1. Introduction

In this tutorial, we're going to explore the concept of recursion in C++. Recursion is a powerful tool in programming. It's a technique where a function calls itself in its own definition. If used correctly, recursion can make your code shorter and easier to understand.

By the end of this tutorial, you will:
- Understand what recursion is
- Learn how to implement recursive functions in C++
- Be able to solve problems using recursion

To get the most out of this tutorial, you should have a basic understanding of:
- C++ syntax and data types
- Function declaration and definition in C++
- Conditional statements (if, else) in C++

2. Step-by-Step Guide

Recursion is a process where a function calls itself as a subroutine. This allows the function to be repeated several times, as it can call itself during its execution.

The concept might seem complex at first, but it's actually pretty simple once you understand it. Let's break it down:

Base Case

The base case is a condition in the recursive function that does not result in a further recursive call. It's a way to stop the recursion. Without a base case, the function would call itself indefinitely, resulting in an infinite loop.

Recursive Case

The recursive case is the condition in which the function calls itself, thus performing the recursion.

3. Code Examples

Let's look at an example to understand recursion better.

#include <iostream>

// Our recursive function
int factorial(int n) {
    // Base case
    if (n == 0) {
        return 1;
    }
    // Recursive case
    else {
        return n * factorial(n - 1);
    }
}

int main() {
    int number = 5;
    std::cout << "The factorial of " << number << " is " << factorial(number);
    return 0;
}

In the code above, the function factorial() computes the factorial of a number by calling itself. The base case is n == 0, which returns 1. The recursive case is n * factorial(n - 1), which performs the recursion. The expected output of this code is The factorial of 5 is 120.

4. Summary

In this tutorial, we've learned about recursion in C++, how to implement it, and how to use it to solve problems. We've seen that a recursive function needs a base case to stop the recursion and a recursive case to execute the recursion. We've also learned that recursion can be a powerful tool to make our code shorter and easier to understand.

For further learning, you could look into more complex uses of recursion, such as recursive algorithms for sorting and searching.

5. Practice Exercises

Now, let's practice what we've learned with some exercises:

Exercise 1

Write a recursive function that computes the Fibonacci sequence up to a given number.

Exercise 2

Write a recursive function that prints the binary representation of a given non-negative integer.

Solutions

// Solution to Exercise 1
int fibonacci(int n) {
    if (n <= 1) {
        return n;
    }
    else {
        return fibonacci(n - 1) + fibonacci(n - 2);
    }
}

// Solution to Exercise 2
void printBinary(int n) {
    if (n > 1) {
        printBinary(n / 2);
    }
    std::cout << n % 2;
}

In the first solution, the base case is n <= 1, which returns n. The recursive case is fibonacci(n - 1) + fibonacci(n - 2), which performs the recursion.

In the second solution, the base case is when n becomes 0 or 1, and the binary representation is printed. The recursive case is printBinary(n / 2), where we continue to divide n by 2 to get the binary representation.

Keep practicing recursion with different problems to get more comfortable with the concept. Happy coding!