Multiply Two Decimal Digit Strings
Company: Amazon
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Other
### Problem
You receive two decimal digit strings, `left` and `right`, representing nonnegative integers. Return their exact product in decimal notation as a string.
Work with the digit strings directly. You must not convert either complete input into an integer or use a built-in big-integer library.
Each input uses the usual decimal representation: it has no leading zeroes unless the entire string is `"0"`.
### Examples
**Example 1**
```text
Input: left = "305", right = "24"
Output: "7320"
```
The product of the represented numbers is `7320`.
**Example 2**
```text
Input: left = "0", right = "807"
Output: "0"
```
Multiplying by zero gives the single-digit representation `"0"`.
### Constraints
- Each input string has length between `1` and `200`, inclusive.
- Both strings contain only decimal digits `0` through `9`.
- A leading `0` is permitted only in the one-character string `"0"`.
Overview: Multiply two nonnegative decimal strings exactly without parsing complete inputs as integers or using a built-in big-integer library.
