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Concept visual
Recursion is when a function calls itself. Recursion is a common mathematical and programming concept. It means that a function calls itself. This has the benefit of meaning that you can loop through data to reach a result. The developer should be very careful with recursion as it can be quite easy to slip into writing a function which never terminates, or one that uses excess amounts of memory or processor power.
Formula
However, when written correctly recursion can be a very efficient and mathematically - elegant approach to programming.A simple recursive function that counts down from 5:
def countdown(n):
if n <= 0:
print("Done!")
else:
print(n)Formula
countdown(n - 1)countdown(5)
Every recursive function must have two parts: A base case - A condition that stops the recursion A recursive case - The function calling itself with a modified argument Without a base case, the function would call itself forever, causing a stack overflow error.
Identifying base case and recursive case:
def factorial(n):
# Base case if n == 0 or n == 1:
return 1
# Recursive case else:
return n * factorial(n - 1)
print(factorial(5))The base case is crucial. Always make sure your recursive function has a condition that will eventually be met.
The Fibonacci sequence is a classic example where each number is the sum of the two preceding ones. The sequence starts with 0 and 1: 0, 1, 1, 2, 3, 5, 8, 13, ... The sequence continues indefinitely, with each number being the sum of the two preceding ones. We can use recursion to find a specific number in the sequence:
Find the 7th number in the Fibonacci sequence:
def fibonacci(n):
if n <= 1:
return n else:
return fibonacci(n - 1) + fibonacci(n - 2)
print(fibonacci(7))Recursion can be used to process lists by handling one element at a time:
Calculate the sum of all elements in a list:
def sum_list(numbers):
if len(numbers) == 0:
return 0 else:
return numbers[0] + sum_list(numbers[1:])
my_list = [1, 2, 3, 4, 5]
print(sum_list(my_list))Find the maximum value in a list:
def find_max(numbers):
if len(numbers) == 1:
return numbers[0]
else:Formula
max_of_rest = find_max(numbers[1:])return numbers[0] if numbers[0] > max_of_rest else max_of_rest my_list = [3, 7, 2, 9, 1]
print(find_max(my_list))Python has a limit on how deep recursion can go. The default limit is usually around 1000 recursive calls.
import sys print(sys.getrecursionlimit())If you need deeper recursion, you can increase the limit, but be careful as this can cause crashes:
Example import sys sys.setrecursionlimit(2000)
print(sys.getrecursionlimit())Increasing the recursion limit should be done with caution. For very deep recursion, consider using iteration instead.