n = arr.Length;    int k = 3;     kMinXOR(arr, n, k);  }} // This code is contributed by divyesh072019.

## Javascript


Output:
Prime XOR = 27
Composite XOR = 8

My Personal Notes arrow_drop_up