/**
 * Hash Set - seen dynamic
 * Time O(log(N)) | Space O(log(N))
 * https://leetcode.com/problems/happy-number/
 * @param {number} n
 * @return {boolean}
 */
var isHappy = (n, seen = new Set()) => {
    const hasCycle = () => n === 1 || seen.has(n);
    while (!hasCycle()) {
        /* Time O(log(N)) */
        seen.add(n); /* Space O(log(N)) */
        n = getNext(n); /* Time O(log(N)) */
    }

    return n === 1;
};

var getNext = (n, sum = 0) => {
    while (0 < n) {
        /* Time O(log(N)) */
        const remainder = n % 10;

        n = Math.floor(n / 10);
        sum += remainder * remainder;
    }

    return sum;
};

/**
 * Hash Set - seen static
 * Time O(log(N)) | Space O(1)
 * https://leetcode.com/problems/happy-number/
 * @param {number} n
 * @return {boolean}
 */
var isHappy = (n) => {
    const cycles = [4, 16, 37, 58, 89, 145, 42, 20];
    const seen = new Set(cycles); /* Time O(1)      | Space O(1) */

    const hasCycle = () => n === 1 || seen.has(n);
    while (!hasCycle()) {
        /* Time O(log(N)) | Space O(1) */
        n = getNext(n);
    }

    return n === 1;
};

var getNext = (n, sum = 0) => {
    while (0 < n) {
        /* Time O(log(N)) */
        const remainder = n % 10;

        n = Math.floor(n / 10);
        sum += remainder * remainder;
    }

    return sum;
};

/**
 * Pointer - n === 1 || n === 4
 * Time O(log(N)) | Space O(1)
 * https://leetcode.com/problems/happy-number/
 * @param {number} n
 * @return {boolean}
 */
var isHappy = (n) => {
    const hasCycle = () => n === 1 || n === 4;
    while (!hasCycle()) {
        /* Time O(log(N)) */
        n = getNext(n); /* Time O(log(N)) */
    }

    return n === 1;
};

var getNext = (n, sum = 0) => {
    while (0 < n) {
        /* Time O(log(N)) */
        const remainder = n % 10;

        n = Math.floor(n / 10);
        sum += remainder * remainder;
    }

    return sum;
};

/**
 * Slow Fast
 * Time O(log(N)) | Space O(1)
 * https://leetcode.com/problems/happy-number/
 * @param {number} n
 * @return {boolean}
 */
var isHappy = (n) => {
    let [slow, fast] = [n, getNext(n)];

    const hasCyle = () => fast === 1 || slow === fast;
    while (!hasCyle()) {
        /* Time O(log(N)) */
        slow = getNext(slow); /* Time O(log(N)) */
        fast = getNext(getNext(fast)); /* Time O(log(N)) */
    }

    return fast === 1;
};

var getNext = (n, sum = 0) => {
    while (0 < n) {
        /* Time O(log(N)) */
        const remainder = n % 10;

        n = Math.floor(n / 10);
        sum += remainder * remainder;
    }

    return sum;
};