1175. Prime Arrangements-质数排列

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

Soluiton in python:

class Solution:
    def numPrimeArrangements(self, n: int) -> int:
        def isprime(num):
            if num == 1:
                return False
            i = 2
            while i < int(sqrt(num))+1:
                if num % i == 0:
                    return False
                i += 1
            return True 
        def factor(num):
            result = 1
            for i in range(1, num+1):
                result *= i
            return result
        prime = 0
        nprime = 0
        for i in range(1, n+1):
            if isprime(i):
                prime += 1
            else:
                nprime += 1
        return (factor(prime)*factor(nprime)) % (10**9+7)