【leetcode】1175. Prime Arrangements

题目如下：

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

解题思路：题目不难，对于给定一个正整数n，很容易可以求出在1~n这个区间有几个素数。假设素数有x个，x个素数占据x的位置，其排列方式的总和是x!；同理非素数有(n-x)个，那么这些非素数的排列方式就有(n-x)!个，两者的乘积即为最终的答案。

代码如下：

class Solution(object):
    def numPrimeArrangements(self, n):
        """
        :type n: int
        :rtype: int
        """
        prime = [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]
        import bisect
        prime_count = bisect.bisect_right(prime,n)
        no_prime_count = n - prime_count
        def calc(num):
            factorial = 1
            for i in range(1, num + 1):
                factorial = factorial * i
            return factorial

        total = calc(prime_count) * calc(no_prime_count)
        return total % (10**9 + 7)