# Solution Alignment The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests. ## Problem Restatement You have restaurant menus and orders for a food delivery platform. Part 1: Given a user location and a set of restaurants (each with its menu items and prices), return the restaurant offering the lowest total price for a specified basket and the nearest such restaurant if there are ties; define distance computation assumptions. Part 2: Given a stream of orders with timestamps and item-level prices, compute over a time window the total revenue, order count, and average order value; support multiple overlapping windows efficiently. Part 3: Over a time window, return the Top-K orders by total price and the Top-K items by units sold; design data structures/algorithms to handle updates in real ti... ## Recommended Approach For one-time top-K, use a size-K min-heap or quickselect plus sorting the selected K. For streaming windows, maintain counts in a hash map plus a heap with lazy deletion or bucketed frequency structures when updates must be near O(1). Define deterministic tie-breaking. ## Correctness The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call. ## Complexity One-time heap: O(n log k) time and O(k) space. Quickselect: expected O(n) plus O(k log k) to order output. Streaming complexity depends on window eviction and tie-breaking. ## Edge Cases and Tests k = 0, k > n, duplicate values, ties, negative values, stale heap entries, and deterministic output ordering.