**π‘ Problem Formulation:** Consider a scenario where there’s a game show with multiple rooms, and a prize can be hidden in one or more of these rooms. Participants need to guess the correct rooms to win. As developers, our goal is to write a Python program that determines the number of possible rooms in which a prize can be hidden based on a set of constraints provided. For example, given an input of `10`

total rooms with `3`

rooms that cannot contain the prize, the desired output would be `7`

possible rooms.

## Method 1: Using Basic Subtraction

This method involves subtracting the number of rooms where the prize cannot be from the total number of rooms to find the number of rooms where the prize can be hidden. It’s a straightforward approach and easy to implement.

Here’s an example:

def find_possible_rooms(total_rooms, restricted_rooms): return total_rooms - restricted_rooms possible_rooms = find_possible_rooms(10, 3) print(possible_rooms)

Output:

`7`

This example defines a function `find_possible_rooms`

that takes the total number of rooms and the number of rooms where the prize cannot be hidden. It simply returns the result of the subtraction, showing that if there are 10 rooms and the prize cannot be hidden in 3, it can be in any of the remaining 7 rooms.

## Method 2: Using Lists to Represent Rooms

In this method, we create a list to represent rooms, marking each room where the prize can be hidden. It allows for more complex scenarios, such as when certain rooms are preferred.

Here’s an example:

def find_possible_rooms(total_rooms, restricted_rooms_list): rooms = [True for _ in range(total_rooms)] for restricted in restricted_rooms_list: rooms[restricted] = False return sum(1 for room in rooms if room) possible_rooms = find_possible_rooms(10, [0, 2, 4]) print(possible_rooms)

Output:

`7`

This example utilizes a list comprehension to create a list named `rooms`

representing each room with a boolean value. Rooms that are restricted have their value set to `False`

. The function then counts and returns the number of `True`

values, indicating possible rooms.

## Method 3: Utilizing Set Operations

Set operations are valuable when dealing with unique items. This method employs set subtraction to easily calculate the possible rooms by removing the set of restricted rooms from the set of all rooms.

Here’s an example:

def find_possible_rooms(total_rooms, restricted_rooms_set): return len(set(range(total_rooms)) - restricted_rooms_set) possible_rooms = find_possible_rooms(10, {0, 2, 4}) print(possible_rooms)

Output:

`7`

The `find_possible_rooms`

function creates a set of all rooms, then subtracts the set of restricted rooms, and returns the length of the resulting set. This provides the number of rooms where the prize can be hidden.

## Method 4: Using Bitwise Operations

For a different approach, bitwise operations can be used if room availability is represented in binary, with bits indicating if a room can (1) or cannot (0) hold the prize. This method is compact and efficient for a fixed number of rooms.

Here’s an example:

def find_possible_rooms(total_rooms, no_prize_mask): return bin((1 << total_rooms) - 1 & ~no_prize_mask).count('1') possible_rooms = find_possible_rooms(10, 0b10101) # 0b10101 represents rooms 0, 2, and 4 are restricted print(possible_rooms)

Output:

`7`

Here, `find_possible_rooms`

uses bitwise left shift to create a binary number with `total_rooms`

bits set to 1. It then applies a bitwise NOT to the mask of rooms without a prize and performs a bitwise AND with the full room set. The count of 1s in the binary representation gives the number of rooms where a prize can be.

## Bonus One-Liner Method 5: Lambda Expressions

A lambda function can be used for a quick, one-line solution. This method is useful for simple calculations and concise code writing.

Here’s an example:

find_possible_rooms = lambda total, restricted: total - restricted print(find_possible_rooms(10, 3))

Output:

`7`

The lambda function here takes two arguments, the total number of rooms and the number of restricted rooms, and simply subtracts the latter from the former to determine the possible rooms.

## Summary/Discussion

**Method 1: Basic Subtraction.**Strengths: Simple and straightforward. Weaknesses: Not very flexible for more complex scenarios.**Method 2: Using Lists to Represent Rooms.**Strengths: More detailed modeling of individual rooms. Weaknesses: May be less efficient for a large number of rooms.**Method 3: Utilizing Set Operations.**Strengths: Efficient for operations on unique items. Weaknesses: Still requires conversion to set types.**Method 4: Using Bitwise Operations.**Strengths: Compact and efficient. Weaknesses: Limited by the number of bits and potentially confusing for non-binary thinkers.**Bonus Method 5: Lambda Expressions.**Strengths: Quick and concise. Weaknesses: Limited in complexity and may sacrifice readability.