# Length of Longest Prime Subsequence in an Array

Given an array arr containing non-negative integers, the task is to print the length of the longest subsequence of prime numbers in the array.

Examples:

Input: arr[] = { 3, 4, 11, 2, 9, 21 }
Output: 3
Longest Prime Subsequence is {3, 2, 11} and hence the answer is 3.

Input: arr[] = { 6, 4, 10, 13, 9, 25 }
Output: 1

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

Approach:

• Traverse the given array.
• For each element in the array, check if it prime or not.
• If the element is prime, it will be in Longest Prime Subsequence. Hence increment the required length of Longest Prime Subsequence by 1

Below is the implementation of the above approach:

## C++

 `// C++ program to find the length of ` `// Longest Prime Subsequence in an Array ` ` `  `#include ` `using` `namespace` `std; ` `#define N 100005 ` ` `  `// Function to create Sieve ` `// to check primes ` `void` `SieveOfEratosthenes( ` `    ``bool` `prime[], ``int` `p_size) ` `{ ` ` `  `    ``// False here indicates ` `    ``// that it is not prime ` `    ``prime[0] = ``false``; ` `    ``prime[1] = ``false``; ` ` `  `    ``for` `(``int` `p = 2; p * p <= p_size; p++) { ` ` `  `        ``// If prime[p] is not changed, ` `        ``// then it is a prime ` `        ``if` `(prime[p]) { ` ` `  `            ``// Update all multiples of p, ` `            ``// set them to non-prime ` `            ``for` `(``int` `i = p * 2; ` `                 ``i <= p_size; ` `                 ``i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` `} ` ` `  `// Function to find the longest subsequence ` `// which contain all prime numbers ` `int` `longestPrimeSubsequence(``int` `arr[], ``int` `n) ` `{ ` `    ``bool` `prime[N + 1]; ` `    ``memset``(prime, ``true``, ``sizeof``(prime)); ` ` `  `    ``// Precompute N primes ` `    ``SieveOfEratosthenes(prime, N); ` ` `  `    ``int` `answer = 0; ` ` `  `    ``// Find the length of ` `    ``// longest prime subsequence ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``if` `(prime[arr[i]]) { ` `            ``answer++; ` `        ``} ` `    ``} ` ` `  `    ``return` `answer; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 3, 4, 11, 2, 9, 21 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` ` `  `    ``// Function call ` `    ``cout << longestPrimeSubsequence(arr, n) ` `         ``<< endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find the length of ` `// Longest Prime Subsequence in an Array ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` `static` `final` `int` `N = ``100005``; ` `  `  `// Function to create Sieve ` `// to check primes ` `static` `void` `SieveOfEratosthenes( ` `    ``boolean` `prime[], ``int` `p_size) ` `{ ` `  `  `    ``// False here indicates ` `    ``// that it is not prime ` `    ``prime[``0``] = ``false``; ` `    ``prime[``1``] = ``false``; ` `  `  `    ``for` `(``int` `p = ``2``; p * p <= p_size; p++) { ` `  `  `        ``// If prime[p] is not changed, ` `        ``// then it is a prime ` `        ``if` `(prime[p]) { ` `  `  `            ``// Update all multiples of p, ` `            ``// set them to non-prime ` `            ``for` `(``int` `i = p * ``2``; ` `                 ``i <= p_size; ` `                 ``i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` `} ` `  `  `// Function to find the longest subsequence ` `// which contain all prime numbers ` `static` `int` `longestPrimeSubsequence(``int` `arr[], ``int` `n) ` `{ ` `    ``boolean` `[]prime = ``new` `boolean``[N + ``1``]; ` `    ``Arrays.fill(prime, ``true``); ` `  `  `    ``// Precompute N primes ` `    ``SieveOfEratosthenes(prime, N); ` `  `  `    ``int` `answer = ``0``; ` `  `  `    ``// Find the length of ` `    ``// longest prime subsequence ` `    ``for` `(``int` `i = ``0``; i < n; i++) { ` `        ``if` `(prime[arr[i]]) { ` `            ``answer++; ` `        ``} ` `    ``} ` `  `  `    ``return` `answer; ` `} ` `  `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `arr[] = { ``3``, ``4``, ``11``, ``2``, ``9``, ``21` `}; ` `    ``int` `n = arr.length; ` `  `  `    ``// Function call ` `    ``System.out.print(longestPrimeSubsequence(arr, n) ` `         ``+``"\n"``);  ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## Python3

 `# Python 3 program to find the length of ` `# Longest Prime Subsequence in an Array  ` `N ``=` `100005` `  `  `# Function to create Sieve ` `# to check primes ` `def` `SieveOfEratosthenes(prime,  p_size): ` `  `  `    ``# False here indicates ` `    ``# that it is not prime ` `    ``prime[``0``] ``=` `False` `    ``prime[``1``] ``=` `False` `  `  `    ``p ``=` `2` `    ``while`  `p ``*` `p <``=` `p_size: ` `  `  `        ``# If prime[p] is not changed, ` `        ``# then it is a prime ` `        ``if` `(prime[p]): ` `  `  `            ``# Update all multiples of p, ` `            ``# set them to non-prime ` `            ``for` `i ``in` `range``( p ``*` `2``, p_size ``+` `1``, p): ` `                ``prime[i] ``=` `False`  ` `  `        ``p ``+``=` `1` `       `  `# Function to find the longest subsequence ` `# which contain all prime numbers ` `def` `longestPrimeSubsequence( arr, n): ` `    ``prime ``=` `[``True``]``*``(N ``+` `1``) ` `  `  `    ``# Precompute N primes ` `    ``SieveOfEratosthenes(prime, N) ` `  `  `    ``answer ``=` `0` `  `  `    ``# Find the length of ` `    ``# longest prime subsequence ` `    ``for` `i ``in` `range` `(n): ` `        ``if` `(prime[arr[i]]): ` `            ``answer ``+``=` `1` `  `  `    ``return` `answer ` `  `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``arr ``=` `[ ``3``, ``4``, ``11``, ``2``, ``9``, ``21` `] ` `    ``n ``=` `len``(arr) ` `  `  `    ``# Function call ` `    ``print` `(longestPrimeSubsequence(arr, n)) ` ` `  `# This code is contributed by chitranayal `

## C#

 `// C# program to find the length of ` `// longest Prime Subsequence in an Array ` `using` `System; ` ` `  `class` `GFG ` `{ ` `static` `readonly` `int` `N = 100005; ` `   `  `// Function to create Sieve ` `// to check primes ` `static` `void` `SieveOfEratosthenes( ` `    ``bool` `[]prime, ``int` `p_size) ` `{ ` `   `  `    ``// False here indicates ` `    ``// that it is not prime ` `    ``prime[0] = ``false``; ` `    ``prime[1] = ``false``; ` `   `  `    ``for` `(``int` `p = 2; p * p <= p_size; p++) { ` `   `  `        ``// If prime[p] is not changed, ` `        ``// then it is a prime ` `        ``if` `(prime[p]) { ` `   `  `            ``// Update all multiples of p, ` `            ``// set them to non-prime ` `            ``for` `(``int` `i = p * 2; ` `                 ``i <= p_size; ` `                 ``i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` `} ` `   `  `// Function to find the longest subsequence ` `// which contain all prime numbers ` `static` `int` `longestPrimeSubsequence(``int` `[]arr, ``int` `n) ` `{ ` `    ``bool` `[]prime = ``new` `bool``[N + 1]; ` `    ``for` `(``int` `i = 0; i < N+1; i++) ` `        ``prime[i] = ``true``; ` `   `  `    ``// Precompute N primes ` `    ``SieveOfEratosthenes(prime, N); ` `   `  `    ``int` `answer = 0; ` `   `  `    ``// Find the length of ` `    ``// longest prime subsequence ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``if` `(prime[arr[i]]) { ` `            ``answer++; ` `        ``} ` `    ``} ` `   `  `    ``return` `answer; ` `} ` `   `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `[]arr = { 3, 4, 11, 2, 9, 21 }; ` `    ``int` `n = arr.Length; ` `   `  `    ``// Function call ` `    ``Console.Write(longestPrimeSubsequence(arr, n) ` `         ``+``"\n"``);  ` `} ` `} ` `  `  `// This code is contributed by 29AjayKumar `

Output:

```3
```

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Improved By : 29AjayKumar, chitranayal