Leetcode/Problem-1175.cpp at master · VikasKumarRoy/Leetcode · GitHub

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//Problem - 1175
// https://leetcode.com/problems/prime-arrangements/

// O(n) time comlexity

class Solution {
public:
    int mod = 1e9 + 7;

    bool isPrime(int n) {
    if (n <= 1)
        return false;
    if (n <= 3)
        return true;

    if (n % 2 == 0 || n % 3 == 0)
        return false;

    for (int i = 5; i * i <= n; i = i + 6)
        if (n % i == 0 || n % (i + 2) == 0)
            return false;
    return true;
    }

    long long fact(int n) {
        long long fac = 1;
        int x = 2;
        while(x <= n) {
            fac = (fac*x)%mod;
            x++;
        }
        return fac;
    }

    int numPrimeArrangements(int n) {
        int primes = 0, nonprimes = 0;
        for(int i = 1; i <= n; i++)
            if(isPrime(i))
                primes++;
        nonprimes = n - primes;
        return (fact(primes) * fact(nonprimes) )%mod;
    }
};