**π‘ Problem Formulation:** Our goal is to determine the highest altitude that a hiker reaches on a hike as given by a list of relative heights (gains or losses). For example, if we have the list of changes in altitude `[1, -1, 5, -2]`

, the highest point reached would be 5 (starting from 0 and adding each change one by one).

## Method 1: Brute Force Iteration

This method involves initializing an accumulator to keep track of the current altitude, and simply iterating through each altitude change in the list. At every step, the accumulator is updated and a separate variable keeps track of the highest altitude reached.

Here’s an example:

altitude_changes = [1, -1, 5, -2] current_altitude = highest_altitude = 0 for change in altitude_changes: current_altitude += change highest_altitude = max(highest_altitude, current_altitude) print(highest_altitude)

Output: 5

This method systematically checks the altitude after each change, ensuring that the highest point is accounted for, which is robust and straightforward in understanding.

## Method 2: Using Python’s Built-in max() Function

With this approach, we accumulate the altitude change at each step and use Pythonβs `max()`

function to maintain the highest altitude seen so far. This is similar to the brute force method but streamlined using the max function.

Here’s an example:

altitude_changes = [1, -1, 5, -2] print(max(0, max([sum(altitude_changes[:i+1]) for i in range(len(altitude_changes))])))

Output: 5

Here the list comprehension builds a list of the current altitude at each change, and then we find the maximum value within this list. It’s more Pythonic and compact but slightly less efficient due to the creation of an intermediate list.

## Method 3: Cumulative Sum with itertools.accumulate()

This method leverages the `itertools.accumulate()`

function to create a running total of the altitudes. By applying `max()`

on the result, we find the highest altitude achieved.

Here’s an example:

from itertools import accumulate altitude_changes = [1, -1, 5, -2] highest_altitude = max(0, max(accumulate(altitude_changes))) print(highest_altitude)

Output: 5

This code snippet is elegant and utilizes itertools, a powerful module in the Python standard library known for efficient looping capabilities. This method is memory efficient since `accumulate()`

generates values on the fly.

## Method 4: Using a Custom Function

Creating a custom function that encapsulates the logic gives reusability and better structure to the code. This function iterates through each altitude change, just as in Method 1, but keeps all related logic encapsulated in a function.

Here’s an example:

def find_highest_altitude(altitude_changes): highest_altitude = current_altitude = 0 for change in altitude_changes: current_altitude += change highest_altitude = max(highest_altitude, current_altitude) return highest_altitude altitude_changes = [1, -1, 5, -2] print(find_highest_altitude(altitude_changes))

Output: 5

The custom function, `find_highest_altitude`

, can be easily understood and reused with various input data. It provides clear separation of logic, making the code maintainable.

## Bonus One-Liner Method 5: Using Python List Comprehension and max() Function

This one-liner combines the elegance of list comprehensions with the utility of the `max()`

function to achieve a concise yet powerful statement to find the highest altitude.

Here’s an example:

print(max(0, max([sum(altitude_changes[:i+1]) for i, _ in enumerate(altitude_changes)])))

Output: 5

Despite being a one-liner, this code is somewhat less readable due to its density. However, for Python enthusiasts who appreciate brevity and inline expressiveness, this is an efficient and nifty approach.

## Summary/Discussion

**Method 1: Brute Force Iteration.**Strengths: Simplicity, no dependencies. Weaknesses: Verbosity compared to other methods.**Method 2: Built-in max() Function.**Strengths: Pythonic, concise. Weaknesses: Higher memory usage with large datasets due to list creation.**Method 3: itertools.accumulate().**Strengths: Efficient memory usage, elegant. Weaknesses: Less readable for those unfamiliar with itertools module.**Method 4: Custom Function.**Strengths: Reusability, maintainability. Weaknesses: Overhead of function definition for simple tasks.**Bonus Method 5: One-Liner.**Strengths: Brevity, in-line. Weaknesses: Potentially lower readability.