将所有特殊素数按其相对位置排序

给定一个大小为N的正整数数组arr[] ，任务是对所有特殊素数的相对位置进行排序(不影响其他元素的位置)。特殊素数是一个素数，它可以表示为两个其他素数之和。

例子：

Input: arr[] = {31, 5, 2, 1, 7} 
Output: 5 7 2 1 31 
The special primes are 31 (29 + 2), 5 (2 + 3), 7 (5 + 2). 
Sort them, we get 5, 7 and 31. 
So, the original array becomes {5, 7, 2, 1, 31}

Input: arr[] = {3, 13, 11, 43, 2, 19, 17} 
Output: 3 13 11 19 2 43 17 
 

方法：

• 开始遍历数组，对于每个元素arr[i] ，如果arr[i]是一个特殊的素数，则将其存储在一个向量中并更新arr[i] = -1
• 在列表中存储了所有特殊素数后，对更新后的列表进行排序。
• 再次遍历数组，对于每个元素，
  • 如果arr[i] = -1则打印列表中之前没有打印过的第一个元素。
  • 否则，打印arr[i] 。

下面是上述方法的实现：

C++

// C++ implementation of the approach
#include 
using namespace std;
 
// Function for the Sieve of Eratosthenes
void sieveOfEratosthenes(bool prime[], int n)
{
    prime[0] = 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] == true) {
 
            // Update all multiples of p greater than or
            // equal to the square of it
            // numbers which are multiple of p and are
            // less than p^2 are already been marked.
            for (int i = p * p; i <= n; i += p)
                prime[i] = false;
        }
    }
}
 
// Function to sort the special primes
// in their relative positions
void sortSpecialPrimes(int arr[], int n)
{
 
    // Maximum element from the array
    int maxVal = *max_element(arr, arr + n);
 
    // prime[i] will be true if i is a prime
    bool prime[maxVal + 1];
    memset(prime, true, sizeof(prime));
    sieveOfEratosthenes(prime, maxVal);
 
    // To store the special primes
    // from the array
    vector list;
 
    for (int i = 0; i < n; i++) {
 
        // If current element is a special prime
        if (prime[arr[i]] && prime[arr[i] - 2]) {
 
            // Add it to the ArrayList
            // and set arr[i] to -1
            list.push_back(arr[i]);
            arr[i] = -1;
        }
    }
 
    // Sort the special primes
    sort(list.begin(), list.end());
 
    int j = 0;
    for (int i = 0; i < n; i++) {
 
        // Position of a special prime
        if (arr[i] == -1)
            cout << list[j++] << " ";
        else
            cout << arr[i] << " ";
    }
}
 
// Driver code
int main()
{
    int arr[] = { 31, 5, 2, 1, 7 };
    int n = sizeof(arr) / sizeof(int);
 
    sortSpecialPrimes(arr, n);
 
    return 0;
}

Java

// Java implementation of the above approach
import java.util.*;
 
class GFG{
 
// Function for the Sieve of Eratosthenes
static void sieveOfEratosthenes(boolean prime[],
                                int n)
{
    prime[0] = 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] == true)
        {
 
            // Update all multiples of p
            // greater than or equal to the
            // square of it numbers which are
            // multiple of p and are less than
            // p^2 are already been marked.
            for(int i = p * p; i <= n; i += p)
                prime[i] = false;
        }
    }
}
 
// Function to sort the special primes
// in their relative positions
static void sortSpecialPrimes(int arr[], int n)
{
     
    // Maximum element from the array
    int maxVal = Arrays.stream(arr).max().getAsInt();
 
    // prime[i] will be true if i is a prime
    boolean []prime = new boolean[maxVal + 1];
    for(int i = 0; i < prime.length; i++)
        prime[i] = true;
         
    sieveOfEratosthenes(prime, maxVal);
 
    // To store the special primes
    // from the array
    Vector list = new Vector();
 
    for(int i = 0; i < n; i++)
    {
         
        // If current element is a special prime
        if (prime[arr[i]] && prime[arr[i] - 2])
        {
             
            // Add it to the ArrayList
            // and set arr[i] to -1
            list.add(arr[i]);
            arr[i] = -1;
        }
    }
 
    // Sort the special primes
    Collections.sort(list);
 
    int j = 0;
    for(int i = 0; i < n; i++)
    {
         
        // Position of a special prime
        if (arr[i] == -1)
            System.out.print(list.get(j++) + " ");
        else
            System.out.print(arr[i] + " ");
    }
}
 
// Driver code
public static void main(String[] args)
{
    int arr[] = { 31, 5, 2, 1, 7 };
    int n = arr.length;
 
    sortSpecialPrimes(arr, n);
}
}
 
// This code is contributed by PrinciRaj1992

C#

// C# implementation of the above approach
using System;
using System.Collections.Generic;
using System.Linq;
 
class GFG{
 
// Function for the Sieve of Eratosthenes
static void sieveOfEratosthenes(bool []prime,
                                int n)
{
    prime[0] = 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] == true)
        {
             
            // Update all multiples of p
            // greater than or equal to the
            // square of it numbers which are
            // multiple of p and are less than
            // p^2 are already been marked.
            for(int i = p * p; i <= n; i += p)
                prime[i] = false;
        }
    }
}
 
// Function to sort the special primes
// in their relative positions
static void sortSpecialPrimes(int []arr, int n)
{
     
    // Maximum element from the array
    int maxVal = arr.Max();
 
    // prime[i] will be true if i is a prime
    bool []prime = new bool[maxVal + 1];
    for(int i = 0; i < prime.Length; i++)
        prime[i] = true;
         
    sieveOfEratosthenes(prime, maxVal);
 
    // To store the special primes
    // from the array
    List list = new List();
 
    for(int i = 0; i < n; i++)
    {
         
        // If current element is a special prime
        if (prime[arr[i]] && prime[arr[i] - 2])
        {
             
            // Add it to the List
            // and set arr[i] to -1
            list.Add(arr[i]);
            arr[i] = -1;
        }
    }
 
    // Sort the special primes
    list.Sort();
 
    int j = 0;
    for(int i = 0; i < n; i++)
    {
         
        // Position of a special prime
        if (arr[i] == -1)
            Console.Write(list[j++] + " ");
        else
            Console.Write(arr[i] + " ");
    }
}
 
// Driver code
public static void Main(String[] args)
{
    int []arr = { 31, 5, 2, 1, 7 };
    int n = arr.Length;
 
    sortSpecialPrimes(arr, n);
}
}
 
// This code is contributed by PrinciRaj1992

Javascript

 
// Javascript implementation of the above approach
 
// Function for the Sieve of Eratosthenes
function sieveOfEratosthenes(prime, n)
{
    prime[0] = prime[1] = false;
    for(let p = 2; p * p <= n; p++)
    {
         
        // If prime[p] is not changed,
        // then it is a prime
        if (prime[p] == true)
        {
               
            // Update all multiples of p
            // greater than or equal to the
            // square of it numbers which are
            // multiple of p and are less than
            // p^2 are already been marked.
            for(let i = p * p; i <= n; i += p)
                prime[i] = false;
        }
    }
}
   
// Function to sort the special primes
// in their relative positions
function sortSpecialPrimes(arr, n)
{
       
    // Maximum element from the array
    let maxVal = Math.max(...arr);
   
    // prime[i] will be true if i is a prime
    let prime = Array.from(
        {length: maxVal + 1}, (_, i) => 0);
    for(let i = 0; i < prime.length; i++)
        prime[i] = true;
           
    sieveOfEratosthenes(prime, maxVal);
   
    // To store the special primes
    // from the array
    let list = [];
   
    for(let i = 0; i < n; i++)
    {
           
        // If current element is a special prime
        if (prime[arr[i]] && prime[arr[i] - 2])
        {
               
            // Add it to the List
            // and set arr[i] to -1
            list.push(arr[i]);
            arr[i] = -1;
        }
    }
   
    // Sort the special primes
    list.sort((a, b) => a - b);
   
    let j = 0;
    for(let i = 0; i < n; i++)
    {
           
        // Position of a special prime
        if (arr[i] == -1)
            document.write(list[j++] + " ");
        else
            document.write(arr[i] + " ");
    }
}
 
// Driver Code
let arr = [ 31, 5, 2, 1, 7 ];
let n = arr.length;
 
sortSpecialPrimes(arr, n);
   
// This code is contributed by target_2
   

输出：

5 7 2 1 31

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