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.