Recursion Made Simple: Understanding the Concept with Examples

Recursion is a concept used in computer programming that can be quite difficult to understand, even for adults. However, I will do my best to explain it in a way that a five-year-old can understand. In this article, we will cover the basics of recursion, including what it is, how it works, and some examples of how it can be used.

What is recursion?

Recursion is a concept in computer programming that involves calling a function from within itself. This may sound confusing at first, but let me explain with an analogy.

Imagine that you have a set of nesting dolls, where each doll is smaller than the one before it. When you open up the largest doll, you find another doll inside, and so on, until you reach the smallest doll. In computer programming, recursion works in a similar way. When a function calls itself, it creates a new instance of itself within the current instance.

How does recursion work?

To understand how recursion works, let’s take a look at a simple example. Imagine that you are trying to count the number of fingers on your hand. You might start by counting one finger at a time, but you could also use recursion to count them all at once. Here’s how it would work:

1. Hold up your hand and look at your fingers.
2. Count the number of fingers on one hand (let’s say you have 5).
3. Now, instead of counting the fingers on your other hand separately, you can use recursion to count them all at once.
4. Hold up your other hand and look at your fingers.
5. Call the same function that you used to count the fingers on the first hand.
6. When the function is called again, it will count the fingers on the second hand and return the result to the first instance of the function.
7. The first instance of the function will then add the two counts together to get the total number of fingers on both hands.

This example demonstrates how recursion works by breaking a problem down into smaller subproblems and solving them individually before combining the results.

Examples of recursion

Now that we have a basic understanding of what recursion is and how it works, let’s take a look at some examples of how it can be used in computer programming.

Fibonacci sequence:

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding numbers. The sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. To generate the nth number in the sequence, you can use a recursive function that calls itself with the two preceding numbers as arguments. Here’s an example in Python:

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

This function uses recursion to generate the nth number in the Fibonacci sequence by adding together the two preceding numbers. If the input is 0 or 1, the function returns the input. Otherwise, it calls itself twice with the preceding numbers and adds them together.

Factorial:

The factorial of a positive integer n is the product of all positive integers less than or equal to n. For example, the factorial of 5 is 5 x 4 x 3 x 2 x 1 = 120. You can calculate the factorial of a number using a recursive function that calls itself with n-1 as the argument until it reaches 1. Here’s an example in Python:

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

This function uses recursion to calculate the factorial of a number by multiplying the input by the factorial of the input minus one. If the input is 1, the function returns 1. Otherwise, it calls itself with n-1 as the argument and multiplies the result by n.

Binary search:

Binary search is an algorithm for searching a sorted list by repeatedly dividing the search interval in half. You can implement binary search using a recursive function that calls itself with the updated search interval until it finds the target value or determines that the value is not in the list. Here’s an example in Python:

def binary_search(arr, low, high, target):
  if high >= low:
    mid = (high + low) // 2
    if arr[mid] == target:
      return mid
    elif arr[mid] > target:
      return binary_search(arr, low, mid-1, target)
    else:
      return binary_search(arr, mid+1, high, target)
  else:
    return -1

This function uses recursion to implement binary search by dividing the search interval in half and calling itself with the updated interval based on whether the target value is greater than or less than the middle element. If the target value is found, the function returns its index. Otherwise, it returns -1.

Conclusion

In conclusion, recursion is a concept in computer programming that involves calling a function from within itself. It can be used to break down complex problems into smaller subproblems and solve them individually before combining the results. Some examples of how recursion can be used in computer programming include generating the Fibonacci sequence, calculating the factorial of a number, and implementing binary search. Although recursion can be difficult to understand at first, it is a powerful tool that can be used to write efficient and elegant code.