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Queries for the difference between the count of composite and prime numbers in a given range

  • Last Updated : 11 May, 2021

Given Q queries where each query consists of two positive integers L and R and the task is to find the absolute difference between the count of prime numbers and the count of composite numbers in the range [L, R]
Examples: 
 

Input: queries[][] = {{1, 10}} 
Output: 

2, 3, 5 and 7 are the only primes in the given range. 
So, rest of the 6 integers are composite. 
|6 – 4| = 2
Input: queries[][] = {{4, 10}, {5, 30}} 
Output: 

10 
 

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Approach: 
 

  • Using Sieve of Eratosthenes, generate an array prime[i] such that prime[i] = 1 if i is prime else 0.
  • Now update the prime[] array such that prime[i] stores the count of prime numbers which are ≤ i.
  • For every query, the count of prime numbers in the range [L, R] can be found out by prime[R] – prime[L – 1], and the count of composite numbers will be the count of prime numbers subtracted from the total elements.
  • Print the absolute difference between the count of primes and the count of composites found in the previous step.

Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
#define MAX 1000000
int prime[MAX + 1];
 
// Function to update prime[]
// such prime[i] stores the
// count of prime numbers <= i
void updatePrimes()
{
    // prime[] marks all prime numbers as true
    // so prime[i] = 1 if ith number is a prime
 
    // Initialization
    for (int i = 2; i <= MAX; i++) {
        prime[i] = 1;
    }
 
    // 0 and 1 are not primes
    prime[0] = prime[1] = 0;
 
    // Mark composite numbers as false
    // and prime numbers as true
    for (int i = 2; i * i <= MAX; i++) {
        if (prime[i] == 1) {
            for (int j = i * i; j <= MAX; j += i) {
                prime[j] = 0;
            }
        }
    }
 
    // Update prime[] such that
    // prime[i] will store the count of
    // all the prime numbers <= i
    for (int i = 1; i <= MAX; i++) {
        prime[i] += prime[i - 1];
    }
}
 
// Function to return the absolute difference
// between the number of primes and the number
// of composite numbers in the range [l, r]
int getDifference(int l, int r)
{
 
    // Total elements in the range
    int total = r - l + 1;
 
    // Count of primes in the range [l, r]
    int primes = prime[r] - prime[l - 1];
 
    // Count of composite numbers
    // in the range [l, r]
    int composites = total - primes;
 
    // Return the sbsolute difference
    return (abs(primes - composites));
}
 
// Driver code
int main()
{
    int queries[][2] = { { 1, 10 }, { 5, 30 } };
    int q = sizeof(queries) / sizeof(queries[0]);
 
    updatePrimes();
 
    // Perform queries
    for (int i = 0; i < q; i++)
        cout << getDifference(queries[i][0],
                              queries[i][1])
             << endl;
 
    return 0;
}

Java




// Java implementation of the approach
import java.io.*;
 
class GFG
{
    static int MAX = 1000000;
    static int []prime = new int[MAX + 1];
 
    // Function to update prime[]
    // such prime[i] stores the
    // count of prime numbers <= i
    static void updatePrimes()
    {
        // prime[] marks all prime numbers as true
        // so prime[i] = 1 if ith number is a prime
     
        // Initialization
        for (int i = 2; i <= MAX; i++)
        {
            prime[i] = 1;
        }
     
        // 0 and 1 are not primes
        prime[0] = prime[1] = 0;
     
        // Mark composite numbers as false
        // and prime numbers as true
        for (int i = 2; i * i <= MAX; i++)
        {
            if (prime[i] == 1)
            {
                for (int j = i * i; j <= MAX; j += i)
                {
                    prime[j] = 0;
                }
            }
        }
 
        // Update prime[] such that
        // prime[i] will store the count of
        // all the prime numbers <= i
        for (int i = 1; i <= MAX; i++)
        {
            prime[i] += prime[i - 1];
        }
    }
 
    // Function to return the absolute difference
    // between the number of primes and the number
    // of composite numbers in the range [l, r]
    static int getDifference(int l, int r)
    {
     
        // Total elements in the range
        int total = r - l + 1;
     
        // Count of primes in the range [l, r]
        int primes = prime[r] - prime[l - 1];
     
        // Count of composite numbers
        // in the range [l, r]
        int composites = total - primes;
     
        // Return the sbsolute difference
        return (Math.abs(primes - composites));
    }
 
    // Driver code
    public static void main (String[] args)
    {
 
        int queries[][] = { { 1, 10 }, { 5, 30 } };
        int q = queries.length;
        updatePrimes();
         
        // Perform queries
        for (int i = 0; i < q; i++)
            System.out.println (getDifference(queries[i][0],
                                queries[i][1]));
 
    }
}
 
// This code is contributed by jit_t

Python3




# Python3 implementation of the approach
from math import sqrt
 
MAX = 1000000
prime = [0]*(MAX + 1);
 
# Function to update prime[]
# such prime[i] stores the
# count of prime numbers <= i
def updatePrimes() :
 
    # prime[] marks all prime numbers as true
    # so prime[i] = 1 if ith number is a prime
 
    # Initialization
    for i in range(2, MAX + 1) :
        prime[i] = 1;
 
    # 0 and 1 are not primes
    prime[0] = prime[1] = 0;
 
    # Mark composite numbers as false
    # and prime numbers as true
    for i in range(2, int(sqrt(MAX) + 1)) :
        if (prime[i] == 1) :
            for j in range(i*i, MAX, i) :
                prime[j] = 0;
 
    # Update prime[] such that
    # prime[i] will store the count of
    # all the prime numbers <= i
    for i in range(1, MAX) :
        prime[i] += prime[i - 1];
 
# Function to return the absolute difference
# between the number of primes and the number
# of composite numbers in the range [l, r]
def getDifference(l, r) :
 
    # Total elements in the range
    total = r - l + 1;
 
    # Count of primes in the range [l, r]
    primes = prime[r] - prime[l - 1];
 
    # Count of composite numbers
    # in the range [l, r]
    composites = total - primes;
 
    # Return the sbsolute difference
    return (abs(primes - composites));
 
 
# Driver code
if __name__ == "__main__" :
 
    queries = [ [ 1, 10 ],[ 5, 30 ] ];
    q = len(queries);
 
    updatePrimes();
 
    # Perform queries
    for i in range(q) :
        print(getDifference(queries[i][0],
                            queries[i][1]))
             
# This code is contributed by AnkitRai01

C#




// C# implementation of the approach
using System;
     
class GFG
{
    static int MAX = 1000000;
    static int []prime = new int[MAX + 1];
 
    // Function to update prime[]
    // such prime[i] stores the
    // count of prime numbers <= i
    static void updatePrimes()
    {
        // prime[] marks all prime numbers as true
        // so prime[i] = 1 if ith number is a prime
     
        // Initialization
        for (int i = 2; i <= MAX; i++)
        {
            prime[i] = 1;
        }
     
        // 0 and 1 are not primes
        prime[0] = prime[1] = 0;
     
        // Mark composite numbers as false
        // and prime numbers as true
        for (int i = 2; i * i <= MAX; i++)
        {
            if (prime[i] == 1)
            {
                for (int j = i * i; j <= MAX; j += i)
                {
                    prime[j] = 0;
                }
            }
        }
 
        // Update prime[] such that
        // prime[i] will store the count of
        // all the prime numbers <= i
        for (int i = 1; i <= MAX; i++)
        {
            prime[i] += prime[i - 1];
        }
    }
 
    // Function to return the absolute difference
    // between the number of primes and the number
    // of composite numbers in the range [l, r]
    static int getDifference(int l, int r)
    {
     
        // Total elements in the range
        int total = r - l + 1;
     
        // Count of primes in the range [l, r]
        int primes = prime[r] - prime[l - 1];
     
        // Count of composite numbers
        // in the range [l, r]
        int composites = total - primes;
     
        // Return the sbsolute difference
        return (Math.Abs(primes - composites));
    }
 
    // Driver code
    public static void Main ()
    {
 
        int [,]queries = { { 1, 10 }, { 5, 30 } };
        int q = queries.GetLength(0);
        updatePrimes();
         
        // Perform queries
        for (int i = 0; i < q; i++)
            Console.WriteLine(getDifference(queries[i,0],
                                queries[i,1]));
 
    }
}
 
/* This code contributed by PrinciRaj1992 */

Javascript




<script>
 
// Javascript implementation of the approach
 
const MAX = 1000000;
let prime = new Array(MAX + 1);
 
// Function to update prime[]
// such prime[i] stores the
// count of prime numbers <= i
function updatePrimes()
{
    // prime[] marks all prime numbers as true
    // so prime[i] = 1 if ith number is a prime
 
    // Initialization
    for (let i = 2; i <= MAX; i++) {
        prime[i] = 1;
    }
 
    // 0 and 1 are not primes
    prime[0] = prime[1] = 0;
 
    // Mark composite numbers as false
    // and prime numbers as true
    for (let i = 2; i * i <= MAX; i++) {
        if (prime[i] == 1) {
            for (let j = i * i; j <= MAX; j += i)
            {
                prime[j] = 0;
            }
        }
    }
 
    // Update prime[] such that
    // prime[i] will store the count of
    // all the prime numbers <= i
    for (let i = 1; i <= MAX; i++) {
        prime[i] += prime[i - 1];
    }
}
 
// Function to return the absolute difference
// between the number of primes and the number
// of composite numbers in the range [l, r]
function getDifference(l, r)
{
 
    // Total elements in the range
    let total = r - l + 1;
 
    // Count of primes in the range [l, r]
    let primes = prime[r] - prime[l - 1];
 
    // Count of composite numbers
    // in the range [l, r]
    let composites = total - primes;
 
    // Return the sbsolute difference
    return (Math.abs(primes - composites));
}
 
// Driver code
    let queries = [ [ 1, 10 ], [ 5, 30 ] ];
    let q = queries.length;
 
    updatePrimes();
 
    // Perform queries
    for (let i = 0; i < q; i++)
        document.write(getDifference(queries[i][0],
                          queries[i][1]) + "<br>");
 
</script>
Output: 
2
10

 




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