Introduction to Recursion in Data Structure
Hey guys! You must be aware of the data structures in programming, today we will discuss an interesting topic in programming that is recursion in data structure. Computers, mobiles, cars, airplanes do you know what they have in common? Coding! Every technology that we rely on today is powered by coding or programming.
Nowadays many schools are even giving basic coding knowledge in primary classes. A lot of programming languages incorporate an immense collection of built-in data structures for organizing code and data. Computer systems use binary codes and all the software that is in there runs the system using 0’s and 1’s only.
Do you know? There can be infinite combinations of these two digits as a result new software can be written all the time. We will give you in-depth guidance for everything possible related to recursion in data structure. Even if you are a complete beginner in programming don’t worry, we will discuss every topic from scratch.
Note: With recursion in Data Structures you must also know about the graph in data structure
What is Data Structure?
The data structure term implies by itself that organizing the data in memory. You will find numerous ways of arranging the information in the memory like the array present in C language. The array is a set of memory components in which info is saved sequentially, i.e., one right after another. Put simply, we can state that the array stores the components in a consistent fashion.
This kind of organization of details is accomplished with the assistance of an array of data structures. Additionally, there are alternative approaches to managing the data in memory. Let us look at the various sorts of data structures.
The data structure just isn’t any programming language as C, Java, C++, etc. It’s a set of algorithms that we can apply in almost any programming language to structure the information in the memory.
To structure the data in memory,’ n’ number of algorithms had been suggested, and the majority of these algorithms are referred to as Abstract data types. These abstract data types are a set of rules.
What is Recursion in Data Structure?
In general terms recursion means the process to define a problem or the solution for a problem in a much simpler way compared to the original version. It is a problem-solving programming technique that has a remarkable and unique characteristic.
In recursion in data structure, a method or a function has the capability to decode an issue. In the process of recursion, a problem is resolved by transforming it into small variations of itself. In this procedure, the function can call itself either directly or indirectly. Based on the differences in call recursion in data structure can be categorized into different categories. You will get to know about these categories later in the blog.
Recursion in data structure is additionally an adequate programming technique. A recursive subroutine is described as one that directly or indirectly calls itself. Calling a subroutine specifically indicates that the characterization of the subroutine already has the call statement of calling the subroutine that has been defined.
Moreover, the indirect calling of the subroutine takes place whenever a subroutine calls another subroutine, which in turn calls the first subroutine. Recursion in data structure can use several lines of code to refer to an elaborate job.
Let us understand Recursion with a Real-Life Example:
Recursion is when 3 telephone calls are put on hold prior to a lunch decision being made.
Astha would want to have lunch with Bikram.
Astha calls Bikram.
Astha says: Hi Bikram, do you wish to go for a lunch meal in the student facility?
Bikram says to Astha: That is an awesome plan, however, I was intending to meet with Chitra today.
Please let me place you on hold and call her.
He calls Chitra
Bikram says: Hi Chitra, do you wish to go for lunch in the student facility?
Chitra says to Bikram: That is a great idea, though I was hoping to meet with Danish today.
Allow me to put you on hold and call them.
Chitra calls Danish
Chitra says: Hi Danish, would you like to go for lunch in the student facility?
Danish says to Chitra: That’s a cool suggestion, but I was hoping to meet with Emilia today.
Let me place you on hold and call them.
They call Emilia
They say: Hi Emilia, do you want to go for lunch in the student facility?
Emilia says to Danish: Yes! I will meet you at the student facility.
Emilia hangs up
Danny says to Cynthia: Yes! I will meet you at the student facility.
Danish hangs up
Chitra says to Bikram: Yes! I will meet you at the student facility.
Chitra hangs up
Bikram says to Astha: Yes! I will meet you at the student facility.
Bikram hangs up
Astha is happy. All telephone calls are concluded and our friends can go to lunch!
What is a Recursive Algorithm?
A recursive algorithm calls itself with small input values & returns the outcome for the present input by executing fundamental functions on the returned value for the small input. By and large, if a problem could be sorted out by using remedies to smaller adaptations of the same problem, in addition to the smaller variations reduced to conveniently solvable cases, then the problem could be fixed employing a recursive algorithm.
How does Recursion work?
Several programming languages provide recursive functions to call themselves directly or indirectly by calling another function that eventually ends up calling the initial function. The memory devoted anytime a function is called upon is once again relocated besides memory allocated to the calling function while duplicates of local variables are made for every single call.
As soon as the root issue has been developed, functions return their value to functions through which they are called. The moment this takes place, memories are de-allocated and the cycle repeats.
One crucial element of a recursive function is the serious need for a base instance or termination point. Every program created with recursion must make sure the functions are terminated, failing which could result in the system crashing errors.
5 Important Recursion in Data Structure Methods
There are 5 effective recursion techniques programmers can make use of in functional programming. And, they are
Tail Recursion in Data Structure
Even though linear recursion is by far the most widely used technique, tail recursion is considerably more beneficial. When you use the tail recursion process, the recursive functions are called in the end.
Binary Recursion in Data Structure
When working with binary recursion, functions are called upon 2 times rather than being called one by one. This specific form of recursion data structure is used in operations like merging and also tree traversal.
Linear Recursion in Data Structure
It is the most widely used recursion method. applying this approach, functions call them
selves in a non-complex form and then terminate the function with a termination condition. This particular strategy consists of functions making one-off calls to itself during execution.
Mutual Recursion in Data Structure
It is the approach where a function will use others recursively. Functions turn out calling one another in this technique. This strategy is particularly used when writing programs making use of programming languages that often do not support recursive calling functions. Hence, implementing mutual recursion can serve as an alternative for a recursion function. In mutual recursion, starting circumstances are used for a single, several, or even all of the functions.
Nested Recursion in Data structure
It is an exception wherein these sorts of recursions can’t be transformed into an iterative format. Within this technique, recursive functions pass the parameters as recursive calls that translate to recursions in recursions.
Types of Recursion in Data Structure
There are five types of recursion in data structure that are broadly categorized into two major types of recursion. These are direct recursion and indirect recursion.
Direct Recursion in Data Structure
In the direct recursion, functions call themselves. This kind of operation consists of a single-stage recursive call by the function from within itself. Why don’t we investigate precisely how to carry out direct recursion to determine the square root of a number.
{
// base case
if (x == 0)
{
return x;
}
// recursive case
else
{
return square(x-1) + (2*x) – 1;
}
}
int main() {
// execution of square function
int input=3;
cout << input<<“^4 = “<<square(input);
return 0;
}
The output would be displayed like this:
3^4 = 9
Indirect Recursion in Data Structure
Indirect recursion happens when functions call other functions to call the initial function. This specific course of action consists of 2 simple steps when developing a recursive call, essentially making functions call functions to generate a recursive call. Mutual recursion could be referred to as indirect recursion.
Let’s examine precisely how to put into action indirect recursion to print or perhaps find out all of the figures from 10 to 20.
using namespace std;
int n=10;
// declaring functions
void foo1(void);
void foo2(void);
// defining recursive functions
void foo1()
{
if (n <= 20)
{
cout<<n<<” “; // prints n
n++; // increments n by 1
foo2(); // calls foo2()
}
else
return;
}
void foo2()
{
if (n <= 20)
{
cout<<n<<” “; // prints n
n++; // increments n by 1
foo1(); // calls foo1()
}
else
return;
}
The output would be displayed like this:
10 11 12 13 14 15 16 17 18 19 20
Tailed Recursion in Data Structure
A recursive function is referred to as tail-recursive if the recursive call is the end execution executed by the function. Let us try to figure out the definition with the help of one example.
int fun(int z)
{
printf(“%d”,z);
fun(z-1);
//Recursive call is last executed statement
}
If you notice this particular program, you can observe that the last line ADI is going to execute for method fun is a recursive call. And due to that, there’s no need to recall any earlier state of the program.
Non-Tailed Recursion in Data Structure
A recursive function is said to be non-tail recursive in case the recursion call isn’t the final thing performed by the function. After reverting back, there’s another thing still there to assess. Now, look at the example.
int fun(int z)
{
fun(z-1);
printf(“%d”,z);
//Recursive call is not the last executed statement
}
In this particular function, you can notice that there is another operation following the recursive call. Hence the ADI is going to have to remember the preceding state within this specific method block. That’s the reason this program could be regarded as non-tail recursive.
When is Recursion in Data Structure Used?
You’ll find circumstances where you can take advantage of iteration or recursion in data structure. Nevertheless, you must always select a solution that seems to be the considerably more natural fit for a challenge. A recursion in data structure is, obviously, the right choice when we talk about data abstraction. Folks generally use recursive definitions to describe data along with associated operations.
It will not be inaccurate to imply that recursion in data structure is usually the natural alternative for issues related to the application of distinct operations on data. Nevertheless, you can get certain things related to recursion in data structure that could not make it the ideal answer for every situation. In these situations, a solution such as the iterative technique is the greatest fit.
The implementation of recursion in data structure uses a good deal of stack space, which may usually lead to redundancy. Whenever we make use of recursion in data structure, we call a method that results in the formation of a whole new instance of that approach. A new instance holds variables and parameters that are kept on the stack, and therefore are taken on the return. So while recursion in data structure is a slightly more straightforward option as opposed to others, it is not often the most practical.
Additionally, we do not have some predefined guidelines that may help select recursion or iteration for various issues. The most significant advantage of using recursion in data structure is that it’s a concise technique. This process makes checking out and maintaining it much easier than usual. But recursive methods are not the most effective approaches available to us as they take a good deal of storage capacity and use up plenty of time during implementation.
Acknowledging a couple of factors can make it easier to determine if selecting a recursion in data structure for a problem is the appropriate way to go or not. You must opt for recursion if the issue that you’re intending to fix is pointed out in recursive terms and the recursive solution appears to be less complicated.
You must remember that recursion in data structure, in nearly all cases, simplifies the implementation of the algorithms that you would like to use. However, if the complexities connected with making use of iteration and recursion are the same for a specified issue, you must opt for iteration as the prospects of it being a lot more effective are higher.
Difference between Recursion and Iteration
| Criteria | Recursion | Iteration |
| Definition | When a function calls itself directly or indirectly | When t here are some set of instructions that are carried out repeatedly |
| Implementation | Recursion is implemented with the use of function calls | Iteration is implemented by the use of loops |
| Memory Usage | Stack memory is used to store local variables & parameters | No memory is used except for the initialization of control variables |
| Speed | Slow speed of execution | Fast speed of execution |
| Code Size | Recursion code is usually smaller and simpler | Iterative code is usually big |
| Format | Recursive and base case association is specified | It includes initializing control variable, control variable update, and termination condition |
| Progression | The base case is approached by the function state | The termination value is approached by the control variable |
| Current State | It is defined by the parameters kept in the stack | It is defined by the value of control variables |
| Overhead | Includes overhead of repeated function call | As there are no function calls therefore no overhead |
| Repetition | If the base case is undefined or not reached then it will cause a stack overflow error | If the control variable is unable to reach termination value then it will cause an infinite loop |
Memory Allocation of Recursive Method
Each recursive call causes a new version of that method in the memory. When the data is returned by this method, the copy is taken out of the memory. Since all the variables and other stuff declared within the function get saved in the stack. As a result, a separate stack is maintained at each recursive call. After the value is returned from the corresponding function, the stack will get wiped out. Recursion in data structure consists of a lot of complexity in solving and monitoring the values at each recursive call. Thus we need to maintain the stack and monitor the values of the variables determined in the stack.
How to Use Recursion in Data Structure?
Let us figure out how to efficiently apply recursion in data structure using different programming languages to create a few easy programs or seek answers to divers problems. Being recognized as one of the most compact and optimized strategies of generating functions call or deploy functions when programming, recursion in data structure could be used to effectively employ many algorithms and functions.
Using Recursion in Data Structure C++
Recursion in data structure is quite widely used in programming languages including C++. Let’s examine exactly how to work with the recursive function in C++ to carry out recursion in data structure when creating a program to obtain the factorial of 6.
using namespace std;
// Factorial function
int f(int n)
{
// Stop condition
if ( n == 0 || n == 1 )
return 1;
// Recursive condition
else
return n * f(n – 1);
}
// Driver code
int main()
{
int n = 6;
cout<<“Required factorial of 6 “<<n<<” = “<<f(n);
return 0;
}
The output is displayed as:
Required factorial of 6 = 720
Implementing Recursion in Data Structure C
Let’s apply recursion in data structure in C to determine the sum of consecutive numbers from 0.
#include
int sum(int n);
int main() {
int number, result;
printf(“Enter the last number: “);
scanf(“%d”, &number);
result = sum(number);
printf(“Value of consecutive no. = %d”, result);
return 0;
}
int sum(int n) {
if (n != 0)
// sum() function calls itself
return n + sum(n-1);
else
return n;
}
The output will be displayed as:
Enter the last number: (Let’s use the positive integer 6, then the consecutive numbers are 1, 2, 3, 4, 5, and 6)
Enter the last number: 6
Value of consecutive no. = 21
Recursion in Data Structure Example
Reversing an Array
Let’s look at the issue of reversing the n components of an array, A so that the first component turns into the final, the 2nd component will become the 2nd to the last, and so forth. We can work out this specific challenge with the linear recursion in data structure, by paying attention to how the reversal of an array could be done by swapping the first and last components and subsequently recursively reversing the rest of the components in the array.
Algorithm Reverse Array(A, i, j):
Input: An array A & non-negative integer indices i & j
Output: Reversal of the elements in A starting from index i & ending at j
if i < j then
Swap A[i] and A[j]
ReverseArray(A, i+1, j-1)
return
Fibonacci Sequence
Fibonacci sequences are the sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…. The initial two numbers of the sequence are the two 1, while every succeeding number is the sum of the two numbers prior to it. We can set a function F(n) that will calculate the nth Fibonacci number.
Algorithm Linear Fib(n) {
Input: A nonnegative integer n
Output: Pair of Fibonacci numbers (Fn, Fn-1)
if (n <= 1) then
return (n, 0)
else
(i, j) <– LinearFib(n-1)
return (i + j, i)
}
Drawbacks of Recursion in Data Structure
- Recursion uses stack space: Each recursive method call creates a new instance of the method, one with a brand new set of local variables. The complete stack space consumed is dependent upon the degree of nesting of this recursion method, and the number of local variables along with parameters.
- Recursion might carry out redundant computations: Look at the recursive computation of the Fibonacci sequence.
In total, an individual has to weigh the ease of the code presented by recursion against its downsides as outlined above. When a straightforward iterative alternative is achievable, it’s undoubtedly a much better option.
Conclusion
In this valuable recursive algorithm blog, you discovered what is recursion in data structures, What’s a Recursive Algorithm, How does recursion in data structure operates, five Important Recursion Methods, Types of recursion, When is recursion used. Additionally, you looked at the different good examples of recursion. Finally, you also understood the approach of How to Use Recursion.
Creating a recursive function to power programs with the help of the programming language of the choice is a good way to boost programming and ensure easy post-development debugging. Generally, there can be circumstances in which making a choice might not be that simple. You’ve to choose between simplicity and efficiency.
You have to place significance on the distinctive kinds of recursion in data structure techniques and their various applications in different languages to find out the best way to efficiently employ them for optimum usage.
Newbies should also make sure to aim at the way recursion in data structure functions by understanding the basic principles of applying recursive techniques when coding.
Frequently Asked Questions
Why do we use Recursion in Data Structure?
A recursive data structure could be described as a data structure that may be divided into miniature or simple cases of itself. For instance, trees are composed of little trees plus leaf nodes while lists can include smaller lists as their components.
Although, recursion in the data structure can be outlined as a technique by which conditions are split up into smaller-sized sub-problems to look for a fix. This Is carried out by replicating the function on a smaller level, making it call itself, and then simply incorporating them collectively to fix issues.
Recursion offers a natural approach in declaring several algorithms and is also extremely beneficial in functional programming. Developers can significantly employ recursion rather than loop functions for example “for loop” or “while loop”.
What is the difference between Direct and Indirect Recursion in data structure?
| Direct Recursion | Indirect Recursion |
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What are Recursion advantages and disadvantages?
- Reduce the needless calling of functions.
- Because of Recursion one may fix issues in a way that is easy while its iterative alternative is quite large and complicated.
- Incredibly handy when applying a similar solution.
- The recursive method is usually logical and it’s extremely hard to trace.
- In recursive we have to have an if statement somewhere to induce the function to return without the recursive call being carried out, or else the function won’t ever return.
- Recursion in data structure uses much more processor time.
What is the difference between Recursion and Iteration?
Recursion in data structure and Iteration are the simple approaches to consistently carry out a specified set of instructions in any type of programming language, and hence, every software application engineer should be acquainted with these topics. Lots of software engineering interview problems are generally tackled by the basic use of recursion in data structure.
At times we come across an issue that is pretty difficult to solve directly. Generally, we attempt to break such problems down into smaller parts. Next, we can find a method to resolve these smaller sections and then work up a solution to the whole issue. This’s the overall concept behind recursion in data structure.
Recursion in data structure is when a function calls itself indirectly or directly, and the function calling itself is known as a recursive function. It’s generally used when the answer to a larger issue could be depicted in terms of smaller problems.
To terminate the recursion in data structure, we make use of several circumstances so that the function knows when not To make any additional recursive call To itself and return; or else, it will lead To infinite recursion in data structure when the function is called. These conditions are called base conditions in the recursion in data structure.
Iteration takes place when we perform a set of instructions repeatedly until the condition managing the loop gets false. It consists of initialization, comparison, carrying out statements inside the iteration, along with updating the control variable. In iteration, it’s essential to have the proper controlling condition; else, the program might go in an infinite loop.
Recursion in data structure and iteration are both distinct approaches to carry out a set of instructions repeatedly. The major distinction between these two is that in recursion in data structure, we employ function calls to carry out the statements repeatedly inside the function body, while in iteration, we apply loops like “while” and “for” to do the same.
What are the basic rules of Recursion?
- A recursive algorithm has to call itself, recursively.
- A recursive algorithm requires a base case.
- A recursive algorithm must alter its move and state toward the base case.
What is the difference between Function and Recursion?
A function is a chunk of code you create to work out a thing (partially or completely), compute something for a sub-problem, etc. Recursion on the contrary is a concept or technique that’s accomplished by calling a function from within itself.
Which is better Recursion or Loop?
Recursion isn’t intrinsically more effective or worse compared to loops – each has pros and cons, and these even rely on the programming language plus implementation.
Technically, iterative loops accommodate traditional computer systems more efficiently on the hardware level: at the machine code level, a loop is simply a test in addition to a conditional jump, while recursion in data structure (implemented with inexperience) consists of pressing a stack popping, returning, jumping, and frame back from the stack.
On the other hand, many instances of recursion in data structure (especially the ones that are trivially comparable to iterative loops) could be written so that the stack push/pop could be avoided. This Is possible once the recursive function call is the last thing that occurs in the function body before returning, and it is generally recognized as a tail call optimization (or tail recursion optimization).
Why is Recursion preferred over Iteration?
Recursion in data structure consists of calling the exact same function again, and hence, has an impressively little length of code. Nevertheless, as we observed in the evaluation, the time complexity of recursion in data structure can increase exponentially when there’re a significant amount of recursive calls. Hence, the use of recursion in data structure is useful in smaller code, but with increased time complexity.
Is Recursion slower than Loops?
There are two ways of observing this:
Recursion could be slower compared to iteration: In addition to processing the loop content. It takes care of the recursive call stack frame. This means far more code has to be run, and that implies that it’ll be slower.
A recursive function that is well written that is compiled in a language that does tail call optimization is going to eliminate that overhead, therefore it’ll carry out more or less in addition to iteration. But there are several “ifs” on this & some algorithms can’t be written in such a manner that they could be so optimized.
Recursion could be faster compared to iteration: Given that multi-core chips are the norm, performance could be enhanced by distributing the load over the cores. However this’s not accomplished in iterative methods as it’s complicated, and at times extremely hard, optimization to execute.
But languages that depend on stateless idempotent methods can’t perform iteration, therefore the coder must use recursion in data structure. The point that the methods are idempotent and stateless suggests that the optimizer can always spread the load across several cores, enhancing performance.
So the answer is: This will depend. Assuming that you are using Java, recursion in data structure generally is going to be slower compared to iteration and utilize a lot more stack space at the same time.
The conclusion is that iteration is quicker compared to recursion in data structure, however, in many cases if the code is well-written along with the compiler supporting tail call optimization, the two may function equally well.
What are the limitations of Recursion?
- Recursive functions are usually slower compared to non-recursive functions.
- It might need a considerable amount of memory space to hold intermediate outcomes on the system stacks.
- Difficult to assess or grasp the code.
- It’s not very effective in terms of space and time complexity.
- The laptop or computer might run out of memory in case the recursive calls aren’t correctly checked.
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