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Abhishek Chaudhary
Abhishek Chaudhary

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Prime Arrangements

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

SOLUTION:

import math class Solution: def isPrime(self, n): if n <= 1: return False if n == 2: return True if n % 2 == 0: return False for i in range(3, int(math.sqrt(n)) + 1, 2): if n % i == 0: return False return True def factorial(self, n): if n <= 1: return 1 return n * self.factorial(n - 1) def numPrimeArrangements(self, n: int) -> int: numPrimes = 0 for i in range(1, n + 1): if self.isPrime(i): numPrimes += 1 return (self.factorial(numPrimes) * self.factorial(n - numPrimes)) % (10 ** 9 + 7) 
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