Problem

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2, also represented as a string.

Example 1:

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

Example 2:

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

Note:

The length of both num1 and num2 is < 110.
Both num1 and num2 contain only digits 0-9.
Both num1 and num2 do not contain any leading zero, except the number 0 itself.
You must not use any built-in BigInteger library or convert the inputs to integer directly.

Solution: Simulation

Simulate multiplication one digit at a time.

Time complexity: O(l1*l2)

Space complexity: O(l1 + l2)

C++

// Author: Huahua

// Running time: 4 ms

class Solution {

public:

string multiply(string num1, string num2) {

const int l1 = num1.length();

const int l2 = num2.length();

string ans(l1 + l2, '0');

for (int i = l1 - 1; i >= 0; --i)

for (int j = l2 - 1; j >= 0; --j) {

int sum = (ans[i + j + 1] - '0') + (num1[i] - '0') * (num2[j] - '0');

ans[i + j + 1] = (sum % 10) + '0';

ans[i + j] += sum / 10;

}

for (int i = 0; i < ans.length(); ++i)

if (ans[i] != '0' || i == ans.length() - 1) return ans.substr(i);

return "";

}

};

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