**π‘ Problem Formulation:** We aim to solve the challenge of computing the maximum average pass ratio from a collection of statistics. The typical input would be a list of tuples, where each tuple represents a school’s pass and total student count, like `[(20, 30), (50, 60), (45, 50)]`

. Our goal is to find the highest average pass ratio of the provided schools, which for this example, would be the ratio `45/50`

as the output.

## Method 1: Using Basic Loop and Division

This method involves iterating over each tuple, calculating the pass ratio, and updating a variable to store the maximum value found. It is simple and intuitive, making it an excellent choice for beginners to understand the mechanics behind finding a maximum average.

Here’s an example:

def max_pass_ratio(pass_totals): max_ratio = 0 for passed, total in pass_totals: ratio = passed / total max_ratio = max(max_ratio, ratio) return max_ratio schools = [(20, 30), (50, 60), (45, 50)] print(max_pass_ratio(schools))

Output: `0.9`

This snippet defines a function `max_pass_ratio()`

that accepts a list of tuples. It loops through each tuple, calculates the ratio of passes to total, and compares it with the current maximum ratio, updating it when a new maximum is found.

## Method 2: Using List Comprehension and the Max Function

Python’s list comprehensions and the built-in `max()`

function allow for a more concise and idiomatic approach to finding the maximum average pass ratio. This method reduces the line of code and makes the program more Pythonic.

Here’s an example:

schools = [(20, 30), (50, 60), (45, 50)] max_ratio = max(p / t for p, t in schools) print(max_ratio)

Output: `0.9`

The code snippet uses list comprehension to generate a list of pass ratios and immediately applies the `max()`

function to find the highest ratio. It is a more succinct version of Method 1.

## Method 3: Using the Reduce Function from functools

The `reduce()`

function from the `functools`

module can be used to carry out a rolling computation to find the maximum ratio. Itβs more complex but shows an alternative functional programming approach in Python.

Here’s an example:

from functools import reduce def reducer(max_ratio, school): p, t = school return max(max_ratio, p / t) schools = [(20, 30), (50, 60), (45, 50)] max_ratio = reduce(reducer, schools, 0) print(max_ratio)

Output: `0.9`

The code defines a `reducer()`

function that finds the maximum ratio when called iteratively on each tuple from the list. `reduce()`

applies `reducer()`

across the `schools`

list, starting with an initial maximum ratio of 0.

## Method 4: Using NumPy for Large Datasets

For larger datasets, NumPy’s vectorized operations can be significantly faster. This method involves treating the problem as an array operation, which is both efficient and scalable.

Here’s an example:

import numpy as np schools = np.array([(20, 30), (50, 60), (45, 50)]) ratios = schools[:, 0] / schools[:, 1] max_ratio = np.max(ratios) print(max_ratio)

Output: `0.9`

This snippet creates a NumPy array from the list of tuples. It then calculates the ratios of all schools at once with a vectorized division operation and applies `np.max()`

to find the highest ratio.

## Bonus One-Liner Method 5: Using Generator Expression

A more Pythonic one-liner solution applies a generator expression directly within the `max()`

function, resulting in clean and efficient code.

Here’s an example:

print(max(p/t for p, t in [(20, 30), (50, 60), (45, 50)]))

Output: `0.9`

Here, the generator expression calculates the pass ratio for each school inline, with the `max()`

function consuming the generated values to find the highest ratio.

## Summary/Discussion

**Method 1: Basic Loop and Division.**Easy to understand and implement. Can be slow for large datasets. No external dependencies.**Method 2: List Comprehension and Max Function.**Short and Pythonic. Good balance of readability and brevity. Not as efficient for very large lists.**Method 3: Reduce Function from functools.**Functional programming approach. Somewhat more complex syntax. May be less intuitive for those unfamiliar with functional programming.**Method 4: Using NumPy for Large Datasets.**Very performant for large datasets. Requires NumPy, which may not be suitable for all environments.**Bonus Method 5: Generator Expression.**Extremely concise and efficient. Excellent for one-off calculations or when input data is straightforward.