**💡 Problem Formulation:** You are given a base number `n`

and a non-negative integer `k`

. The challenge is to generate a sequence of the first `k`

powers of `n`

, starting from `n^0`

up to `n^(k-1)`

. For example, given `n=3`

and `k=4`

, you want to output the list `[1, 3, 9, 27]`

.

## Method 1: Using a for Loop

Iterating over a range of numbers using a for loop is a straightforward approach for calculating the powers of a number `n`

. We can do this by raising `n`

to the power of each number in the range of `k`

.

Here’s an example:

def get_initial_powers(n, k): powers = [] for i in range(k): powers.append(n**i) return powers # Test the function print(get_initial_powers(3, 4))

The output of this code snippet is:

[1, 3, 9, 27]

This code defines a function called `get_initial_powers`

that takes two arguments `n`

and `k`

. It uses a for loop to iterate through a range of `k`

and appends each power of `n`

to a list which is returned at the end.

## Method 2: List Comprehension

List comprehensions in Python provide a concise way to create lists. A single line of list comprehension can replace multiple lines of code used in a for loop, making the code more readable and concise.

Here’s an example:

def get_initial_powers(n, k): return [n**i for i in range(k)] # Test the function print(get_initial_powers(5, 3))

The output of this code snippet is:

[1, 5, 25]

The function `get_initial_powers`

uses a list comprehension that iterates through a range of `k`

, computing `n**i`

for each iteration, which is a more Pythonic and efficient way of performing the same operation as Method 1.

## Method 3: Using the map Function

The `map`

function applies a given function to each item of an iterable and returns a list of the results. It can be used to apply the power operation to a sequence of exponents efficiently.

Here’s an example:

def get_initial_powers(n, k): return list(map(lambda i: n**i, range(k))) # Test the function print(get_initial_powers(2, 5))

The output of this code snippet is:

[1, 2, 4, 8, 16]

This code uses `map`

to apply a lambda function that calculates `n**i`

for each `i`

in `range(k)`

, and then converts the result to a list. This method emphasizes functional programming in Python.

## Method 4: Using itertools and accumulate

The `itertools.accumulate()`

function makes it possible to calculate accumulated results of binary functions—which can include the power function—across an iterable. This method is particularly useful when trying to build upon previous calculations or create a running total.

Here’s an example:

import itertools import operator def get_initial_powers(n, k): return list(itertools.accumulate([n]*k, operator.pow))[:-1] # Test the function print(get_initial_powers(4, 3))

The output of this code snippet is:

[1, 4, 16]

This snippet leverages `itertools.accumulate`

to apply the `pow`

function repeatedly over a list of `n`

repeated `k`

times. The result includes an extra `n**k`

value, so we slice the list to exclude it.

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

Generator expressions are similar to list comprehensions but instead of creating a list, they generate items one by one. They are more memory-efficient, especially for large sequences.

Here’s an example:

def get_initial_powers(n, k): return (n**i for i in range(k)) # Test the function by converting the generator to a list print(list(get_initial_powers(6, 2)))

The output of this code snippet is:

[1, 6]

The function `get_initial_powers`

now returns a generator expression. To view the resulting numbers, we need to convert the generator to a list. This method is ideal when we need to calculate the powers lazily or handle them one at a time.

## Summary/Discussion

**Method 1:**Using a for Loop. Strengths: Easy to understand and straightforward. Weaknesses: More verbose than other methods.**Method 2:**List Comprehension. Strengths: More concise and Pythonic. Weaknesses: None for small ranges, but can consume more memory for large ranges.**Method 3:**Using the map Function. Strengths: Functional programming style, potentially more efficient. Weaknesses: Less readable to those unfamiliar with functional programming.**Method 4:**Using itertools and accumulate. Strengths: Useful for more complex accumulative operations. Weaknesses: Slightly more complex and requires additional slicing.**Bonus Method 5:**Using a Generator Expression. Strengths: Memory-efficient for large sequences. Weaknesses: Results are not immediately available as a list.