Count and Sum of composite elements in an array

Given an array ‘arr’ of positive integers, the task is to count the number of composite numbers in the array. 

Note: 1 is neither Prime nor Composite.

Examples:

Input: arr[] = {1, 3, 4, 5, 7} 
Output: 1 
4 is the only composite number.

Input: arr[] = {1, 2, 3, 4, 5, 6, 7} 
Output: 2 

Naive Approach: A simple solution is to traverse the array and do a primality test on every element.

Efficient 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. Also add 0 and 1 as a prime so that they don’t get counted as composite numbers. Now traverse the array and find the count of those elements which are composite using the generated boolean vector.

Below is the implementation of the above approach: 

C++

// C++ program to count the
// number of composite numbers
// in the given array
#include <bits/stdc++.h>
using namespace std;

// Function that returns the
// the count of composite numbers
int compositeCount(int arr[], int n, int* sum)
{
    // 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
    // Create a boolean array "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);

    // Set 0 and 1 as primes as
    // they don't need to be
    // counted as composite numbers
    prime[0] = true;
    prime[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;
        }
    }

    // Count all composite
    // numbers in the arr[]
    int count = 0;
    for (int i = 0; i < n; i++)
        if (!prime[arr[i]]) {
            count++;
            *sum = *sum + arr[i];
        }

    return count;
}

// Driver code
int main()
{

    int arr[] = { 1, 2, 3, 4, 5, 6, 7 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int sum = 0;

    cout << "Count of Composite Numbers = "
          << compositeCount(arr, n, &sum);

    cout << "\nSum of Composite Numbers = " << sum;

    return 0;
}

Java

import java.util.*;

// Java program to count the
// number of composite numbers
// in the given array

class GFG
{

    static int sum = 0;

    // Function that returns the
    // the count of composite numbers
    static int compositeCount(int arr[], int n)
    {
        // Find maximum value in the array
        int max_val = Arrays.stream(arr).max().getAsInt();

        // Use sieve to find all prime numbers
        // less than or equal to max_val
        // Create a boolean array "prime[0..n]". A
        // value in prime[i] will finally be false
        // if i is Not a prime, else true.
        Vector<Boolean> prime = new Vector<Boolean>(max_val + 1);
        for (int i = 0; i < max_val + 1; i++)
        {
            prime.add(i, Boolean.TRUE);
        }
        // Set 0 and 1 as primes as
        // they don't need to be
        // counted as composite numbers
        prime.add(0, Boolean.TRUE);
        prime.add(1, Boolean.TRUE);
        for (int p = 2; p * p <= max_val; p++)
        {

            // If prime[p] is not changed, then
            // it is a prime
            if (prime.get(p) == true)
            {

                // Update all multiples of p
                for (int i = p * 2; i <= max_val; i += p)
                {
                    prime.add(i, Boolean.FALSE);
                }
            }
        }

        // Count all composite
        // numbers in the arr[]
        int count = 0;
        for (int i = 0; i < n; i++)
        {
            if (!prime.get(arr[i]))
            {
                count++;
                sum = sum + arr[i];
            }
        }
        return count;
    }

    // Driver code
    public static void main(String[] args)
    {
        int arr[] = {1, 2, 3, 4, 5, 6, 7};
        int n = arr.length;

        System.out.print("Count of Composite Numbers = "
                + compositeCount(arr, n));

        System.out.print("\nSum of Composite Numbers = " + sum);
    }
}

// This code has been contributed by 29AjayKumar

Python3

# Python3 program to count the
# number of composite numbers
# in the given array

# Function that returns the
# the count of composite numbers
def compositeCount(arr, n):
    Sum = 0

    # Find maximum value in the array
    max_val = max(arr)

    # Use sieve to find all prime numbers
    # less than or equal to max_val
    # Create a boolean array "prime[0..n]".
    # A value in prime[i] will finally be
    # false if i is Not a prime, else True.
    prime = [True for i in range(max_val + 1)]

    # Set 0 and 1 as primes as
    # they don't need to be
    # counted as composite numbers
    prime[0] = True
    prime[1] = True
    for p in range(2, max_val + 1):

        if p * p > max_val:
            break

        # If prime[p] is not changed,
        # then it is a prime
        if (prime[p] == True):

            # Update all multiples of p
            for i in range(p * 2, max_val + 1, p):
                prime[i] = False

    # Count all composite numbers
    # in the arr[]
    count = 0
    for i in range(n):
        if (prime[arr[i]] == False):
            count += 1
            Sum = Sum + arr[i]

    return count, Sum

# Driver code
arr = [1, 2, 3, 4, 5, 6, 7 ]
n = len(arr)
count, Sum = compositeCount(arr, n)

print("Count of Composite Numbers = ", count)

print("Sum of Composite Numbers = ", Sum)

// This code is contributed by Mohit Kumar

C#

// C# program to count the
// number of composite numbers
// in the given array
using System;
using System.Linq;
using System.Collections;

class GFG
{

static int sum1=0;

// Function that returns the
// the count of composite numbers
static int compositeCount(int []arr, int n, int sum)
{
    // Find maximum value in the array
    int max_val = arr.Max();

    // Use sieve to find all prime numbers
    // less than or equal to max_val
    // Create a boolean array "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];

    // Set 0 and 1 as primes as
    // they don't need to be
    // counted as composite 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] == false)
        {

            // Update all multiples of p
            for (int i = p * 2; i <= max_val; i += p)
                prime[i] = true;
        }
    }

    // Count all composite
    // numbers in the arr[]
    int count = 0;
    for (int i = 0; i < n; i++)
        if (prime[arr[i]])
        {
            count++;
            sum = sum + arr[i];
        }
    sum1 = sum;
    return count;
}

// Driver code
static void Main()
{

    int []arr = { 1, 2, 3, 4, 5, 6, 7 };
    int n = arr.Length;
    int sum = 0;

    Console.Write("Count of Composite Numbers = "+
                    compositeCount(arr, n, sum));

    Console.Write("\nSum of Composite Numbers = "+sum1);
}
}

// This code is contributed by mits

PHP

<?php
// PHP program to count the
// number of composite numbers
// in the given array


// Function that returns the
// the count of composite numbers
function compositeCount($arr, $n, &$sum)
{
    // Find maximum value in the array
    $max_val = max($arr);

    // Use sieve to find all prime numbers
    // less than or equal to max_val
    // Create a boolean array "prime[0..n]". A
    // value in prime[i] will finally be false
    // if i is Not a prime, else true.
    $prime=array_fill(0,$max_val + 1, true);

    // Set 0 and 1 as primes as
    // they don't need to be
    // counted as composite numbers
    $prime[0] = true;
    $prime[1] = true;
    for ($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 ($i = $p * 2; $i <= $max_val; $i += $p)
                $prime[$i] = false;
        }
    }

    // Count all composite
    // numbers in the arr[]
    $count = 0;
    for ($i = 0; $i < $n; $i++)
        if (!$prime[$arr[$i]])
        {
            $count++;
            $sum = $sum + $arr[$i];
        }

    return $count;
}

// Driver code

$arr = array( 1, 2, 3, 4, 5, 6, 7 );
$n = count($arr);
$sum = 0;

echo "Count of Composite Numbers = ".compositeCount($arr, $n, $sum);

echo "\nSum of Composite Numbers = ".$sum;

// This code is contributed by mits
?>

Javascript

<script>
// Javascript program to count the
// number of composite numbers
// in the given array


// Function that returns the
// the count of composite numbers

let sum = 0;
function compositeCount(arr, n)
{

    // Find maximum value in the array
    let max_val = arr.sort((a, b) => b - a)[0];

    // Use sieve to find all prime numbers
    // less than or equal to max_val
    // Create a boolean array "prime[0..n]". A
    // value in prime[i] will finally be false
    // if i is Not a prime, else true.
    let prime = new Array(max_val + 1).fill(true);

    // Set 0 and 1 as primes as
    // they don't need to be
    // counted as composite numbers
    prime[0] = true;
    prime[1] = true;
    for (let 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 (let i = p * 2; i <= max_val; i += p)
                prime[i] = false;
        }
    }

    // Count all composite
    // numbers in the arr[]
    let count = 0;
    for (let i = 0; i < n; i++)
        if (!prime[arr[i]]) {
            count++;
            sum = sum + arr[i];
        }

    return count;
}

// Driver code

let arr = new Array(1, 2, 3, 4, 5, 6, 7);
let n = arr.length;

document.write("Count of Composite Numbers = " + compositeCount(arr, n, sum));

document.write("<br>Sum of Composite Numbers = " + sum);

// This code is contributed by gfgking
</script>

Output

Count of Composite Numbers = 2
Sum of Composite Numbers = 10

Complexity Analysis:

• Time complexity : O(n log(log n))
• Space complexity: O(n) since auxiliary space is being used