Sum and product of k smallest and k largest composite numbers in the array

Given an integer k and an array of integers arr, the task is to find the sum and product of k smallest and k largest composite numbers in the array.
Assume that there are at least k composite numbers in the array.

Examples:

Input: arr[] = {2, 5, 6, 8, 10, 11}, k = 2
Output: Sum of k-minimum composite numbers is 14
Sum of k-maximum composite numbers is 18
Product of k-minimum composite numbers is 48
Product of k-maximum composite numbers is 80
{6, 8, 10} are the only comsposite numbers from the array. {6, 8} are the 2 smallest and {8, 10} are the 2 largest among them.

Input: arr[] = {6, 4, 2, 12, 13, 5, 19, 10}, k = 3
Output: Sum of k-minimum composite numbers is 20
Sum of k-maximum composite numbers is 28
Product of k-minimum composite numbers is 240
Product of k-maximum composite numbers is 720

Approach:

1. 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 composite or not.
2. Also set 0 and 1 as prime so that they don’t get counted as composite numbers.
3. Now traverse the array and insert all the numbers which are composite in two heaps, a min heap and a max heap.
4. Now, pop out top k elements from the min heap and take the sum and product of the minimum k composite numbers.
5. Do the same with the max heap to get the sum and product of the max k composite numbers.
6. Finally, print the results.

Below is the implementation of the above approach:

C++

// C++ program to find the sum and
// product of k smallest and k largest
// composite numbers in an array
#include <bits/stdc++.h>
using namespace std;

vector<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.
    vector<bool> prime(max_val + 1, true);
    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 sum
// and product of k smallest and k
// largest composite numbers in an array
void compositeSumAndProduct(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<bool> prime = SieveOfEratosthenes(max_val);

    // Set 0 and 1 as primes so that
    // they don't get counted as
    // composite numbers
    prime[0] = true;
    prime[1] = true;

    // Max Heap to store all the composite numbers
    priority_queue<int> maxHeap;

    // Min Heap to store all the composite numbers
    priority_queue<int, vector<int>, greater<int>>
        minHeap;

    // Push all the composite numbers
    // from the array to the heaps
    for (int i = 0; i < n; i++)
        if (!prime[arr[i]]) {
            minHeap.push(arr[i]);
            maxHeap.push(arr[i]);
        }
    long long int minProduct = 1
        , maxProduct = 1
        , minSum = 0
        , maxSum = 0;
    while (k--) {

        // Calculate the products
        minProduct *= minHeap.top();
        maxProduct *= maxHeap.top();

        // Calculate the sum
        minSum += minHeap.top();
        maxSum += maxHeap.top();

        // Pop the current minimum element
        minHeap.pop();

        // Pop the current maximum element
        maxHeap.pop();
    }

    cout << "Sum of k-minimum composite numbers is "
         << minSum << "\n";
    cout << "Sum of k-maximum composite numbers is "
         << maxSum << "\n";
    cout << "Product of k-minimum composite numbers is "
         << minProduct << "\n";
    cout << "Product of k-maximum composite numbers is "
         << maxProduct;
}

// Driver code
int main()
{

    int arr[] = { 4, 2, 12, 13, 5, 19 };
    int n = sizeof(arr) / sizeof(arr[0]);

    int k = 3;

    compositeSumAndProduct(arr, n, k);

    return 0;
}

Java

// Java program to find the sum and
// product of k smallest and k largest
// composite numbers in an array
import java.util.*;

class GFG
{
    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);

        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 sum
    // and product of k smallest and k
    // largest composite numbers in an array
    static void compositeSumAndProduct(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);

        // Set 0 and 1 as primes so that
        // they don't get counted as
        // composite numbers
        prime[0] = true;
        prime[1] = true;

        // Max Heap to store all the composite numbers
        PriorityQueue<Integer> maxHeap =
                  new PriorityQueue<Integer>((x, y) -> y - x);

        // Min Heap to store all the composite numbers
        PriorityQueue<Integer> minHeap = new PriorityQueue<>();

        // Push all the composite numbers
        // from the array to the heaps
        for (int i = 0; i < n; i++)
        {
            if (!prime[arr[i]])
            {
                minHeap.add(arr[i]);
                maxHeap.add(arr[i]);
            }
        }

        long minProduct = 1, maxProduct = 1,
                 minSum = 0, maxSum = 0;
        Integer lastMin = 0, lastMax = 0;
        while (k-- > 0)
        {
            if (minHeap.peek() != null ||
                maxHeap.peek() != null)
            {

                // Calculate the products
                minProduct *= minHeap.peek();
                maxProduct *= maxHeap.peek();

                // Calculate the sum
                minSum += minHeap.peek();
                maxSum += maxHeap.peek();

                // Pop the current minimum element
                lastMin = minHeap.poll();

                // Pop the current maximum element
                lastMax = maxHeap.poll();
            }
            else
            {

                // when maxHeap or minHeap is exhausted
                // then this consition will run
                minProduct *= lastMin;
                maxProduct *= lastMax;

                minSum += lastMin;
                maxSum += lastMax;
            }
        }

        System.out.println("Sum of k-minimum composite" +
                                " numbers is " + minSum);
        System.out.println("Sum of k-maximum composite" +
                                " numbers is " + maxSum);
        System.out.println("Product of k-minimum composite" +
                                " numbers is " + minProduct);
        System.out.println("Product of k-maximum composite" +
                                " numbers is " + maxProduct);
    }

    // Driver Code
    public static void main(String[] args)
    {
        Integer[] arr = { 4, 2, 12, 13, 5, 19 };
        int n = arr.length;
        int k = 3;

        compositeSumAndProduct(arr, n, k);
    }
}

// This code is contributed by
// sanjeev2552

Output:

Sum of k-minimum composite numbers is 28
Sum of k-maximum composite numbers is 20
Product of k-minimum composite numbers is 576
Product of k-maximum composite numbers is 192

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