Prime Arrangements in Python

We have to find the number of permutations of 1 to n, so the prime numbers are placed at prime indices. The answers may be large, return the answer modulo 10^9 + 7. So if n = 5, then output will be 12. So there will be 12 permutations. one possible permutation will be [1,2,5,4,3], one invalid permutation is [5,2,3,4,1] because 5 is placed at index 1, that is not prime.

To solve this, we will follow these steps −

• Define one method called getNum, as follows −
• prime := list of all primes from 2 to 100
• set i := 0
• while i < length of prime list
  • if prime[i] > n, then return i
  • i := i + 1
• return length of prime
• The actual problem will be solved as follows
• x := getNum(n), p := 1, m := 10^9 + 7
• for i := x down to 0
  • p := p * i
  • p := p mod m
• for i := n – x down to 0
  • p := p * i
  • p := p mod m
• return p

Example

Let us see the following implementation to get better understanding −

 Live Demo

class Solution(object):
   def getNum(self,n):
      primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97]
      i = 0
      while i < len(primes):
         if primes[i]>n:
            return i
         i+=1
      return len(primes)
   def numPrimeArrangements(self, n):
      """
      :type n: int
      :rtype: int
      """
      x = self.getNum(n)
      p = 1
      m = 1000000000+7
      for i in range(x,0,-1):
         p*=i
         p%=m
      for i in range(n-x,0,-1):
         p*=i
         p%=m
      return p
ob1 = Solution()
print(ob1.numPrimeArrangements(100))

Input

100

Output

682289015

Arnab Chakraborty

Updated on: 29-Apr-2020

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