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by Sumit Chourasia | Oct 02, 2020 | Category :coding | Tags : algorithm data-structure easy leetcode maths

Prime Arrangements - Math - Easy - LeetCode

Prime Arrangements - Math - Easy - LeetCode

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

public class Solution {
    public int NumPrimeArrangements(int n) {        
        int mod = (int)Math.Pow(10, 9) + 7;
        int count = 0;
        for (int i = 2; i <= n; i++){
            if (IsPrime(i)){
                count++;   
            }                
        }            

        long res = 1;
        for (int i = count; i > 0; i--)
        {
            res = (res * i) % mod;
            res %= mod;
        }

        for (int i = n - count; i > 0; i--)
        {
            res = (res * i) % mod;
            res %= mod;
        }

        return (int)res;
    }
    
    bool IsPrime(int num)
    {
        for (int i = 2; i <= num / 2; i++){
            if (num % i == 0){
                return false;    
            }                  
        }            

        return true;
    }
}

Time Complexity: O(n^2)

Space Complexity: O(1)