Chapter 19: Problem 9

___ recursion is when function A calls function B, which in turns calls function A.

Short Answer

Expert verified

Based on the given step by step solution, answer the following question: Q: Explain the concept of recursion, and discuss its properties with the help of an example. A: Recursion is a programming concept where a function calls itself or another function that eventually calls the original function, creating a loop of function calls. Recursive functions have two main properties: a base case and a recursive case. The base case is a condition where the recursion terminates, preventing infinite loops. The recursive case is where the function calls itself with a new set of input parameters, working towards reaching the base case. A common example of recursion is calculating the factorial of a positive integer, where the base case is when the input value is 0 or 1, and the recursive case is when the function returns the input value multiplied by the factorial of the input value minus 1.

Step by step solution

Understand Recursion

Recursion is a programming concept in which a function calls itself or another function that eventually calls the original function. This creates a loop of function calls, as each new call relies on the results of the previous calls. It's a helpful technique for solving problems that can be broken down into smaller, more manageable tasks that are similar or identical in nature to the overall problem.

Recognize the Properties of Recursion

There are two main properties that a recursive function should have: 1. Base Case: The base case is a condition where the recursion terminates. There should be at least one base case in a recursive function to prevent infinite loops and avoid the function from calling itself indefinitely. 2. Recursive Case: The recursive case is where the function calls itself with a new set of input parameters. In this case, the function is working towards reaching the base case.

Example of Recursion

Let's look at an example of recursion to demonstrate the concept. Consider the problem of calculating the factorial of a positive integer. The factorial of a number is the product of all positive integers less than or equal to that number. For example, the factorial of 5 is 5 * 4 * 3 * 2 * 1 = 120. A recursive function to calculate the factorial of a positive integer n can be written as follows: ``` int factorial(int n) { // Base Case if (n == 0 || n == 1) { return 1; } // Recursive Case else { return n * factorial(n - 1); } } ``` In this example, the base case is when n is 0 or 1, in which case the function returns 1. The recursive case is when n is not 0 or 1, and the function returns n multiplied by the factorial of (n - 1), effectively calling itself with a new input. The recursion will continue to call the factorial function with decreasing values of n until the base case is reached, and the final result will be calculated and returned.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Recursive Function

A recursive function is a function that calls itself during its execution. This technique allows for solutions to complex problems to be expressed in a simple and elegant way. In programming, recursion helps in breaking down large problems into smaller, more manageable parts that resemble the overall problem. To prevent a recursive function from running indefinitely, it must have a well-defined termination condition, known as a base case, which tells the function when to cease recursing.

Through recursion, a daunting task is simplified by dividing it into sub-tasks that are essentially smaller instances of the same activity.
Recursive functions can lead to clean and concise code that is easier to understand and maintain, assuming the recursion logic is not too complex.
Because of the self-referential nature, debugging recursive functions can be more challenging since it may involve tracing through multiple levels of function calls.

Base Case

In recursion, the base case is critical as it represents the condition under which the recursive chain of function calls will terminate. Without a base case, a recursive function will continue to call itself indefinitely, leading to a stack overflow or an infinite loop.

The base case is typically a simple scenario that does not require further recursion—often an edge case of the problem.
For a recursive algorithm to be correct and functional, the recursive steps must eventually lead to the base case.
Choosing the right base case is essential for ensuring the correctness and performance of a recursive function.

Characteristics of a Good Base Case

It should be simple enough to handle without recursion.
It should be reached after a finite number of recursive calls.
It should cover all the possible scenarios that don't need further breakdown.

Recursive Case

The recursive case is the part of a recursive function where the function calls itself. It defines how the function moves closer to the base case, preventing infinite recursion. The recursive case usually involves the function calling itself with modified arguments that progress towards the base case.

It is essentially the set of rules that reduce the complexity of the problem during each function call.
The recursive case must alter the problem in some way, usually by breaking it down into a smaller piece.
If a recursive case does not make progress toward the base case, it will cause uncontrolled recursion, quickly consuming system resources.

Designing a Recursive Case

It should move the current state closer to the base case.
The changes that lead to the base case should be consistent and logical.
It usually involves manipulating function input parameters to be less complex than the original inputs.

Function Calls

Function calls in the context of recursion represent the instances when a recursive function executes by calling itself. Each time the recursive function is called, a new frame is pushed onto the call stack, which keeps track of the various function calls and their respective local variables and execution context.

With each recursive call, the stack grows, and it’s vital to reach the base case before the stack becomes too large.
Understanding the call stack is imperative to grasp how recursive functions operate and why too many recursive calls can result in a stack overflow error.
The call stack can be thought of as a stack of books, where each book represents a single function call. As you add more books to the top, you get deeper into recursive calls. Completing a task and removing a book from the stack corresponds to hitting a base case and unwinding the recursion.

___ recursion is when function A calls function B, which in turns calls function A.

Short Answer

Step by step solution

Understand Recursion

Recognize the Properties of Recursion

Example of Recursion

Key Concepts

Recursive Function

Base Case

Characteristics of a Good Base Case

Recursive Case

Designing a Recursive Case

Function Calls

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Computer Network

Data Representation in Computer Science

Theory of Computation

Computer Programming

Issues in Computer Science

Data Structures

Study anywhere. Anytime. Across all devices.