Program to find the Nth Composite Number

Given a positive integer N, the task is to find the N^th Composite Number.

Examples:

Input: N = 1
Output: 4

Input: N = 3 
Output: 8

Approach: The given problem can be solved by using the concept of Sieve of Eratosthenes. Follow the steps below to solve the problem:

• Mark all the Prime Numbers till 10⁵ in a boolean array say isPrime[] using Sieve of Eratosthenes.
• Initialize an array, say composites[] that stores all the composite numbers.
• Traverse the array isPrime[] using the variable i, if the value of isPrime[i] is false, then insert the number i in the array composites[].
• After completing the above steps, print the value composites[N – 1] as the N^th Composite Number.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

#define MAX_SIZE 1000005

// Function to find the Nth Composite
// Numbers using Sieve of Eratosthenes
int NthComposite(int N)
{
    // Sieve of prime numbers
    bool IsPrime[MAX_SIZE];

    // Initialize the array to true
    memset(IsPrime, true, sizeof(IsPrime));

    // Iterate over the range [2, MAX_SIZE]
    for (int p = 2;
         p * p < MAX_SIZE; p++) {

        // If IsPrime[p] is true
        if (IsPrime[p] == true) {

            // Iterate over the
            // range [p * p, MAX_SIZE]
            for (int i = p * p;
                 i < MAX_SIZE; i += p)
                IsPrime[i] = false;
        }
    }

    // Stores the list of composite numbers
    vector<int> Composites;

    // Iterate over the range [4, MAX_SIZE]
    for (int p = 4; p < MAX_SIZE; p++)

        // If i is not prime
        if (!IsPrime[p])
            Composites.push_back(p);

    // Return Nth Composite Number
    return Composites[N - 1];
}

// Driver Code
int main()
{
    int N = 4;
    cout << NthComposite(N);
    return 0;
}

Java

// Java program for the above approach
import java.util.*;
public class GFG
{

// Function to find the Nth Composite
// Numbers using Sieve of Eratosthenes
public static int NthComposite(int N)
{
    int MAX_SIZE = 1000005;

    // Sieve of prime numbers
    boolean[] IsPrime = new boolean[MAX_SIZE];

    // Initialize the array to true
    Arrays.fill(IsPrime, true);

    // Iterate over the range [2, MAX_SIZE]
    for (int p = 2; p * p < MAX_SIZE; p++) {

        // If IsPrime[p] is true
        if (IsPrime[p] == true) {

            // Iterate over the
            // range [p * p, MAX_SIZE]
            for (int i = p * p;
                 i < MAX_SIZE; i += p)
                IsPrime[i] = false;
        }
    }

    // Stores the list of composite numbers
    Vector<Integer> Composites = new Vector<Integer>();

    // Iterate over the range [4, MAX_SIZE]
    for (int p = 4; p < MAX_SIZE; p++)

        // If i is not prime
        if (!IsPrime[p])
            Composites.add(p);

    // Return Nth Composite Number
    return Composites.get(N - 1);
}

// Driver Code
   public static void main(String args[])
   {
     int N = 4;
     System.out.println(NthComposite(N));
    }
}

// This code is contributed by SoumikMondal.

Python3

# Python3 program for the above approach

# Function to find the Nth Composite
# Numbers using Sieve of Eratosthenes
def NthComposite(N):

    # Sieve of prime numbers
    IsPrime = [True]*1000005

    # Iterate over the range [2, 1000005]
    for p in range(2, 1000005):
        if p * p > 1000005:
            break

        # If IsPrime[p] is true
        if (IsPrime[p] == True):

            # Iterate over the
            # range [p * p, 1000005]
            for i in range(p*p,1000005,p):
                IsPrime[i] = False

    # Stores the list of composite numbers
    Composites = []

    # Iterate over the range [4, 1000005]
    for p in range(4,1000005):

        # If i is not prime
        if (not IsPrime[p]):
            Composites.append(p)

    # Return Nth Composite Number
    return Composites[N - 1]

# Driver Code
if __name__ == '__main__':
    N = 4
    print (NthComposite(N))

# This code is contributed by mohit kumar 29.

C#

using System;
using System.Collections.Generic;

public class GFG{

  // Function to find the Nth Composite
  // Numbers using Sieve of Eratosthenes
  public static int NthComposite(int N)
  {
    int MAX_SIZE = 1000005;

    // Sieve of prime numbers
    bool[] IsPrime = new bool[MAX_SIZE];

    // Initialize the array to true
    Array.Fill(IsPrime, true);

    // Iterate over the range [2, MAX_SIZE]
    for (int p = 2; p * p < MAX_SIZE; p++) {

      // If IsPrime[p] is true
      if (IsPrime[p] == true) {

        // Iterate over the
        // range [p * p, MAX_SIZE]
        for (int i = p * p;
             i < MAX_SIZE; i += p)
          IsPrime[i] = false;
      }
    }

    // Stores the list of composite numbers
    List<int> Composites = new List<int>();

    // Iterate over the range [4, MAX_SIZE]
    for (int p = 4; p < MAX_SIZE; p++)

      // If i is not prime
      if (!IsPrime[p])
        Composites.Add(p);

    // Return Nth Composite Number
    return Composites[N - 1];
  }

  // Driver Code
  static public void Main ()
  {

    int N = 4;
    Console.WriteLine(NthComposite(N));

  }
}

// This code is contributed by patel2127

Javascript

<script>

// JavaScript program for the above approach

let MAX_SIZE =  1000005;

// Function to find the Nth Composite
// Numbers using Sieve of Eratosthenes
function NthComposite( N)
{
    // Sieve of prime numbers
    let IsPrime = [];

    // Initialize the array to true
    for(let i = 0;i<MAX_SIZE;i++)
        IsPrime.push(true);

    // Iterate over the range [2, MAX_SIZE]
    for (let p = 2;
         p * p < MAX_SIZE; p++) {

        // If IsPrime[p] is true
        if (IsPrime[p] == true) {

            // Iterate over the
            // range [p * p, MAX_SIZE]
            for (let i = p * p;
                 i < MAX_SIZE; i += p)
                IsPrime[i] = false;
        }
    }

    // Stores the list of composite numbers
    let Composites = [];

    // Iterate over the range [4, MAX_SIZE]
    for (let p = 4; p < MAX_SIZE; p++)

        // If i is not prime
        if (!IsPrime[p])
            Composites.push(p);

    // Return Nth Composite Number
    return Composites[N - 1];
}

// Driver Code
let N = 4;
document.write(NthComposite(N));

</script>

Output

9

Time Complexity: O(N + M * log(log(M)), where [2, M] is the range where Sieve of Eratosthenes is performed.
Auxiliary Space: O(N)

Program to find the Nth Composite Number in python using Brute Force approach

Example 2: By using Brute Force approach 

Approach:

1. Define a function is_composite(n) that takes a number n as input and returns True if n is composite (i.e., has a factor other than 1 and itself), and False otherwise. This function checks for factors by iterating from 2 to the square root of n, and returning True if any of these numbers divides n evenly.
2. Define a function nth_composite_brute_force(n) that takes an integer n as input and returns the n-th composite number. The function initializes a counter count to 0, and a number num to 4 (since 4 is the smallest composite number).
3. The function then enters a loop that continues until count is equal to n. Within the loop, the function checks if num is composite by calling the is_composite function. If num is composite, the function increments count by 1.
4. Regardless of whether num is composite or not, the function increments num by 1 and continues to the next iteration of the loop.
5. When the loop exits (i.e., when count is equal to n), the function returns the value of num minus 1 (since the loop incremented num one too many times).
6. Overall, this approach checks every number starting from 4 until it finds the n-th composite number. Since it checks each number up to its square root, the time complexity of the is_composite function is O(sqrt(n)). Since we call this function for every number from 4 to the n-th composite number, the total time complexity of this approach is O(n^2 * sqrt(n)). The space complexity is O(1), since we only store a counter and a single number.

C++

#include <iostream>
#include <cmath>

using namespace std; // Add this line to use the std namespace

// Function to check if a number is composite
bool isComposite(int n) {
    for (int i = 2; i <= sqrt(n); ++i) {
        if (n % i == 0) {
            return true;
        }
    }
    return false;
}

// Function to find the nth composite number using a brute force approach
int nthCompositeBruteForce(int n) {
    int count = 0;
    int num = 4;
    while (count < n) {
        if (isComposite(num)) {
            count++;
        }
        num++;
    }
    return num - 1;
}

int main() {
    // Test the function with N = 1 and N = 3
    cout << "N = 1, Output = " << nthCompositeBruteForce(1) << endl;
    cout << "N = 3, Output = " << nthCompositeBruteForce(3) << endl;

    return 0;
}

Java

import java.util.Scanner;

public class Main {
    // Function to check if a number is composite
    static boolean isComposite(int n) {
        for (int i = 2; i <= Math.sqrt(n); ++i) {
            if (n % i == 0) {
                return true;
            }
        }
        return false;
    }

    // Function to find the nth composite number using a brute-force approach
    static int nthCompositeBruteForce(int n) {
        int count = 0;
        int num = 4;
        while (count < n) {
            if (isComposite(num)) {
                count++;
            }
            num++;
        }
        return num - 1;
    }

    public static void main(String[] args) {
        // Test the function with N = 1 and N = 3
        System.out.println("N = 1, Output = " + nthCompositeBruteForce(1));
        System.out.println("N = 3, Output = " + nthCompositeBruteForce(3));
    }
}

Python3

import time

# Brute Force approach
def is_composite(n):
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            return True
    return False

def nth_composite_brute_force(n):
    count = 0
    num = 4
    while count < n:
        if is_composite(num):
            count += 1
        num += 1
    return num - 1

# Test the function with N = 1 and N = 3
print("N = 1, Output = ", nth_composite_brute_force(1))

print("N = 3, Output = ", nth_composite_brute_force(3))

C#

using System;

class Program {
    // Function to check if a number is composite
    static bool IsComposite(int n)
    {
        for (int i = 2; i <= Math.Sqrt(n); i++) {
            if (n % i == 0) {
                return true;
            }
        }
        return false;
    }

    // Function to find the nth composite number using a
    // brute force approach
    static int NthCompositeBruteForce(int n)
    {
        int count = 0;
        int num = 4;
        while (count < n) {
            if (IsComposite(num)) {
                count++;
            }
            num++;
        }
        return num - 1;
    }

    static void Main()
    {
        // Test the function with N = 1 and N = 3
        Console.WriteLine("N = 1, Output = "
                          + NthCompositeBruteForce(1));
        Console.WriteLine("N = 3, Output = "
                          + NthCompositeBruteForce(3));
    }
}

Javascript

//Javascript code for the above approach

// Function to check if a number is composite
function isComposite(n) {
    for (let i = 2; i <= Math.sqrt(n); ++i) {
        if (n % i === 0) {
            return true;
        }
    }
    return false;
}

// Function to find the nth composite number using a brute force approach
function nthCompositeBruteForce(n) {
    let count = 0;
    let num = 4;
    while (count < n) {
        if (isComposite(num)) {
            count++;
        }
        num++;
    }
    return num - 1;
}

// Test the function with N = 1 and N = 3
console.log("N = 1, Output = " + nthCompositeBruteForce(1));
console.log("N = 3, Output = " + nthCompositeBruteForce(3));

Output

N = 1, Output =  4
N = 3, Output =  8

Time Complexity: O(N^2 * logN)
Space Complexity: O(1)