# Product of all the Composite Numbers in an array

Given an array of integers. The task is to calculate the product of all the composite numbers in an array.
Note: 1 is neither prime nor composite.

Examples:

```Input: arr[] = {2, 3, 4, 5, 6, 7}
Output: 24
Composite numbers are 4 and 6.
So, product = 24

Input: arr[] = {11, 13, 17, 20, 19}
Output: 20
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive Approach: A simple solution is to traverse the array and do a primality test on every element. If the element is not prime nor 1, multiply it to the running product.
Time Complexity – O(Nsqrt(N))

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 product of those elements which are composite using the generated boolean vector.

## C++

 `// C++ program to find the product ` `// of all the composite numbers ` `// in an array ` `#include ` `using` `namespace` `std; ` ` `  `// Function that returns the ` `// the product of all composite numbers ` `int` `compositeProduct(``int` `arr[], ``int` `n) ` `{ ` `    ``// 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 = ``true``; ` `    ``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] == ``true``) { ` ` `  `            ``// Update all multiples of p ` `            ``for` `(``int` `i = p * 2; i <= max_val; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` ` `  `    ``// Find the product of all ` `    ``// composite numbers in the arr[] ` `    ``int` `product = 1; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``if` `(!prime[arr[i]]) { ` `            ``product *= arr[i]; ` `        ``} ` ` `  `    ``return` `product; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `arr[] = { 2, 3, 4, 5, 6, 7 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` ` `  `    ``cout << compositeProduct(arr, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find the product ` `// of all the composite numbers ` `// in an array ` `import` `java.util.*; ` ` `  `class` `GFG { ` ` `  `    ``// Function that returns the ` `    ``// the product of all composite numbers ` `    ``static` `int` `compositeProduct(``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. ` `        ``boolean``[] prime = ``new` `boolean``[max_val + ``1``]; ` `        ``Arrays.fill(prime, ``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``; ` `                ``} ` `            ``} ` `        ``} ` ` `  `        ``// Find the product of all ` `        ``// composite numbers in the arr[] ` `        ``int` `product = ``1``; ` `        ``for` `(``int` `i = ``0``; i < n; i++) { ` `            ``if` `(!prime[arr[i]]) { ` `                ``product *= arr[i]; ` `            ``} ` `        ``} ` ` `  `        ``return` `product; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[] = { ``2``, ``3``, ``4``, ``5``, ``6``, ``7` `}; ` `        ``int` `n = arr.length; ` ` `  `        ``System.out.println(compositeProduct(arr, n)); ` `    ``} ` `} ` ` `  `// This code has been contributed by 29AjayKumar `

## Python3

 `''' ` `Python3 program to find product of ` `all the composite numberes in given array'''` `import` `math as mt ` `''' ` `function to find the product of all composite ` `niumbers in the given array ` `'''` `def` `compositeProduct(arr, n): ` `     `  `      `  `    ``# find the 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``, mt.ceil(mt.sqrt(max_val))): ` `        ``# Remaining part of SIEVE ` `        ``''' ` `        ``if prime[p] is not changed, than it is prime ` `        ``'''` `        ``if` `prime[p]: ` `            ``# update all multiples of p ` `            ``for` `i ``in` `range``(p ``*` `2``, max_val ``+` `1``, p): ` `                ``prime[i]``=` `False` `     `  `    ``# find the product of all composite numbers in the arr[] ` `    ``product ``=` `1` `     `  `    ``for` `i ``in` `range``(n): ` `        ``if` `prime[arr[i]]``=``=` `False``: ` `            ``product``*``=` `arr[i] ` `     `  `    ``return` `product ` ` `  `# Driver code ` ` `  `arr ``=``[``2``, ``3``, ``4``, ``5``, ``6``, ``7``] ` ` `  `n ``=` `len``(arr) ` ` `  `print``(compositeProduct(arr, n)) ` ` `  `# contributed by Mohit kumar 29 ` `        `

## C#

 `// C# program to find the product ` `// of all the composite numbers ` `// in an array ` `using` `System; ` `using` `System.Linq; ` `public` `class` `GFG { ` ` `  `    ``// Function that returns the ` `    ``// the product of all composite numbers ` `    ``static` `int` `compositeProduct(``int``[] arr, ``int` `n) ` `    ``{ ` `        ``// 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]; ` `        ``for` `(``int` `i = 0; i < max_val + 1; i++) ` `            ``prime[i] = ``true``; ` ` `  `        ``// Set 0 and 1 as primes as ` `        ``// they don't need to be ` `        ``// counted as composite numbers ` `        ``prime = ``true``; ` `        ``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] == ``true``) { ` ` `  `                ``// Update all multiples of p ` `                ``for` `(``int` `i = p * 2; i <= max_val; i += p) { ` `                    ``prime[i] = ``false``; ` `                ``} ` `            ``} ` `        ``} ` ` `  `        ``// Find the product of all ` `        ``// composite numbers in the arr[] ` `        ``int` `product = 1; ` `        ``for` `(``int` `i = 0; i < n; i++) { ` `            ``if` `(!prime[arr[i]]) { ` `                ``product *= arr[i]; ` `            ``} ` `        ``} ` ` `  `        ``return` `product; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int``[] arr = { 2, 3, 4, 5, 6, 7 }; ` `        ``int` `n = arr.Length; ` ` `  `        ``Console.WriteLine(compositeProduct(arr, n)); ` `    ``} ` `} ` `/* This code contributed by PrinciRaj1992 */`

## PHP

 ` `

Output:

```24
```

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