1279. Prime Arrangements

• Difficulty: Easy

• Topics: Math

• Similar Questions:

Problem:

Return the number of permutations of 1 to n so that prime numbers are at prime indices (1-indexed.)

(Recall that an integer is prime if and only if it is greater than 1, and cannot be written as a product of two positive integers both smaller than it.)

Since the answer may be large, return the answer modulo 10^9 + 7.

Example 1:

Input: n = 5
Output: 12
Explanation: For example [1,2,5,4,3] is a valid permutation, but [5,2,3,4,1] is not because the prime number 5 is at index 1.

Example 2:

Input: n = 100
Output: 682289015

Constraints:

• 1 <= n <= 100

Solutions:

class Solution {
public:
    int numPrimeArrangements(int n) {
        int prime = primeCount(n);
        long ret = 1;
        for (int i = 2; i <= prime; ++i) {
            ret = (ret * i) % MOD;
        }

        for (int i = 2; i <= n - prime; ++i) {
            ret = (ret * i) % MOD;
        }

        return ret;
    }

private:
    int primeCount(int n) {
        int count = 0;
        for (int i = 2; i <= n; ++i) {
            if (isPrime(i)) ++count;
        }

        return count;
    }

    bool isPrime(int num) {
        for (int i = 2; i <= sqrt(num); ++i) {
            if (num % i == 0)   return false;
        }

        return true;
    }

    const int MOD = 1e9 + 7;

};