/**
 * Matrix
 * Time O(N * M) | Space O(N + M)
 * https://leetcode.com/problems/multiply-strings/
 * @param {string} num1
 * @param {string} num2
 * @return {string}
 */
var multiply = (num1, num2) => {
    const isZero = num1 === '0' || num2 === '0';
    if (isZero) return '0';

    const buffer = initBuffer(num1, num2); /*               | Space (N + M) */

    multiplication(num1, num2, buffer); /* Time O(N * M) */
    removeLeadingZero(buffer); /* Time O(N + M) | Time O(N + M)*/

    return buffer.join(''); /* Time O(N + M) | Space O(N + M) */
};

var initBuffer = (num1, num2) => {
    const size = num1.length + num2.length;

    return new Array(size).fill(0); /* Space (N + M) */
};

var multiplication = (num1, num2, buffer) => {
    for (let i = num1.length - 1; 0 <= i; i--) {
        /* Time O(N) */
        for (let j = num2.length - 1; 0 <= j; j--) {
            /* Time O(M) */
            update(num1, i, num2, j, buffer); /* Space O(N + M) */
        }
    }
};

var removeLeadingZero = (buffer) => {
    const isLeadZero = buffer[0] === 0;
    if (!isLeadZero) return;

    buffer.shift(); /* Time O(N + M) | Time O(N + M) */
};

var update = (num1, i, num2, j, buffer) => {
    const curPos = i + j;
    const prevPos = curPos + 1;

    const carry = buffer[prevPos];
    const product = getProduct(num1, i, num2, j);
    const sum = carry + product;

    const remainder = sum % 10;
    const value = (sum - remainder) / 10;

    buffer[prevPos] = remainder; /* Space O(N + M) */
    buffer[curPos] += value; /* Space O(N + M) */
};

var getProduct = (num1, i, num2, j) => {
    const [iNum, jNum] = [Number(num1[i]), Number(num2[j])];

    return iNum * jNum;
};

/**
 * Matrix
 * Time O(N * M) | Space O(N + M)
 * https://leetcode.com/problems/multiply-strings/
 * @param {string} num1
 * @param {string} num2
 * @return {string}
 */
var multiply = (num1, num2) => {
    const isZero = num1 === '0' || num2 === '0';
    if (isZero) return '0';

    const buffer = initBuffer(num1, num2); /*               | Space O(N + M) */

    multiplication(num1, num2, buffer); /* Time O(N * M) | Space O(N + M) */
    removeLeadingZero(buffer); /* Time O(N + M) | Space O(N + M) */

    return buffer.join(''); /* Time O(N + M) | Space O(N + M) */
};

var initBuffer = (num1, num2) =>
    new Array(num1.length + num2.length).fill(0); /* Space O(N + M) */

var multiplication = (num1, num2, buffer) => {
    [num1, num2] = /* Time O(N + M) */ [reverse(num1), reverse(num2)];

    for (var i1 in num1) {
        /* Time O(N) */
        for (var i2 in num2) {
            /* Time O(M) */
            update(num1, i1, num2, i2, buffer); /* Space O(N + M) */
        }
    }

    buffer.reverse(); /* Time O(N + M) */
};

const reverse = (s) =>
    s
        .split('') /* Time O(K) | Space O (K) */
        .reverse(); /* Time O(K) */

var update = (num1, i1, num2, i2, buffer) => {
    const product = num1[i1] * num2[i2];
    const index = Number(i1) + Number(i2);

    buffer[index] += product; /* Space O(N + M) */
    buffer[index + 1] += Math.floor(buffer[index] / 10); /* Space O(N + M) */
    buffer[index] = buffer[index] % 10; /* Space O(N + M) */
};

var removeLeadingZero = (buffer) => {
    const isZero = buffer[0] === 0;
    if (!isZero) return;

    buffer.shift(); /* Time O(N + M) | Space O(N + M) */
};