# 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<``int``> 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``>()); ` ` `  `    ``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<``int``> v = ``new` `List<``int``>(); ` ` `  `        ``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
```

My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.