查找小于或等于给定数字的最大特殊素数

给定数字N。任务是找到小于或等于N的最大特殊质数。
特殊质数是一个数字，可以通过将数字依次放置来创建，这样所有产生的数字都是质数。
例子：

Input : N = 379
Output : 379
Explanation: 379 can be created as => 3 => 37 => 379
Here, all the numbers ie. 3, 37, 379 are prime.

Input : N = 100
Output : 79
Explanation: 79 can be created as => 7 => 79, 
where both 7, 79 are prime numbers.

方法：这个想法是使用Eratosthenes筛。构造筛网阵列，直到数字N。然后从数字N开始迭代返回，以检查数字是否为质数。如果是素数，请检查它是否是特殊素数。
现在，检查数字是否为特殊质数。继续将数字除以10，然后在每个点检查剩余的数字是否为质数，这可以通过引用已构建的Sieve数组来完成。
下面是上述方法的实现：

C++

// CPP program to find the Largest Special Prime
// which is less than or equal to a given number
 
#include 
using namespace std;
 
// Function to check whether the number
// is a special prime or not
bool checkSpecialPrime(bool* sieve, int num)
{
    // While number is not equal to zero
    while (num) {
        // If the number is not prime
        // return false.
        if (!sieve[num]) {
            return false;
        }
 
        // Else remove the last digit
        // by dividing the number by 10.
        num /= 10;
    }
 
    // If the number has become zero
    // then the number is special prime,
    // hence return true
    return true;
}
 
// Function to find the Largest Special Prime
// which is less than or equal to a given number
void findSpecialPrime(int N)
{
    bool sieve[N + 10];
 
    // Initially all numbers are considered Primes.
    memset(sieve, true, sizeof(sieve));
    sieve[0] = sieve[1] = false;
    for (long long i = 2; i <= N; i++) {
        if (sieve[i]) {
 
            for (long long j = i * i; j <= N; j += i) {
                sieve[j] = false;
            }
        }
    }
 
    // There is always an answer possible
    while (true) {
        // Checking if the number is a
        // special prime or not
        if (checkSpecialPrime(sieve, N)) {
            // If yes print the number
            // and break the loop.
            cout << N << '\n';
            break;
        }
        // Else decrement the number.
        else
            N--;
    }
}
 
// Driver code
int main()
{
    findSpecialPrime(379);
    findSpecialPrime(100);
 
    return 0;
}

Java

// Java program to find the Largest Special Prime
// which is less than or equal to a given number
 
class GFG
{
 
        // Function to check whether the number
        // is a special prime or not
    static boolean checkSpecialPrime(boolean [] sieve, int num)
        {
            // While number is not equal to zero
            while (num!=0) {
                // If the number is not prime
                // return false.
                if (!sieve[num]) {
                    return false;
                }
         
                // Else remove the last digit
                // by dividing the number by 10.
                num /= 10;
            }
         
            // If the number has become zero
            // then the number is special prime,
            // hence return true
            return true;
        }
         
        // Function to find the Largest Special Prime
        // which is less than or equal to a given number
        static void findSpecialPrime(int N)
        {
            boolean []sieve=new boolean[N+10];
            sieve[0] = sieve[1] = false;
 
            // Initially all numbers are considered Primes.
            for(int i=0;i

---

Python 3

# Python 3 program to find the Largest
# Special Prime which is less than or
# equal to a given number
 
# Function to check whether the number
# is a special prime or not
def checkSpecialPrime(sieve, num):
 
    # While number is not equal to zero
    while (num) :
         
        # If the number is not prime
        # return false.
        if (not sieve[num]) :
            return False
 
        # Else remove the last digit
        # by dividing the number by 10.
        num //= 10
 
    # If the number has become zero
    # then the number is special prime,
    # hence return true
    return True
 
# Function to find the Largest Special
# Prime which is less than or equal to
# a given number
def findSpecialPrime(N):
 
    # Initially all numbers are
    # considered Primes.
    sieve = [True] * (N + 10)
    sieve[0] = sieve[1] = False;
    for i in range(2, N + 1) :
        if (sieve[i]) :
 
            for j in range(i * i, N + 1, i) :
                sieve[j] = False
 
    # There is always an answer possible
    while (True) :
         
        # Checking if the number is
        # a special prime or not
        if (checkSpecialPrime(sieve, N)):
             
            # If yes print the number
            # and break the loop.
            print( N)
            break
             
        # Else decrement the number.
        else:
            N -= 1
 
# Driver code
if __name__ == "__main__":
    findSpecialPrime(379)
    findSpecialPrime(100)
 
# This code is contributed
# by ChitraNayal

C#

// C# program to find the Largest Special Prime
// which is less than or equal to a given number
 
using System;
class GFG
{
 
        // Function to check whether the number
        // is a special prime or not
    static bool checkSpecialPrime(bool [] sieve, int num)
        {
            // While number is not equal to zero
            while (num!=0) {
                // If the number is not prime
                // return false.
                if (!sieve[num]) {
                    return false;
                }
         
                // Else remove the last digit
                // by dividing the number by 10.
                num /= 10;
            }
         
            // If the number has become zero
            // then the number is special prime,
            // hence return true
            return true;
        }
         
        // Function to find the Largest Special Prime
        // which is less than or equal to a given number
        static void findSpecialPrime(int N)
        {
            bool []sieve=new bool[N+10];
             
             
            // Initially all numbers are considered Primes.
            for(int i = 0; i < N + 10; i++)
                sieve[i] = true;
                 
            sieve[0] = sieve[1] = false;
            for (int i = 2; i <= N; i++) {
                if (sieve[i]) {
         
                    for ( int j = i * i; j <= N; j += i) {
                        sieve[j] = false;
                    }
                }
            }
         
            // There is always an answer possible
            while (true) {
                // Checking if the number is a
                // special prime or not
                if (checkSpecialPrime(sieve, N)) {
                    // If yes print the number
                    // and break the loop.
                    Console.WriteLine(N);
                    break;
                }
                // Else decrement the number.
                else
                    N--;
            }
        }
         
        // Driver code
        public static void Main()
        {
            findSpecialPrime(379);
            findSpecialPrime(100);
         
             
        }
 
// This code is contributed by ihritik
 
}

Javascript

// Javascript program to find the Largest Special Prime
// which is less than or equal to a given number
     
    // Function to check whether the number
        // is a special prime or not
    function checkSpecialPrime(sieve,num)
    {
         // While number is not equal to zero
            while (num!=0) {
                // If the number is not prime
                // return false.
                if (!sieve[num]) {
                    return false;
                }
           
                // Else remove the last digit
                // by dividing the number by 10.
                num =Math.floor(num/ 10);
            }
           
            // If the number has become zero
            // then the number is special prime,
            // hence return true
            return true;
    }
     
    // Function to find the Largest Special Prime
        // which is less than or equal to a given number
    function findSpecialPrime(N)
    {
        let sieve=new Array(N+10);
            sieve[0] = sieve[1] = false;
   
            // Initially all numbers are considered Primes.
            for(let i=0;i<N+10;i++)
                sieve[i]=true;
               
            for (let i = 2; i <= N; i++) {
                if (sieve[i]) {
           
                    for ( let j = i * i; j <= N; j += i) {
                        sieve[j] = false;
                    }
                }
            }
           
            // There is always an answer possible
            while (true) {
                // Checking if the number is a
                // special prime or not
                if (checkSpecialPrime(sieve, N)) {
                    // If yes print the number
                    // and break the loop.
                    document.write(N+"<br>");
                    break;
                }
                // Else decrement the number.
                else
                    N--;
            }
    }
     
    // Driver code
    findSpecialPrime(379);
    findSpecialPrime(100);
     
 
// This code is contributed by rag2127

输出：

379
79

时间复杂度： O(N * log(log N))

如果您希望与行业专家一起参加现场课程，请参阅《 Geeks现场课程》和《 Geeks现场课程美国》。