Implement four data-structure/string geometry tasks

## Problem A — Multiply two non-negative integer strings You are given two strings `num1` and `num2` representing non-negative integers in base-10. - Return their product as a base-10 string. - You **must not** convert the inputs to built-in integer/big-integer types. - The output must not contain leading zeros (unless the value is exactly `"0"`). **Input:** `num1`, `num2` (strings) **Output:** product as a string **Constraints (typical):** `1 <= len(num1), len(num2) <= 10^4`, digits only. --- ## Problem B — Parse email addresses from a huge log string You are given a very large string `s` that contains multiple **records**. Conceptually: - Records are separated by a semicolon `;` **only when the semicolon is not inside**: - double quotes `"..."` (display name), or - parentheses `(...)` (a comment). - Each record corresponds to one email entry, but the record can contain optional parts: - an optional display name (possibly quoted), - an email address token containing exactly one `@`, - optional comments in parentheses, and a comment may appear **anywhere** in the record. **Task:** Extract all email addresses from the string and return a **deduplicated** list. - If an email appears multiple times, keep only the first occurrence. - You may assume the email address itself does not contain spaces/semicolons/parentheses/quotes. **Input:** one string `s` **Output:** list of unique email strings --- ## Problem C — Maximum area axis-aligned rectangle from points You are given `N` distinct points on a 2D integer grid: `points[i] = (xi, yi)`. A rectangle is **axis-aligned** (sides parallel to axes). A valid rectangle requires all four corners to be present in the input set. **Task:** Return the maximum rectangle area possible. If no rectangle can be formed, return `0`. **Input:** array of points **Output:** integer maximum area (or `0`) **Constraints (typical):** `1 <= N <= 2000` (or similar), coordinates fit in 32-bit signed int. --- ## Problem D — Stock price tracker with corrections Design a data structure supporting these operations: - `update(timestamp, price)`: record the stock price at `timestamp`. - If the timestamp already exists, this call **overwrites/corrects** the previous price. - `current()`: return the latest stock price (price at the maximum timestamp seen so far). - `maximum()`: return the maximum price among all timestamps currently stored. - `minimum()`: return the minimum price among all timestamps currently stored. **Input:** sequence of operations **Output:** values returned by `current/maximum/minimum` **Constraints (typical):** up to `2e5` operations; timestamps and prices are positive integers.