Find prime groups after dividing the range 1 to N into K equal sections

Given a positive integer N and an integer K, The task is to find all prime numbers in the range of 1 to N that can be divided into K equal sections

Example:

Input: N = 20, K = 4 
Output: 2, 3, 5, 7, 11, 13, 17, 19

Input: N = 30, K = 5
Output: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Approach: Sieve of Eratosthenes

The Sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It works by iterating over all numbers from 2 up to a given number N and marking all its multiples as composite (not prime).

Follow the below steps for the above approach:

• Create a vector sieve of size N+1 and mark it as true to store all prime numbers.
• Then, set number 0 and 1 as not prime number.
• Start marking all multiples of members as non-prime.
• Take the next number in the list that is not marked as composite and mark its multiples in the list as composite.
• Create a vector to store all prime numbers in a range of 1 to N.
• Then, Divide the prime numbers into k equal sections.
• Add all prime numbers in each sections.

Below is the implementation of the above approach:

C++

#include <iostream>
#include <vector>

using namespace std;

// Function to find prime numbers in
// the range of 1 to N and divide them
// into K equal sections
vector<int> primeNumberDivision(int N, int K)
{
    // sieve[] is used to mark
    // prime numbers in range
    vector<bool> sieve(N + 1, true);

    // set 0 and 1 as not prime
    sieve[0] = sieve[1] = false;

    // mark all multiples of numbers
    // as non-prime
    for (int i = 2; i * i <= N; i++) {
        if (sieve[i] == true) {
            for (int j = i * i; j <= N; j += i) {
                sieve[j] = false;
            }
        }
    }

    // vector to store all
    // prime numbers in range
    vector<int> prime;

    // find all prime numbers
    // in the range of 1 to N
    for (int i = 2; i <= N; i++) {
        if (sieve[i] == true) {
            prime.push_back(i);
        }
    }

    // divide the prime numbers
    // into K equal sections
    vector<int> ans;
    int size = prime.size();

    // check if it's possible
    // to divide into K sections
    if (size % K != 0) {
        return ans;
    }

    int step = size / K;
    int start = 0;
    int end = step;

    // add all prime numbers
    // in each section
    while (start < size) {
        for (int i = start; i < end; i++) {
            ans.push_back(prime[i]);
        }
        start = end;
        end += step;
    }

    return ans;
}

void printAns(vector<int>& ans)
{
    for (auto a : ans) {
        cout << a << " ";
    }
    cout << endl;
}

// Driver Code
int main()
{
    int N = 20;
    int K = 4;
    vector<int> ans = primeNumberDivision(N, K);
    printAns(ans);
    return 0;
}

Java

// Java implementation
import java.io.*;
import java.util.*;

class GFG {

  // Function to find prime numbers in
  // the range of 1 to N and divide them
  // into K equal sections
  static List<Integer> primeNumberDivision(int N, int K)
  {
    // sieve[] is used to mark
    // prime numbers in range
    boolean[] sieve = new boolean[N + 1];
    for (int i = 0; i < sieve.length; i++) {
      sieve[i] = true;
    }

    // set 0 and 1 as not prime
    sieve[0] = sieve[1] = false;

    // mark all multiples of numbers
    // as non-prime
    for (int i = 2; i * i <= N; i++) {
      if (sieve[i]) {
        for (int j = i * i; j <= N; j += i) {
          sieve[j] = false;
        }
      }
    }

    // list to store all
    // prime numbers in range
    List<Integer> prime = new ArrayList<>();

    // find all prime numbers
    // in the range of 1 to N
    for (int i = 2; i <= N; i++) {
      if (sieve[i]) {
        prime.add(i);
      }
    }

    // divide the prime numbers
    // into K equal sections
    List<Integer> ans = new ArrayList<>();
    int size = prime.size();

    // check if it's possible
    // to divide into K sections
    if (size % K != 0) {
      return ans;
    }

    int step = size / K;
    int start = 0;
    int end = step;

    // add all prime numbers
    // in each section
    while (start < size) {
      for (int i = start; i < end; i++) {
        ans.add(prime.get(i));
      }
      start = end;
      end += step;
    }

    return ans;
  }

  static void printAns(List<Integer> ans)
  {
    for (int a : ans) {
      System.out.print(a + " ");
    }
    System.out.println();
  }

  public static void main(String[] args)
  {
    int N = 20;
    int K = 4;
    List<Integer> ans = primeNumberDivision(N, K);
    printAns(ans);
  }
}

// This code is contributed by lokeshmvs21.

Python3

# Python implementation
from typing import List

def primeNumberDivision(N: int, K: int) -> List[int]:

    # sieve[] is used to mark prime numbers in range
    sieve = [True] * (N + 1)

    # set 0 and 1 as not prime
    sieve[0] = sieve[1] = False

    # mark all multiples of numbers as non-prime
    for i in range(2, int(N ** 0.5) + 1):
        if sieve[i] == True:
            for j in range(i * i, N + 1, i):
                sieve[j] = False

    # vector to store all prime numbers in range
    prime = []

    # find all prime numbers in the range of 1 to N
    for i in range(2, N + 1):
        if sieve[i] == True:
            prime.append(i)

    # divide the prime numbers into K equal sections
    ans = []
    size = len(prime)

    # check if it's possible to divide into K sections
    if size % K != 0:
        return ans

    step = size // K
    start = 0
    end = step

    # add all prime numbers in each section
    while start < size:
        for i in range(start, end):
            ans.append(prime[i])
        start = end
        end += step

    return ans

def printAns(ans: List[int]) -> None:
    for a in ans:
        print(a, end=' ')
    print()

# Driver Code
def main():
    N = 20
    K = 4
    ans = primeNumberDivision(N, K)
    printAns(ans)

if __name__ == '__main__':
    main()

# This code is contributed by ksam24000

C#

// C# code to implement the above approach

using System;
using System.Collections.Generic;

public class GFG {

  // Function to find prime numbers in
  // the range of 1 to N and divide them
  // into K equal sections
  static List<int> primeNumberDivision(int N, int K)
  {
    // sieve[] is used to mark
    // prime numbers in range
    bool[] sieve = new bool[N + 1];
    for (int i = 0; i < sieve.Length; i++) {
      sieve[i] = true;
    }

    // set 0 and 1 as not prime
    sieve[0] = sieve[1] = false;

    // mark all multiples of numbers
    // as non-prime
    for (int i = 2; i * i <= N; i++) {
      if (sieve[i]) {
        for (int j = i * i; j <= N; j += i) {
          sieve[j] = false;
        }
      }
    }

    // list to store all
    // prime numbers in range
    List<int> prime = new List<int>();

    // find all prime numbers
    // in the range of 1 to N
    for (int i = 2; i <= N; i++) {
      if (sieve[i]) {
        prime.Add(i);
      }
    }

    // divide the prime numbers
    // into K equal sections
    List<int> ans = new List<int>();
    int size = prime.Count;

    // check if it's possible
    // to divide into K sections
    if (size % K != 0) {
      return ans;
    }

    int step = size / K;
    int start = 0;
    int end = step;

    // add all prime numbers
    // in each section
    while (start < size) {
      for (int i = start; i < end; i++) {
        ans.Add(prime[i]);
      }
      start = end;
      end += step;
    }

    return ans;
  }

  static void printAns(List<int> ans)
  {
    foreach(int a in ans) { Console.Write(a + " "); }
    Console.WriteLine();
  }

  static public void Main()
  {

    // Code
    int N = 20;
    int K = 4;
    List<int> ans = primeNumberDivision(N, K);
    printAns(ans);
  }
}

// This code is contributed by lokesh.

Javascript

  // JS code to implement the approach

  // Function to find prime numbers in
  // the range of 1 to N and divide them
  // into K equal sections
  function primeNumberDivision(N, K) {
    // sieve[] is used to mark
    // prime numbers in range
    let sieve = new Array(N + 1).fill(true);

    // set 0 and 1 as not prime
    sieve[0] = sieve[1] = false;

    // mark all multiples of numbers
    // as non-prime
    for (let i = 2; i * i <= N; i++) {
      if (sieve[i] == true) {
        for (let j = i * i; j <= N; j += i) {
          sieve[j] = false;
        }
      }
    }

    // vector to store all
    // prime numbers in range
    let prime = [];

    // find all prime numbers
    // in the range of 1 to N
    for (let i = 2; i <= N; i++) {
      if (sieve[i] == true) {
        prime.push(i);
      }
    }

    // divide the prime numbers
    // into K equal sections
    let ans = [];
    let size = prime.length;

    // check if it's possible
    // to divide into K sections
    if (size % K != 0) {
      return ans;
    }

    let step = size / K;
    let start = 0;
    let end = step;

    // add all prime numbers
    // in each section
    while (start < size) {
      for (let i = start; i < end; i++) {
        ans.push(prime[i]);
      }
      start = end;
      end += step;
    }

    return ans;
  }

function printAns(ans)
  {
    for (let a of ans) {
      console.log(a + " ");
    }
    console.log("<br>")
  }

  // Driver Code
  let N = 20;
  let K = 4;
  let ans = primeNumberDivision(N, K);
  printAns(ans);


// This code is contributed by Potta Lokesh

Output

2 3 5 7 11 13 17 19 

Complexity Analysis:
Time Complexity: N*log(log(N))
Space Complexity: O(N).