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# Check whether the sum of prime elements of the array is prime or not

Given an array having N elements. The task is to check if the sum of prime elements of the array is prime or not.

Examples:

```Input: arr[] = {1, 2, 3}
Output: Yes
As there are two primes in the array i.e. 2 and 3.
So, the sum of prime is 2 + 3 = 5 and 5 is also prime.

Input: arr[] = {2, 3, 2, 2}
Output: No```

Approach: First find prime number up to 10^5 using Sieve. Then iterate over all elements of the array. If the number is prime then add it to sum. And finally, check whether the sum is prime or not. If prime then prints Yes otherwise No.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach``#include ``#define ll long long int``#define MAX 100000``using` `namespace` `std;``bool` `prime[MAX];` `// Sieve to find prime``void` `sieve()``{``    ``memset``(prime, ``true``, ``sizeof``(prime));``    ``prime[0] = prime[1] = ``false``;``    ``for` `(``int` `i = 2; i < MAX; i++)``        ``if` `(prime[i])``            ``for` `(``int` `j = 2 * i; j < MAX; j += i)``                ``prime[j] = ``false``;``        ` `    ` `}` `// Function to check if the sum of``// prime is prime or not``bool` `checkArray(``int` `arr[], ``int` `n)``{``    ``// find sum of all prime number``    ``ll sum = 0;``    ``for` `(``int` `i = 0; i < n; i++)``        ``if` `(prime[arr[i]])``            ``sum += arr[i];` `    ``// if sum is prime``    ``// then return yes``    ``if` `(prime[sum])``        ``return` `true``;` `    ``return` `false``;``}` `// Driver code``int` `main()``{``    ``// array of elements``    ``int` `arr[] = { 1, 2, 3 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``sieve();` `    ``if` `(checkArray(arr, n))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;` `    ``return` `0;``}`

## Java

 `// Java implementation of the above approach``import` `java.io.*;` `class` `GFG {``    ` `static` `int` `MAX =``100000``;` `static` `boolean` `prime[] = ``new` `boolean``[MAX];` `// Sieve to find prime``static` `void` `sieve()``{``    ``for``(``int` `i=``0``;i

## Python3

 `# Python3 implementation of above approach``from` `math ``import` `gcd, sqrt` `MAX` `=` `100000` `prime ``=` `[``True``] ``*` `MAX` `# Sieve to find prime``def` `sieve() :``    ` `    ``# 0 and 1 are not prime numbers``    ``prime[``0``] ``=` `False``    ``prime[``1``] ``=` `False``    ` `    ``for` `i ``in` `range``(``2``, ``MAX``) :` `        ``if` `prime[i] :``            ``for` `j ``in` `range``(``2``*``*``i, ``MAX``, i) :``                ``prime[j] ``=` `False``    ` `# Function to check if the sum of``# prime is prime or not``def` `checkArray(arr, n) :` `    ``# find sum of all prime number``    ``sum` `=` `0``    ``for` `i ``in` `range``(n) :` `        ``if` `prime[arr[i]] :``            ``sum` `+``=` `arr[i]` `    ``# if sum is prime``    ``# then return yes``    ``if` `prime[``sum``] :``        ``return` `True` `    ``return` `False` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``# list of elements``    ``arr ``=` `[``1``, ``2``, ``3``]``    ``n ``=` `len``(arr)` `    ``sieve()` `    ``if` `checkArray(arr, n) :``        ``print``(``"Yes"``)``    ``else` `:``        ``print``(``"No"``)``        ` `# This code is contributed by ANKITRAI1`

## C#

 `// C# implementation of the above approach``using` `System;` `class` `GFG``{``static` `int` `MAX = 100000;` `static` `bool``[] prime = ``new` `bool``[MAX];` `// Sieve to find prime``static` `void` `sieve()``{``    ``for``(``int` `i = 0; i < MAX; i++)``    ``{``        ``prime[i] = ``true``;``    ``}``    ``prime[0] = prime[1] = ``false``;``    ``for` `(``int` `i = 2; i < MAX; i++)``        ``if` `(prime[i])``            ``for` `(``int` `j = 2 * i;``                     ``j < MAX; j += i)``                ``prime[j] = ``false``;``}` `// Function to check if the sum of``// prime is prime or not``static` `bool` `checkArray(``int``[] arr, ``int` `n)``{``    ``// find sum of all prime number``    ``int` `sum = 0;``    ``for` `(``int` `i = 0; i < n; i++)``        ``if` `(prime[arr[i]])``            ``sum += arr[i];` `    ``// if sum is prime``    ``// then return yes``    ``if` `(prime[sum])``        ``return` `true``;` `    ``return` `false``;``}` `// Driver code``public` `static` `void` `Main ()``{``    ``// array of elements``    ``int``[] arr = ``new` `int``[] { 1, 2, 3 };``    ``int` `n = arr.Length;``    ` `    ``sieve();``    ` `    ``if` `(checkArray(arr, n))``        ``Console.WriteLine(``"Yes"``);``    ``else``        ``Console.WriteLine(``"No"``);``}``}` `// This code is contributed by mits`

## PHP

 ``

## Javascript

 ``

Output

`Yes`

Complexity Analysis:

• Time Complexity: O(n * log(log n))
• Auxiliary Space: O(MAX)

Approach 2:Without Sieve Array(No Extra Space)

The previous code used a sieve to pre-compute all primes up to a certain limit, and then used this pre-computed information to check if the sum of primes in the array is also prime. This approach requires extra memory to store the sieve array and runs in O(MAX*log(log(MAX))) time complexity, where MAX is the limit up to which primes are computed.

The new code optimizes the previous approach by checking if each number in the array is prime as we go through it. Instead of pre-computing all primes up to a certain limit, we only need to check if each number is divisible by any prime less than or equal to its square root. This approach does not require extra memory to store the sieve array.

## C++

 `#include ``#define ll long long int``using` `namespace` `std;` `// Function to check if a number is prime``bool` `isPrime(``int` `n)``{``    ``if` `(n <= 1)``        ``return` `false``;` `    ``for` `(``int` `i = 2; i*i <= n; i++)``        ``if` `(n % i == 0)``            ``return` `false``;` `    ``return` `true``;``}` `// Function to check if the sum of``// prime is prime or not``bool` `checkArray(``int` `arr[], ``int` `n)``{``    ``// find sum of all prime number``    ``ll sum = 0;``    ``for` `(``int` `i = 0; i < n; i++)``        ``if` `(isPrime(arr[i]))``            ``sum += arr[i];` `    ``// if sum is prime``    ``// then return yes``    ``if` `(isPrime(sum))``        ``return` `true``;` `    ``return` `false``;``}` `// Driver code``int` `main()``{``    ``// array of elements``    ``int` `arr[] = { 2,3,2,2 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``if` `(checkArray(arr, n))``        ``cout << ``"Yes"``;``    ``else``        ``cout << ``"No"``;` `    ``return` `0;``}`

## Java

 `/*package whatever //do not write package name here */` `import` `java.lang.Math;` `public` `class` `Main {``    ``// Function to check if a number is prime``    ``static` `boolean` `isPrime(``int` `n) {``        ``if` `(n <= ``1``) {``            ``return` `false``;``        ``}` `        ``for` `(``int` `i = ``2``; i <= Math.sqrt(n); i++) {``            ``if` `(n % i == ``0``) {``                ``return` `false``;``            ``}``        ``}` `        ``return` `true``;``    ``}` `    ``// Function to check if the sum of prime is prime or not``    ``static` `boolean` `checkArray(``int``[] arr, ``int` `n) {``        ``// find sum of all prime number``        ``int` `sum = ``0``;``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``if` `(isPrime(arr[i])) {``                ``sum += arr[i];``            ``}``        ``}` `        ``// if sum is prime then return true``        ``if` `(isPrime(sum)) {``            ``return` `true``;``        ``}` `        ``return` `false``;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args) {``        ``int``[] arr = {``1``, ``2``, ``3``};``        ``int` `n = arr.length;` `        ``if` `(checkArray(arr, n)) {``            ``System.out.println(``"Yes"``);``        ``} ``else` `{``            ``System.out.println(``"No"``);``        ``}``    ``}``}`

## Python3

 `# Function to check if a number is prime``def` `isPrime(n):``    ``if` `n <``=` `1``:``        ``return` `False` `    ``for` `i ``in` `range``(``2``, ``int``(n``*``*``0.5``) ``+` `1``):``        ``if` `n ``%` `i ``=``=` `0``:``            ``return` `False` `    ``return` `True` `# Function to check if the sum of``# prime is prime or not``def` `checkArray(arr, n):``    ``# find sum of all prime number``    ``sum` `=` `0``    ``for` `i ``in` `range``(n):``        ``if` `isPrime(arr[i]):``            ``sum` `+``=` `arr[i]` `    ``# if sum is prime``    ``# then return yes``    ``if` `isPrime(``sum``):``        ``return` `True` `    ``return` `False` `# Driver code``arr ``=` `[``1``, ``2``, ``3``]``n ``=` `len``(arr)` `if` `checkArray(arr, n):``    ``print``(``"Yes"``)``else``:``    ``print``(``"No"``)`

## C#

 `using` `System;` `public` `class` `MainClass {``    ``// Function to check if a number is prime``    ``static` `bool` `IsPrime(``int` `n) {``        ``if` `(n <= 1) {``            ``return` `false``;``        ``}` `        ``for` `(``int` `i = 2; i <= Math.Sqrt(n); i++) {``            ``if` `(n % i == 0) {``                ``return` `false``;``            ``}``        ``}` `        ``return` `true``;``    ``}` `    ``// Function to check if the sum of prime is prime or not``    ``static` `bool` `CheckArray(``int``[] arr, ``int` `n) {``        ``// find sum of all prime number``        ``int` `sum = 0;``        ``for` `(``int` `i = 0; i < n; i++) {``            ``if` `(IsPrime(arr[i])) {``                ``sum += arr[i];``            ``}``        ``}` `        ``// if sum is prime then return true``        ``if` `(IsPrime(sum)) {``            ``return` `true``;``        ``}` `        ``return` `false``;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main() {``        ``int``[] arr = {1, 2, 3};``        ``int` `n = arr.Length;` `        ``if` `(CheckArray(arr, n)) {``            ``Console.WriteLine(``"Yes"``);``        ``} ``else` `{``            ``Console.WriteLine(``"No"``);``        ``}``    ``}``}`

## Javascript

 `// Function to check if a number is prime``function` `isPrime(n) {``    ``if` `(n <= 1) {``        ``return` `false``;``    ``}` `    ``for` `(let i = 2; i <= Math.sqrt(n); i++) {``        ``if` `(n % i === 0) {``            ``return` `false``;``        ``}``    ``}` `    ``return` `true``;``}` `// Function to check if the sum of``// prime is prime or not``function` `checkArray(arr, n) {``    ``// find sum of all prime number``    ``let sum = 0;``    ``for` `(let i = 0; i < n; i++) {``        ``if` `(isPrime(arr[i])) {``            ``sum += arr[i];``        ``}``    ``}` `    ``// if sum is prime``    ``// then return yes``    ``if` `(isPrime(sum)) {``        ``return` `true``;``    ``}` `    ``return` `false``;``}` `// Driver code``const arr = [1, 2, 3];``const n = arr.length;` `if` `(checkArray(arr, n)) {``    ``console.log(``"Yes"``);``} ``else` `{``    ``console.log(``"No"``);``}` `// Contributed by adityasha4x71`

Output

`Yes`

Complexity Analysis:

Time Complexity: O(n * sqrt(max(arr))).
Auxiliary Space: O(1)

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