Starting with recursion in python
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introduction to recursion in python
recursion is a programming technique where a function calls itself in order to solve a problem. it is often used to solve problems that can be broken down into smaller, simpler sub-problems. a recursive function typically has two main components:
1. **base case**: this stops the recursion when a certain condition is met, preventing infinite loops.
2. **recursive case**: this is the part of the function where the function calls itself with modified arguments.
when to use recursion
recursion is particularly useful for problems that can be divided into similar sub-problems, like:
factorials
fibonacci sequences
tree traversals
solving puzzles like the tower of hanoi
example: factorial calculation
let's start with a classic example: calculating the factorial of a number.
the factorial of a non-negative integer \( n \) is the product of all positive integers less than or equal to \( n \). it is denoted by \( n! \).
#### mathematical definition:
\( 0! = 1 \) (base case)
\( n! = n \times (n-1)! \) for \( n 0 \) (recursive case)
implementation in python
here's how you can implement a recursive function to calculate the factorial of a number in python:
explanation of the code
1. **base case**: the function checks if \( n \) is 0. if it is, it returns 1, as \( 0! \) is defined to be 1.
2. **recursive case**: if \( n \) is greater than 0, the function returns \( n \) multiplied by the factorial of \( n-1 \). this means the function keeps calling itself with decremented values of \( n \) until it reaches the base case.
visualizing the recursion
if you call `factorial(5)`, the following calls happen:
`factorial(5)` → returns \( 5 \times factorial(4) \)
`factorial(4)` → returns \( 4 \times factorial(3) \)
`factorial(3)` → returns \( 3 \times factorial(2) \)
`factorial(2)` → returns \( 2 \times factorial(1) \)
`factorial(1)` → returns \( 1 \times factorial(0) \)
`factorial(0)` → ...
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