You are given an array complexity of length n. There are n locked computers in a room with labels from 0 to n - 1, each with its own unique password. The password of the computer i has a complexity complexity[i]. The password for the computer label

countPermutations.js

/**
 * @param {number[]} complexity
 * @return {number}
 */
var countPermutations = function(complexity) {
    const n = complexity.length;
    const MOD = 1_000_000_007; // Large prime modulus for preventing overflow

    // Check validity: all elements after the first must be strictly greater
    for (let i = 1; i < n; i++) {
        if (complexity[i] <= complexity[0]) {
            return 0; // Invalid case
        }
    }

    // Compute factorial of (n-1) modulo MOD
    let result = 1;
    for (let i = n - 1; i >= 1; i--) {
        result = (result * i) % MOD;
    }

    return result;
};