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，可以通过将数字一个接一个地放置来创建，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;iPython 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 ChitraNayalC#
// 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
}PHP
输出：
379
79
时间复杂度： O(N * log(log N))