Sort all special primes in their relative positions
Given an array arr[] of size N of positive integers, the task is to sort all the special primes in their relative position (without affecting the position of other elements). A special prime is a prime number which can be represented as the sum of two other prime numbers.
Examples:
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
Approach:
- Start traversing the array and for every element arr[i], if arr[i] is a special prime then store it in a vector and update arr[i] = -1
- After all the special primes have been stored in the list, sort the updated list.
- Again traverse the array and for every element,
- If arr[i] = -1 then print the first element from the list that hasn’t been printed before.
- Else, print arr[i].
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> 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<int> 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<Integer> list = new Vector<Integer>(); 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<int> list = new List<int>(); 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 |
Output:
5 7 2 1 31
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