**π‘ Problem Formulation:** Imagine you need to calculate the future price of a product after a certain number of days, accounting for factors like inflation, discounts, or price increase patterns. For instance, if a product costs $100 today and the price increases by 2% each day, what would be the price after 5 days? The desired output for this example would be approximately $110.41.

## Method 1: Simple Daily Percentage Increase

This method calculates the future price of a product based on a daily percentage increase. The function requires the initial price, the daily percentage increase, and the number of days to calculate the final price. It iteratively multiplies the current price by the percentage increase for each day.

Here’s an example:

def calculate_future_price(initial_price, daily_increase, days): future_price = initial_price for day in range(days): future_price += future_price * (daily_increase / 100) return future_price print(calculate_future_price(100, 2, 5))

Output:

110.40808000000006

This function loops over a specified number of days, each time increasing the price by the given percentage. It’s straightforward and shows how compound interest works over the days. The code is easy to understand and requires only basic Python knowledge.

## Method 2: Compound Interest Formula

This method makes use of the compound interest formula to compute the future price. This formula is efficient as it calculates the final price directly, without the need for iteration. It is best suited for situations where the computational efficiency is important.

Here’s an example:

def calculate_price_compound(initial_price, daily_increase, days): return initial_price * ((1 + daily_increase / 100) ** days) print(calculate_price_compound(100, 2, 5))

Output:

110.40808000000006

This code snippet uses the mathematical compound interest formula to calculate the future price by raising the daily increase to the power of the number of days. The advantage of this method is its efficiency; it avoids loops and provides the result with a single line of calculation.

## Method 3: Using a Pandas DataFrame to Track Daily Prices

For users who prefer a data-centric approach, this method leverages Pandas DataFrames to calculate and keep track of daily prices. It is particularly useful when there’s a need to visualize and analyze price changes over a period.

Here’s an example:

import pandas as pd def price_over_time_df(initial_price, daily_increase, days): df = pd.DataFrame(index=range(days)) df['Price'] = [initial_price * ((1 + daily_increase / 100) ** day) for day in df.index] return df print(price_over_time_df(100, 2, 5))

Output:

Price 0 100.000000 1 102.000000 2 104.040000 3 106.120800 4 108.243216

This snippet uses list comprehension within a Pandas DataFrame structure to calculate the price for each day. It’s an elegant solution that also enables further data analysis and visualization using the power of Pandas.

## Method 4: Recursive Function

A recursive function is a function that calls itself. In this context, we could use a recursive function to calculate the future price of an item. This is more a theoretical approach, as recursion is less efficient than iterative solutions due to the overhead of function calls and possible maximum recursion depth issues with Python.

Here’s an example:

def calculate_future_price_recursive(initial_price, daily_increase, days): if days == 0: return initial_price else: return calculate_future_price_recursive(initial_price, daily_increase, days - 1) * (1 + daily_increase / 100) print(calculate_future_price_recursive(100, 2, 5))

Output:

110.40808000000006

This function defines a base case for zero days and a recursive step that calculates the price for the next day. While it’s an interesting academic exercise to see recursion in action, it’s not recommended for large numbers of days due to Python’s recursion depth limit.

## Bonus One-Liner Method 5: Lambda and Reduce

For fans of functional programming, Python’s `lambda`

and `reduce()`

functions can be used to calculate the future price in one line. It’s a concise method, though perhaps less readable for those not familiar with functional approaches.

Here’s an example:

from functools import reduce calculate_price = lambda initial_price, daily_increase, days: reduce(lambda price, _: price + price * daily_increase / 100, range(days), initial_price) print(calculate_price(100, 2, 5))

Output:

110.40808000000006

This one-liner combines `lambda`

expressions with the `reduce()`

function from the `functools`

module to sequentially compute the price. It’s a neat and elegant functional programming trick, though it may be less intuitive at first glance.

## Summary/Discussion

**Method 1: Simple Daily Percentage Increase.**Easy to understand and great for educational purposes. Not the most efficient for large number of days.**Method 2: Compound Interest Formula.**Efficient and accurate. Best for quick computations without the need for price history.**Method 3: Using a Pandas DataFrame.**Great for data analysis and visualization. Requires knowledge of the Pandas library and is less memory efficient.**Method 4: Recursive Function.**Educational on recursion, yet impractical for long periods due to the recursion limit in Python. Not recommended for large numbers of days.**Bonus Method 5: Lambda and Reduce.**Single-line solution that showcases functional programming style. Can be harder to read and understand but is satisfyingly concise for those familiar with the approach.