**π‘ Problem Formulation:** Imagine a scenario where astronauts are stranded on a distant planet and you are tasked with writing a Python program that calculates the minimum number of rocketships needed for their rescue. Given the total number of astronauts and the maximum capacity of a rocketship, the goal is to find the least number of rocketships required to bring all astronauts back safely. For instance, if there are 50 astronauts and each rocketship can carry a maximum of 8 astronauts, the program should output 7 rocketships.

## Method 1: Using Ceiling Division

This method involves taking the total number of astronauts and dividing it by the maximum capacity of a rocketship, rounding up to the nearest whole number, since you cannot have a fraction of a rocketship. The `math.ceil()`

function from Python’s standard library is perfect for this task.

Here’s an example:

import math def count_rockets(astronauts, capacity): return math.ceil(astronauts / capacity) rockets_needed = count_rockets(50, 8) print(rockets_needed)

Output: 7

This code snippet defines a function called `count_rockets()`

that calculates the minimum number of rocketships needed. It uses the `math.ceil()`

function to ensure the number of rockets is always rounded up to the nearest whole number. This method is straightforward and efficient for the given problem.

## Method 2: Using The Modulus Operator

In this approach, the modulus operator (%) is used to determine whether additional rocketships are needed if astronauts do not perfectly fill up the available seats. If any astronauts remain after filling the last rocketship, one more rocketship will be added.

Here’s an example:

def count_rockets(astronauts, capacity): full_rockets = astronauts // capacity return full_rockets + bool(astronauts % capacity) rockets_needed = count_rockets(50, 8) print(rockets_needed)

Output: 7

The code defines a function `count_rockets()`

that first determines the integer division (floor division) of astronauts by rocket capacity. It then uses the modulus operator to check for any remaining astronauts and adds an additional rocket if required. This method is simple and does not require importing additional modules.

## Method 3: Using Floor Division and Conditional Increment

This method is similar to Method 2, but it explicitly checks if there is a remainder after dividing the astronauts by capacity and conditionally increments the rocketship counter.

Here’s an example:

def count_rockets(astronauts, capacity): rockets = astronauts // capacity if astronauts % capacity != 0: rockets += 1 return rockets rockets_needed = count_rockets(50, 8) print(rockets_needed)

Output: 7

The function `count_rockets()`

performs floor division to find the number of fully occupied rocketships and then adds one more rocketship if there’s any remainder when dividing the number of astronauts by the rocketship capacity. This method is very explicit and clear in its intention.

## Method 4: Using a Generator and Summing

By using a generator expression within the `sum()`

function, we can iterate through a hypothetical list representing slots on rocketships and count how many are needed.

Here’s an example:

def count_rockets(astronauts, capacity): return sum(1 for _ in range(0, astronauts, capacity)) rockets_needed = count_rockets(50, 8) print(rockets_needed)

Output: 7

This snippet uses a generator expression inside the `sum()`

function to iterate over a range from 0 to the number of astronauts, stepping by the capacity of a rocketship, effectively simulating the filling of each rocketship and counting them. This method is a bit more abstract but works well for large numbers.

## Bonus One-Liner Method 5: Using Integer Division and Logical Operators

A concise one-liner that leverages integer division and logical OR operator to round up without explicitly using conditional statements or the `math.ceil()`

function.

Here’s an example:

count_rockets = lambda astronauts, capacity: (astronauts // capacity) + (astronauts % capacity > 0) rockets_needed = count_rockets(50, 8) print(rockets_needed)

Output: 7

The one-liner defines a lambda function that does an integer division to count the full rocketships and adds one if thereβs any remainder-this is determined by a simple comparison operation, making it concise yet clear.

## Summary/Discussion

**Method 1:**Using Ceiling Division. Strengths: very simple and intuitive to understand. Weaknesses: requires importing the`math`

module.**Method 2:**Using The Modulus Operator. Strengths: simple and does not require any external modules. Weaknesses: boolean casting may not be immediately obvious to beginners.**Method 3:**Using Floor Division and Conditional Increment. Strengths: Explicit logic that’s easy to follow. Weaknesses: Slightly more verbose than other one-liners.**Method 4:**Using a Generator and Summing. Strengths: Efficient for large numbers, leveraging Python’s generator expressions. Weaknesses: Abstract concept that may not be readily understood by new programmers.**Method 5:**Bonus One-Liner Using Integer Division and Logical Operators. Strengths: Extremely concise. Weaknesses: May sacrifice some readability for the sake of brevity.