Basic problems in recursion.

Title: "My Journey into Recursion: Day 5 of #100DaysOfCode Challenge"

Recursion: Unveiling the Elegance of Divide and Conquer

On the fifth day of my #100DaysOfCode challenge, I learnt about basic problems in recursion.

Here are 10 fundamental problems I explored, each unlocked with the magic of recursion:

1. Factorial: Problem: Calculate the factorial of a non-negative integer. Explanation: The factorial of an integer n is the product of all positive integers from 1 to n. Code:

    def factorial(n):
        if n == 0:
            return 1
        else:
            return n * factorial(n - 1)
   

2. Fibonacci Sequence: Problem: Generate the nth Fibonacci number. Explanation: The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. Code:

    def fibonacci(n):
        if n <= 1:
            return n
        else:
            return fibonacci(n - 1) + fibonacci(n - 2)
   

3. Sum of Digits: Problem: Find the sum of the digits of a positive integer. Explanation: Recursively sum the digits of the integer. Code:

    def sum_of_digits(n):
        if n < 10:
            return n
        else:
            return n % 10 + sum_of_digits(n // 10)
   

4. Exponentiation: Problem: Calculate the result of x raised to the power of y. Explanation: Use recursion to repeatedly multiply x by itself y times. Code:

    def power(x, y):
        if y == 0:
            return 1
        else:
            return x * power(x, y - 1)
   

They are certainly amazing to learn the basics of recursion and get a hang of it.