使用给定数字的数字构成所有质数

#include <iostream>
#include <unordered_set>
using namespace std;
// Function to check primality of a number
bool is_prime(int num) {
   // Since 2 is the smallest prime number, if the number is less than 2, return false
   if (num < 2) {
     return false;
   }
   // Verify whether the number is divisible by any integer within the range of 2 to the square root of the number.
   for (int i = 2; i*i <= num; i++) {
     if (num % i == 0) {
       return false;
     }
   }
   // If the number is not divisible by any number from 2 to the square root of the number, it is prime
   return true;
}
// Recursive function to generate all prime numbers using the given digits
void generate_primes(int digits[], int index, int num, unordered_set<string>& primes) {
   // If all digits have been used, return
   if (index >= 10) {
     return;
   }
   // Generate all possible combinations of the digits
   for (int i = 0; i < 10; i++) {
     // If the digit has already been used up, skip it
     if (digits[i] == 0) {
       continue;
     }
     // Append the current digit to the number being generated
     int new_num = num*10 + i;
     // If the new number is prime, add it to the set of primes
     if (is_prime(new_num)) {
       primes.insert(to_string(new_num));
     }
     // Decrement the count of the current digit in the digits array
     digits[i]--;
     // Recursively generate all primes using the remaining digits and the new number
     generate_primes(digits, index+1, new_num, primes);
     // Increase the occurrence count of the current digit within the digits array for the purpose of backtracking.
     digits[i]++;
   }
}
int main() {
   // Input number whose digits are used to generate primes
   string number = "17";
   cout << "Given number: " << number << endl;
   // An array is utilized to store the frequency count of each digit present in the input number
   int digits[10] = {0};
   // Count the occurrences of each digit in the input number
   for (char c : number) {
     digits[c-'0']++;
   }
   // Set to store the unique prime numbers generated
   unordered_set<string> primes;
   // Generate all prime numbers using the digits and add them to the set of primes
   generate_primes(digits, 0, 0, primes);
   // Print the number of unique prime numbers generated
   cout << "Number of unique prime numbers that can be formed using digits of a given number: ";
   cout << primes.size() << endl;
   return 0;
}