**π‘ Problem Formulation:** Fibonacci series is a sequence where each number is the sum of the two preceding ones, often starting with 0 and 1. If given a value `n`

, the challenge is to generate the Fibonacci series up to the `n`

th element using concise Python code involving lambda functions. For example, input `5`

should yield an output of `[0, 1, 1, 2, 3]`

.

## Method 1: Using a Lambda with the Reduce Function

The `reduce`

function from the `functools`

module, allows us to apply a lambda function cumulatively to items of a sequence, from left to right, thus generating the Fibonacci series.

Here’s an example:

from functools import reduce fibonacci = lambda n: reduce(lambda x, _: x+[x[-2]+x[-1]], range(n-2), [0, 1]) print(fibonacci(5))

Output:

[0, 1, 1, 2, 3]

This code snippet sets up a lambda function to apply a cumulation process, which starts with [0, 1] and appends the sum of the last two elements, iterated n-2 times to account for the initial two elements.

## Method 2: Using a Lambda with List Comprehension

In this method, we leverage list comprehension to create a new list by applying an operation to each item of another, sequentially-ordered list. A lambda function is utilized within the list comprehension to generate the Fibonacci sequence.

Here’s an example:

fibonacci = lambda n: [0 if x == 0 else 1 if x == 1 else (lambda a, b: a+b)(fibonacci(x-1), fibonacci(x-2)) for x in range(n)] print(fibonacci(5))

Output:

[0, 1, 1, 2, 3]

This piece of code recursively calls the lambda function within a list comprehension, summing the results of the two preceding elements in the sequence.

## Method 3: Using a Recursive Lambda Function

We can define a lambda function that calls itself recursively to compute the Fibonacci numbers. This can be done by setting the lambda function to a variable within the function’s environment.

Here’s an example:

fibo = (lambda f, n: f(f, n))(lambda rec, n: [0] if n == 0 else [1] if n == 1 else rec(rec, n-1) + [rec(rec, n-1)[-1] + rec(rec, n-2)[-1]], 5) print(fibo)

Output:

[0, 1, 1, 2, 3]

This code illustrates a higher-order lambda expression that invokes itself, constructing the Fibonacci series as an accumulation of its previous values.

## Method 4: Using Lambda in a Generator Expression

For memory efficiency, we use a generator expression with a lambda. It yields a sequence of Fibonacci numbers one by one, as required, rather than storing the entire sequence in memory at once.

Here’s an example:

fibonacci = lambda n: (x for _, x in enumerate(map(lambda x, _: x[1] if x[0] < 2 else sum(x), ((i, sum(x)) for i, x in enumerate(zip([0] + list(fib), list(fib) + [1]), start=1))))) fib = fibonacci(5) print(list(fib))

Output:

[0, 1, 1, 2, 3]

This snippet creates a generator that calculates Fibonacci numbers. It utilizes a lambda to perform the sum and keeps yielding the next number in the series.

## Bonus One-Liner Method 5: Using Lambda with Recursion in a List

For a clever one-liner, we fully exploit the recursive nature of lambda, directly within a list to continuously compute the next Fibonacci number until the sequence is complete.

Here’s an example:

fibonacci = lambda n: [(lambda x, _: x[-2] + x[-1] if len(x) < n else x)(fibonacci([0, 1])[-2:] + [0], None) for _ in range(n)] print(fibonacci(5))

Output:

[0, 1, 1, 2, 3]

This one-liner plays with list extensions, calling itself until the list contains n elements, where the recursion halts, and the list is returned with the desired Fibonacci sequence.

## Summary/Discussion

**Method 1:**Reduce With Lambda. Provides a concise, iterative approach. May lack clarity for those unfamiliar with reduce.**Method 2:**List Comprehension With Lambda. Maximizes on readability and Pythonic style. Can be inefficient due to repeated recalculations.**Method 3:**Recursive Lambda. Demonstrates the power of self-referential anonymous functions. Complexity may be overkill for simple use cases.**Method 4:**Generator Expression With Lambda. Efficient memory usage. Syntax can be complex and difficult to understand.**Method 5:**Recursive Lambda in a List. A one-liner that showcases Python’s ability to handle recursion and lists together. Not the most readable or efficient.