43. Multiply Strings

[Tcdian]

43. Multiply Strings

给定两个以字符串形式表示的非负整数 num1 和 num2，返回 num1 和 num2 的乘积，它们的乘积也表示为字符串形式。

Example 1

Input: num1 = "2", num2 = "3"
Output: "6"

Example 2

Input: num1 = "123", num2 = "456"
Output: "56088"

Note

• num1 和 num2 的长度小于110。
• num1 和 num2 只包含数字 0-9。
• num1 和 num2 均不以零开头，除非是数字 0 本身。
• 不能使用任何标准库的大数类型（比如 BigInteger）或直接将输入转换为整数来处理。

[Tcdian]

Solution

• JavaScript Solution

/**
 * @param {string} num1
 * @param {string} num2
 * @return {string}
 */
var multiply = function(num1, num2) {
    return sum(digitMultiply(num1, num2));

    function digitMultiply(num1, num2) {
        num2 = '0' + num2;
        const digitProducts = [];
        for(let i = num1.length - 1; i >= 0; i--) {
            let curry = 0;
            let digitProduct = ''.padEnd(num1.length - 1 - i, '0');
            for (let j = num2.length - 1; j >= 0; j--) {
                const product = Number(num1[i]) * Number(num2[j]) + curry;
                digitProduct = String(product % 10) + digitProduct;
                curry = Math.floor(product / 10);
            }
            digitProducts.push(digitProduct);
        }
        return digitProducts;
    }

    function sum(nums) {
        let result = nums[0];
        for (let i = 1; i < nums.length; i++) {
            let curry = 0;
            let digitSum = '';
            const len = result.length > nums[i].length ? result.length + 1 : nums[i].length + 1;
            result = result.padStart(len, '0');
            const num = nums[i].padStart(len, '0');
            for (let j = len - 1; j >= 0; j--) {
                digitSum = String((Number(result[j]) + Number(num[j]) + curry) % 10) + digitSum;
                curry = Math.floor((Number(result[j]) + Number(num[j]) + curry) / 10);
            }
            result = digitSum;
        }
        let separator = 0;
        while(separator !== result.length - 1 && result[separator] === '0') {
            separator += 1;
        }
        return result.slice(separator);
    }
};

• TypeScript Solution

function multiply(num1: string, num2: string): string {
    return sum(digitMultiply(num1, num2));

    function digitMultiply(num1: string, num2: string): string[] {
        num2 = '0' + num2;
        const digitProducts: string[] = [];
        for(let i = num1.length - 1; i >= 0; i--) {
            let curry = 0;
            let digitProduct = ''.padEnd(num1.length - 1 - i, '0');
            for (let j = num2.length - 1; j >= 0; j--) {
                const product = Number(num1[i]) * Number(num2[j]) + curry;
                digitProduct = String(product % 10) + digitProduct;
                curry = Math.floor(product / 10);
            }
            digitProducts.push(digitProduct);
        }
        return digitProducts;
    }

    function sum(nums: string[]): string {
        let result = nums[0];
        for (let i = 1; i < nums.length; i++) {
            let curry = 0;
            let digitSum = '';
            const len = result.length > nums[i].length ? result.length + 1 : nums[i].length + 1;
            result = result.padStart(len, '0');
            const num = nums[i].padStart(len, '0');
            for (let j = len - 1; j >= 0; j--) {
                digitSum = String((Number(result[j]) + Number(num[j]) + curry) % 10) + digitSum;
                curry = Math.floor((Number(result[j]) + Number(num[j]) + curry) / 10);
            }
            result = digitSum;
        }
        let separator = 0;
        while(separator !== result.length - 1 && result[separator] === '0') {
            separator += 1;
        }
        return result.slice(separator);
    }
};