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:
class Solution {
public int numPrimeArrangements(int n) {
int numOfPrimes = 0;
int mod = (int) 1e9 + 7;
for (int i = 1; i <= n; i ++) {
if (isPrime(i)) {
numOfPrimes ++;
}
}
long res = 1;
int nonPrimes = n - numOfPrimes;
for (int i = numOfPrimes; i > 1; i --) {
res = (i * res) % mod;
}
for (int i = nonPrimes; i > 1; i --) {
res = (i * res) % mod;
}
return (int) (res % mod);
}
private boolean isPrime(int val) {
if (val <= 1) return false;
for (int i = 2; i <= (int) Math.sqrt(val); i ++) {
if (val % i == 0) {
return false;
}
}
return true;
}
}