# Multiply Strings Problem

## Description

LeetCode Problem 43.

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

Note: You must not use any built-in BigInteger library or convert the inputs to integer directly.

Example 1:

``````1
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Input: num1 = "2", num2 = "3"
Output: "6"
``````

Example 2:

``````1
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Input: num1 = "123", num2 = "456"
Output: "56088"
``````

Constraints:

• 1 <= num1.length, num2.length <= 200
• num1 and num2 consist of digits only.
• Both num1 and num2 do not contain any leading zero, except the number 0 itself.

## Sample C++ Code

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class Solution {
public:
string multiply(string num1, string num2) {
// handle edge-case where the product is 0
if (num1 == "0" || num2 == "0") return "0";

// num1.size() + num2.size() == max no. of digits
vector<int> num(num1.size() + num2.size(), 0);

// build the number by multiplying one digit at the time
for (int i = num1.size() - 1; i >= 0; --i) {
for (int j = num2.size() - 1; j >= 0; --j) {
num[i + j + 1] += (num1[i] - '0') * (num2[j] - '0');
num[i + j] += num[i + j + 1] / 10;
num[i + j + 1] %= 10;
}
}

int i = 0;
while (i < num.size() && num[i] == 0) ++i;

// transofrm the vector to a string
string res = "";
while (i < num.size()) res.push_back(num[i++] + '0');

return res;
}
};
``````