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Java-based LeetCode algorithm problem solutions, regularly updated

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package g1101_1200.s1175_prime_arrangements;

// #Easy #Math #2022_06_13_Time_0_ms_(100.00%)_Space_40.2_MB_(64.71%)

/**
 * 1175 - Prime Arrangements\.
 *
 * Easy
 *
 * 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[] a = {
            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
        };
        int c = 0;
        while (c < 25 && n >= a[c]) {
            c++;
        }
        int m = 1000000007;
        long res = 1L;
        while ((n - c) > 0) {
            res *= (n - c);
            res %= m;
            n--;
        }
        while (c > 0) {
            res *= c;
            res %= m;
            c--;
        }
        return (int) res;
    }
}