Queries for the smallest and the largest prime number of given digit

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Given Q queries where every query consists of an integer D, the task is to find the smallest and the largest prime number with D digits. If no such prime number exists then print -1.
Examples:

Input: Q[] = {2, 5}
Output:
11 97
10007 99991
Input: Q[] = {4, 3, 1}
Output:
1009 9973
101 997
1 7

Approach:

D digit numbers start from 10^{(D – 1)} and end at 10^D – 1.
Now, the task is to find the smallest and the largest prime number from this range.
To answer a number of queries for prime numbers, Sieve of Eratosthenes can be used to answer whether a number is prime or not.

Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
#define MAX 100000
 
bool prime[MAX + 1];
 
void SieveOfEratosthenes()
{
 
    // Create a boolean array "prime[0..n]" and initialize
    // all entries it as true. A value in prime[i] will
    // finally be false if i is Not a prime, else true.
    memset(prime, true, sizeof(prime));
 
    for (int p = 2; p * p <= MAX; 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 <= MAX; i += p)
                prime[i] = false;
        }
    }
}
 
// Function to return the smallest prime
// number with d digits
int smallestPrime(int d)
{
    int l = pow(10, d - 1);
    int r = pow(10, d) - 1;
    for (int i = l; i <= r; i++) {
 
        // check if prime
        if (prime[i]) {
            return i;
        }
    }
    return -1;
}
 
// Function to return the largest prime
// number with d digits
int largestPrime(int d)
{
    int l = pow(10, d - 1);
    int r = pow(10, d) - 1;
    for (int i = r; i >= l; i--) {
 
        // check if prime
        if (prime[i]) {
            return i;
        }
    }
    return -1;
}
 
// Driver code
int main()
{
    SieveOfEratosthenes();
 
    int queries[] = { 2, 5 };
    int q = sizeof(queries) / sizeof(queries[0]);
 
    // Perform queries
    for (int i = 0; i < q; i++) {
        cout << smallestPrime(queries[i]) << " "
             << largestPrime(queries[i]) << endl;
    }
 
    return 0;
}

Java

// Java implementation of the approach
import java.util.*;
 
class GFG 
{
static int MAX = 100000;
 
static boolean []prime = new boolean[MAX + 1];
 
static void SieveOfEratosthenes()
{
 
    // Create a boolean array "prime[0..n]" and 
    // initialize all entries it as true. 
    // A value in prime[i] will finally be false
    // if i is Not a prime, else true.
    for (int i = 0; i < MAX + 1; i++)
    {
        prime[i] = true;
    }
    for (int p = 2; p * p <= MAX; 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 <= MAX; i += p)
                prime[i] = false;
        }
    }
}
 
// Function to return the smallest prime
// number with d digits
static int smallestPrime(int d)
{
    int l = (int) Math.pow(10, d - 1);
    int r = (int) Math.pow(10, d) - 1;
    for (int i = l; i <= r; i++)
    {
 
        // check if prime
        if (prime[i])
        {
            return i;
        }
    }
    return -1;
}
 
// Function to return the largest prime
// number with d digits
static int largestPrime(int d)
{
    int l = (int) Math.pow(10, d - 1);
    int r = (int) Math.pow(10, d) - 1;
    for (int i = r; i >= l; i--) 
    {
 
        // check if prime
        if (prime[i])
        {
            return i;
        }
    }
    return -1;
}
 
// Driver code
public static void main(String[] args) 
{
    SieveOfEratosthenes();
 
    int queries[] = { 2, 5 };
    int q = queries.length;
 
    // Perform queries
    for (int i = 0; i < q; i++)
    {
        System.out.println(smallestPrime(queries[i]) + " " + 
                           largestPrime(queries[i]));
    }
}
} 
 
// This code is contributed by Rajput-Ji

Python3

# Python3 implementation of the approach 
from math import sqrt
 
MAX = 100000
 
# Create a boolean array "prime[0..n]" and 
# initialize all entries it as true. 
# A value in prime[i] will finally be false 
# if i is Not a prime, else true. 
prime = [True] * (MAX + 1)
 
def SieveOfEratosthenes() : 
 
    for p in range(2, int(sqrt(MAX)) + 1) : 
 
        # 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 i in range(p * p, MAX + 1, p) :
                prime[i] = False; 
 
# Function to return the smallest prime 
# number with d digits 
def smallestPrime(d) : 
 
    l = 10 ** (d - 1); 
    r = (10 ** d) - 1; 
    for i in range(l, r + 1) : 
 
        # check if prime 
        if (prime[i]) :
            return i; 
 
    return -1; 
 
# Function to return the largest prime 
# number with d digits 
def largestPrime(d) : 
 
    l = 10 ** (d - 1); 
    r = (10 ** d) - 1; 
    for i in range(r, l , -1) :
 
        # check if prime 
        if (prime[i]) :
            return i; 
             
    return -1; 
 
# Driver code 
if __name__ == "__main__" : 
 
    SieveOfEratosthenes(); 
 
    queries = [ 2, 5 ]; 
    q = len(queries); 
 
    # Perform queries 
    for i in range(q) :
        print(smallestPrime(queries[i]), " ",
              largestPrime(queries[i])); 
 
# This code is contributed by AnkitRai01

C#

// C# implementation of the approach
using System;
     
class GFG 
{
static int MAX = 100000;
 
static bool []prime = new bool[MAX + 1];
 
static void SieveOfEratosthenes()
{
 
    // Create a boolean array "prime[0..n]" and 
    // initialize all entries it as true. 
    // A value in prime[i] will finally be false
    // if i is Not a prime, else true.
    for (int i = 0; i < MAX + 1; i++)
    {
        prime[i] = true;
    }
    for (int p = 2; p * p <= MAX; 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 <= MAX; i += p)
                prime[i] = false;
        }
    }
}
 
// Function to return the smallest prime
// number with d digits
static int smallestPrime(int d)
{
    int l = (int) Math.Pow(10, d - 1);
    int r = (int) Math.Pow(10, d) - 1;
    for (int i = l; i <= r; i++)
    {
 
        // check if prime
        if (prime[i])
        {
            return i;
        }
    }
    return -1;
}
 
// Function to return the largest prime
// number with d digits
static int largestPrime(int d)
{
    int l = (int) Math.Pow(10, d - 1);
    int r = (int) Math.Pow(10, d) - 1;
    for (int i = r; i >= l; i--) 
    {
 
        // check if prime
        if (prime[i])
        {
            return i;
        }
    }
    return -1;
}
 
// Driver code
public static void Main(String[] args) 
{
    SieveOfEratosthenes();
 
    int []queries = { 2, 5 };
    int q = queries.Length;
 
    // Perform queries
    for (int i = 0; i < q; i++)
    {
        Console.WriteLine(smallestPrime(queries[i]) + " " + 
                           largestPrime(queries[i]));
    }
}
}
 
// This code is contributed by 29AjayKumar

Javascript

<script>
 
// Javascript implementation of the approach
 
const MAX = 100000;
 
// Create a boolean array 
// "prime[0..n]" and initialize
// all entries it as true. 
// A value in prime[i] will
// finally be false if i is Not a prime,
// else true.
let prime = new Array(MAX + 1).fill(true);
 
function SieveOfEratosthenes()
{
 
    for (let p = 2; p * p <= MAX; 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 <= MAX; i += p)
                prime[i] = false;
        }
    }
}
 
// Function to return the smallest prime
// number with d digits
function smallestPrime(d)
{
    let l = Math.pow(10, d - 1);
    let r = Math.pow(10, d) - 1;
    for (let i = l; i <= r; i++) {
 
        // check if prime
        if (prime[i]) {
            return i;
        }
    }
    return -1;
}
 
// Function to return the largest prime
// number with d digits
function largestPrime(d)
{
    let l = Math.pow(10, d - 1);
    let r = Math.pow(10, d) - 1;
    for (let i = r; i >= l; i--) {
 
        // check if prime
        if (prime[i]) {
            return i;
        }
    }
    return -1;
}
 
// Driver code
    SieveOfEratosthenes();
 
    let queries = [ 2, 5 ];
    let q = queries.length;
 
    // Perform queries
    for (let i = 0; i < q; i++) {
        document.write(smallestPrime(queries[i]) + " "
             + largestPrime(queries[i]) + "<br>");
    }
 
</script>

Output:

11 97
10007 99991

Time Complexity: O(MAX*log(log(MAX)) + q*(r – l))

Auxiliary Space: O(MAX)

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