# What Are the Types of Recursion in Data Structure?

//

Heather Bennett

Recursion is a powerful concept in computer science and plays a significant role in data structures. It allows a function to call itself repeatedly until a specific condition is met.

This technique can simplify complex problems and improve code readability. In this article, we will explore the different types of recursion commonly used in data structures.

## 1. Direct Recursion:

Direct recursion is the most straightforward type of recursion, where a function calls itself directly. Let’s consider an example of calculating the factorial of a number using direct recursion:

``````
function factorial(n)
{
if (n === 0) {
return 1;
} else {
return n * factorial(n - 1);
}
}
```
```

In this example, the factorial() function calls itself with the argument n – 1. It continues to do so until it reaches the base case when n === 0. The function then returns the final result by multiplying n with the factorial of n – 1.

## 2. Indirect Recursion:

Indirect recursion occurs when a function calls another function that eventually calls back the original function. This type of recursion involves multiple functions working together to solve a problem.

Let’s look at an example of indirect recursion using two functions: a() and b().

``````
// Function 'a' calls function 'b'
function a(n)
{
(n > 0)
{
console.log("Function 'a' - n = " + n);
b(n - 1);
}
}

// Function 'b' calls function 'a'
function b(n)
{
(n > 0)
{
console.log("Function 'b' - n = " + n);
a(n / 2);
}
}

(5);
```
```

In this example, the a() function calls the b() function with the argument n – 1. Then, the b() function calls back the a() function with the argument n / 2. This cycle continues until a specific condition is met.

## 3. Tail Recursion:

Tail recursion occurs when a recursive call is the last operation performed in a recursive function. In other words, there are no pending operations after the recursive call.

Consider an example of tail recursion to calculate the sum of all numbers from 1 to N:

``````
function sum(n, acc = 0)
{
if (n === 0) {
return acc;
} else {
return sum(n - 1, acc + n);
}
}
```
```

In this example, the sum() function updates both arguments for each recursive call. The accumulated sum is passed as an argument to avoid recalculating it in each recursion. This approach optimizes memory usage and prevents stack overflow errors.

## 4. Nested Recursion:

Nested recursion occurs when a recursive function passes a recursive call as an argument to another recursive call. It adds an extra level of complexity to recursive algorithms.

Let’s consider an example of nested recursion to calculate the Fibonacci sequence:

``````
function fibonacci(n)
{
if (n === 0 || n === 1) {
return n;
} else {
return fibonacci(fibonacci(n - 1)) + fibonacci(fibonacci(n - 2));
}
}
```
```

In this example, the fibonacci() function calls itself twice. The first recursive call computes the Fibonacci number of n – 1, while the second recursive call computes the Fibonacci number of n – 2. The sum of these two values gives the Fibonacci number for n.

### Conclusion:

Recursion is a fundamental concept in data structures that can be implemented in various ways. Direct recursion, indirect recursion, tail recursion, and nested recursion all have their unique characteristics and use cases. Understanding these types of recursion will help you design efficient algorithms and solve complex problems more effectively.

Now that you have a good understanding of the different types of recursion in data structures, you can apply this knowledge to solve various programming challenges efficiently. Keep practicing and exploring different applications to enhance your problem-solving skills.