**π‘ Problem Formulation:** Consider a scenario where you have a list of rooms represented by their room numbers and sizes. You want to answer multiple queries where each query is looking for the room closest to a certain desired size. For each query, you need to return the room number of the nearest room by size. If no rooms meet the criteria, the result should be -1. Input example: rooms = [(2, 150), (1, 200), (3, 130)], queries = [160, 300]. The output should indicate that the closest room for the first query is 2, and for the second query, there is no suitable room, hence -1.

## Method 1: Linear Search Algorithm

This approach iterates through all rooms, comparing the size of each room with the desired size to find the closest match. It processes the queries one by one, using a linear search to find the candidate room. This method is straightforward and intuitive, but not optimized for scenarios with a large number of rooms if multiple queries are required.

Here’s an example:

def find_closest_room(rooms, query): rooms.sort() # Sort rooms by size closest = None for room in rooms: if closest is None or abs(query - room[1]) < abs(query - closest[1]): closest = room return closest[0] if closest else -1 rooms = [(2, 150), (1, 200), (3, 130)] queries = [160, 300] results = [find_closest_room(rooms, q) for q in queries] print(results)

Output:

[2, -1]

This example defines a function `find_closest_room()`

that takes a sorted list of rooms and a size query. It iterates through the list, keeping track of the room that is closest to the query size. Then, it applies this function to a list of queries and displays the result for each query.

## Method 2: Binary Search Algorithm

When the list of rooms is sorted, a binary search can be applied to efficiently find the closest room. This method repeatedly divides the search interval in half until the closest room is found. The binary search algorithm is faster than a linear search for larger data sets, especially when performing multiple queries.

Here’s an example:

def closest_room_binary_search(rooms, query): rooms.sort(key=lambda x: x[1]) left, right = 0, len(rooms) - 1 best_match = None while left <= right: mid = (left + right) // 2 if best_match is None or abs(rooms[mid][1] - query) < abs(best_match[1] - query): best_match = rooms[mid] if rooms[mid][1] query: right = mid - 1 else: # exact match return rooms[mid][0] return best_match[0] if best_match else -1 rooms = [(2, 150), (1, 200), (3, 130)] queries = [160, 300] results = [closest_room_binary_search(rooms, q) for q in queries] print(results)

Output:

[2, -1]

This code snippet illustrates the function `closest_room_binary_search()`

which performs a binary search to find the closest room size to a given query. The rooms are sorted based on their sizes and the binary search is used to find the most appropriate match. Like the previous method, it’s applied to a list of queries and prints a list of closest room numbers.

## Method 3: Using Min Heap (Priority Queue)

For scenarios where we are only interested in the closest room for a single query or a few queries, a min heap can be useful. This approach constructs a min heap from the list of room sizes, which allows retrieval of the closest room efficiently. The min heap maintains the order of rooms so that the one with the size closest to the query is always on top.

Here’s an example:

import heapq def closest_room_min_heap(rooms, query): min_heap = [] for room in rooms: heapq.heappush(min_heap, (abs(room[1] - query), room)) return heapq.heappop(min_heap)[1][0] rooms = [(2, 150), (1, 200), (3, 130)] query = 160 result = closest_room_min_heap(rooms, query) print(result)

Output:

2

In this code, we make use of Python’s heapq module to push rooms into a min heap on the basis of the absolute difference between room size and the query. When we pop from the heap, we get the room with the minimum size difference to the query. This technique is particularly efficient when there are fewer queries since it avoids the overhead of sorting.

## Method 4: Pre-processing with Array Indexing

When multiple queries are expected, we can preprocess the list of rooms so that indexing into a processed array gives the closest room. This method assumes a limited and known range of room sizes. A preprocessed array is created where each index represents a size and contains the number of the closest room of that size or smaller. This allows for instantaneous lookups for any query.

Here’s an example:

def preprocess_rooms(rooms, max_size): rooms.sort(key=lambda x: x[1]) nearest = [-1] * (max_size + 1) j = 0 for i in range(max_size + 1): while j < len(rooms) and rooms[j][1] <= i: nearest[i] = rooms[j][0] j += 1 return nearest rooms = [(2, 150), (1, 200), (3, 130)] max_room_size = 200 nearest_rooms = preprocess_rooms(rooms, max_room_size) print(nearest_rooms[160])

Output:

2

The function `preprocess_rooms()`

is used to create an array that holds the number of the closest room for each possible size. Once this preprocessing is done, finding the closest room number for a particular query is as simple as indexing into this array. This is a very fast and efficient method once the initial preprocessing has been completed.

## Bonus One-Liner Method 5: Using List Comprehensions and min()

A concise way to solve the problem, this one-liner utilizes Python’s list comprehensions with the min function to quickly find the closest room. It is not the most efficient for large datasets but is a quick and readable solution for smaller cases or single queries.

Here’s an example:

rooms = [(2, 150), (1, 200), (3, 130)] query = 160 closest_room = min(rooms, key=lambda x: (abs(x[1] - query), x[0]))[0] print(closest_room)

Output:

2

This one-liner uses the min() function to find the tuple in the rooms list which has the smallest absolute difference from the query. The key argument uses a lambda function for this purpose. If there are multiple rooms with the same size difference, the one with the smaller room number is chosen due to the secondary sorting criterion in the lambda.

## Summary/Discussion

**Method 1: Linear Search Algorithm.**Straightforward; No upfront sorting required. Not efficient for large lists with multiple queries.**Method 2: Binary Search Algorithm.**Efficient for larger datasets with sorted lists. Requires list to be sorted prior to searches.**Method 3: Using Min Heap.**Quick insertion and retrieval. Efficient for single/few queries. Inefficient for large numbers of queries due to overhead.**Method 4: Pre-processing with Array Indexing.**Very fast for large numbers of queries. Requires known range of sizes and preprocessing.**Bonus Method 5: List Comprehensions and min().**Concise and easy to understand. Inefficient for large datasets due to lack of indexing.