质数排列

// Solution for leetcode problem using Java Streams
// The task is to count the number of permutations of numbers from 1 to n where all prime numbers are at prime indices.
// A prime index is 1-based. We need to return the result modulo 10^9 + 7.

import java.util.stream.IntStream;

public class PrimeArrangementStream {
    private static final int MOD = 1000000007;

    // Function to check if a number is prime
    private static boolean isPrime(int num) {
        if (num <= 1) return false;
        if (num == 2 || num == 3) return true;
        if (num % 2 == 0 || num % 3 == 0) return false;
        for (int i = 5; i * i <= num; i += 6) {
            if (num % i == 0 || num % (i + 2) == 0) return false;
        }
        return true;
    }

    // Function to count primes up to n
    private static int countPrimes(int n) {
        return (int) IntStream.rangeClosed(1, n).filter(PrimeArrangementStream::isPrime).count();
    }

    // Function to calculate factorial modulo MOD
    private static long factorial(int num) {
        return IntStream.rangeClosed(2, num).asLongStream().reduce(1, (a, b) -> (a * b) % MOD);
    }

    public static int numPrimeArrangements(int n) {
        int primeCount = countPrimes(n);
        int nonPrimeCount = n - primeCount;
        long primeFactorial = factorial(primeCount);
        long nonPrimeFactorial = factorial(nonPrimeCount);
        return (int) ((primeFactorial * nonPrimeFactorial) % MOD);
    }

    public static void main(String[] args) {
        System.out.println(numPrimeArrangements(5));  // Output: 12
        System.out.println(numPrimeArrangements(100));  // Output: 682289015
    }
}