# Sort prime numbers of an array in descending order

Given an array of integers ‘arr’, the task is to sort all the prime numbers from the array in descending order in their relative positions i.e. other positions of the other elements must not be affected.

Examples:

Input: arr[] = {2, 5, 8, 4, 3}
Output: 5 3 8 4 2

Input: arr[] = {10, 12, 2, 6, 5}
Output: 10 12 5 6 2

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

Approach:

• Create a sieve to check whether an element is prime or not in O(1).
• Traverse the array and check if the number is prime. If it is prime, store it in a vector.
• Then, sort the vector in descending order.
• Again traverse the array and replace the prime numbers with the vector elements one by one.

Below is the implementation of the above approach:

## C++

 // C++ implementation of the approach #include using namespace std;    bool prime[100005];    void SieveOfEratosthenes(int n) {        memset(prime, true, sizeof(prime));        // false here indicates     // that it is not prime     prime[1] = false;        for (int p = 2; p * p <= n; 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 <= n; i += p)                 prime[i] = false;         }     } }    // Function that sorts // all the prime numbers // from the array in descending void sortPrimes(int arr[], int n) {     SieveOfEratosthenes(100005);        // this vector will contain     // prime numbers to sort     vector v;        for (int i = 0; i < n; i++) {            // if the element is prime         if (prime[arr[i]])             v.push_back(arr[i]);     }        sort(v.begin(), v.end(), greater());        int j = 0;        // update the array elements     for (int i = 0; i < n; i++) {         if (prime[arr[i]])             arr[i] = v[j++];     } }    // Driver code int main() {        int arr[] = { 4, 3, 2, 6, 100, 17 };     int n = sizeof(arr) / sizeof(arr[0]);        sortPrimes(arr, n);        // print the results.     for (int i = 0; i < n; i++) {         cout << arr[i] << " ";     }        return 0; }

## Java

 // Java implementation of the approach import java.util.*;    class GFG {        static boolean prime[] = new boolean[100005];        static void SieveOfEratosthenes(int n)     {            Arrays.fill(prime, true);            // false here indicates         // that it is not prime         prime[1] = false;            for (int p = 2; p * p <= n; 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 < n; i += p)                 {                     prime[i] = false;                 }             }         }     }        // Function that sorts     // all the prime numbers     // from the array in descending     static void sortPrimes(int arr[], int n)     {         SieveOfEratosthenes(100005);            // this vector will contain         // prime numbers to sort         Vector v = new Vector();            for (int i = 0; i < n; i++)         {                // if the element is prime             if (prime[arr[i]])              {                 v.add(arr[i]);             }         }         Comparator comparator = Collections.reverseOrder();         Collections.sort(v, comparator);            int j = 0;            // update the array elements         for (int i = 0; i < n; i++)          {             if (prime[arr[i]])              {                 arr[i] = v.get(j++);             }         }     }        // Driver code     public static void main(String[] args)     {         int arr[] = {4, 3, 2, 6, 100, 17};         int n = arr.length;            sortPrimes(arr, n);            // print the results.         for (int i = 0; i < n; i++)          {             System.out.print(arr[i] + " ");         }     } }    // This code is contributed by 29AjayKumar

## Python3

 # Python3 implementation of the approach     def SieveOfEratosthenes(n):         # false here indicates      # that it is not prime      prime[1] = False     p = 2     while p * p <= n:             # 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, n + 1, p):                  prime[i] = False                    p += 1    # Function that sorts all the prime  # numbers from the array in descending  def sortPrimes(arr, n):         SieveOfEratosthenes(100005)         # This vector will contain      # prime numbers to sort      v = []      for i in range(0, n):             # If the element is prime          if prime[arr[i]]:              v.append(arr[i])         v.sort(reverse = True)      j = 0        # update the array elements      for i in range(0, n):          if prime[arr[i]]:              arr[i] = v[j]             j += 1                    return arr        # Driver code  if __name__ == "__main__":         arr = [4, 3, 2, 6, 100, 17]      n = len(arr)             prime = [True] * 100006     arr = sortPrimes(arr, n)         # print the results.      for i in range(0, n):          print(arr[i], end = " ")         # This code is contributed by Rituraj Jain

## C#

 // C# implementation of the approach using System; using System.Collections.Generic;     class GFG {        static bool []prime = new bool[100005];        static void SieveOfEratosthenes(int n)     {            for(int i = 0; i < 100005; i++)             prime[i] = true;            // false here indicates         // that it is not prime         prime[1] = false;            for (int p = 2; p * p <= n; 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 < n; i += p)                 {                     prime[i] = false;                 }             }         }     }        // Function that sorts     // all the prime numbers     // from the array in descending     static void sortPrimes(int []arr, int n)     {         SieveOfEratosthenes(100005);            // this vector will contain         // prime numbers to sort         List v = new List();            for (int i = 0; i < n; i++)         {                // if the element is prime             if (prime[arr[i]])              {                 v.Add(arr[i]);             }         }         v.Sort();         v.Reverse();            int j = 0;            // update the array elements         for (int i = 0; i < n; i++)          {             if (prime[arr[i]])              {                 arr[i] = v[j++];             }         }     }        // Driver code     public static void Main(String[] args)     {         int []arr = {4, 3, 2, 6, 100, 17};         int n = arr.Length;            sortPrimes(arr, n);            // print the results.         for (int i = 0; i < n; i++)          {             Console.Write(arr[i] + " ");         }     } }    // This code contributed by Rajput-Ji

Output:

4 17 3 6 100 2

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