Recursion: Solving Problems through Recursive Functions

 

Problem 1: Print Your Name n Times

Let's start with a simple problem: printing your name n times using recursion. The generic way to achieve this would be to run a for loop and print your name n times. However, in this case, we want to use recursion.

To solve this problem, we will define a recursive function called f(i, n). The function takes two parameters: i, which represents the current iteration, and n, which represents the total number of times to print your name.

We start by taking the input of n from the user. Then, we call the function f(0, n), which will recursively print your name n times.

Here's how the function works:

1. Check if i is greater than n. If it is, return.
2. Print your name.
3. Call the function f(i + 1, n) to recursively print your name n times.

By following these steps, we can easily print your name n times using recursion.

Problem 2: Print Numbers from 1 to n

Next, let's solve a problem where we need to print numbers from 1 to n in a linear fashion. Again, we will use recursion to achieve this.

Similar to the previous problem, we define a recursive function called f(i, n). The function takes two parameters: i, which represents the current number, and n, which represents the last number to be printed.

We start by taking the input of n from the user. Then, we call the function f(1, n), which will recursively print numbers from 1 to n.

Here's how the function works:

1. Check if i is greater than n. If it is, return.
2. Print i.
3. Call the function f(i + 1, n) to recursively print the next number.

By following these steps, we can easily print numbers from 1 to n using recursion.

Problem 3: Print Numbers from n to 1

Now, let's solve a problem where we need to print numbers from n to 1. Again, we will use recursion, but this time with a slight twist.

Similar to the previous problems, we define a recursive function called f(i, n). The function takes two parameters: i, which represents the current number, and n, which represents the last number to be printed.

We start by taking the input of n from the user. Then, we call the function f(n, n), which will recursively print numbers from n to 1.

Here's how the function works:

1. Check if i is less than 1. If it is, return.
2. Call the function f(i - 1, n) to recursively print the next number.
3. Print i.

By following these steps, we can easily print numbers from n to 1 using recursion.

Problem 4: Challenge - Print Numbers from 1 to 1

For the last problem, I have a challenge for you. What if I ask you to print numbers from 1 to 1, but without using i + 1 in the function call? Can you figure out how to solve this problem?

I'll leave this challenge up to you. I want you to think about it and try to come up with a solution. Feel free to share your answer in the comments below. Remember, the goal is to print numbers from 1 to 1 without using the i + 1 function call.

Conclusion

Recursion is a powerful concept that allows us to solve complex problems by breaking them down into simpler subproblems. In this lecture, we explored the basics of recursion and solved some basic recursion problems. We learned how to print our name multiple times, print numbers in a linear fashion, and print numbers in reverse order using recursion.