CSCI 3137 - Recursion in Scheme
23 Questions
1 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the general form of a parabolic function?

  • y = ax + bx^2 + c
  • y = cx^2 + bx + a
  • y = ax^2 + c
  • y = ax^2 + bx + c (correct)

What maintains the termination of a recursive function?

  • Constant variables
  • Side effects
  • Iterative loops
  • Base cases (correct)

How can iterative structures typically be replaced in functional programming?

  • By loops
  • With global variables
  • Through recursion (correct)
  • Using conditions

What issue occurs when evaluating (factorial 1000)?

<p>StackOverflowError (B)</p> Signup and view all the answers

Which component is NOT essential in defining a recursive function?

<p>Output variable (A)</p> Signup and view all the answers

What does each recursive call in the factorial function do?

<p>Requires its own stack frame (A)</p> Signup and view all the answers

Which of the following statements about recursion is true?

<p>Recursion involves calling a function within itself. (A)</p> Signup and view all the answers

What is the factorial of 0 according to the defined factorial function?

<p>1 (A)</p> Signup and view all the answers

What characterizes a tail-recursive subroutine?

<p>The last action it performs is calling itself. (C)</p> Signup and view all the answers

Why does the factorial function not exhibit tail-recursion?

<p>Each recursive call generates a new stack frame. (A)</p> Signup and view all the answers

What is the potential drawback of using helper functions in recursion?

<p>They tend to clutter the global namespace. (B)</p> Signup and view all the answers

In the provided factorial function structure, what does 'fact-helper' aim to achieve?

<p>Reorganize the factorial function to utilize tail recursion. (B)</p> Signup and view all the answers

What does the 'let' construct accomplish in the context of local binding?

<p>It allows for temporary variable creation that holds expression values. (D)</p> Signup and view all the answers

What happens if a tail-recursive function is called with a large value?

<p>It can be optimized by reusing stack frames. (A)</p> Signup and view all the answers

Which statement about the factorial function and recursion is true?

<p>Tail recursion can help avoid stack overflow issues. (D)</p> Signup and view all the answers

What type of variables can be bound using the 'let' construct?

<p>Local variables that do not depend on each other. (A)</p> Signup and view all the answers

What does the named-let allow in Scheme?

<p>It allows recursion by binding a name to a lambda expression. (C)</p> Signup and view all the answers

In the Fibonacci function provided, what does the expression (if (< n 2) n ...) return when n is less than 2?

<p>It returns the value of n. (D)</p> Signup and view all the answers

What values are initialized for fm and fm-1 in the Fibonacci named-let?

<p>fm = 1 and fm-1 = 1. (A)</p> Signup and view all the answers

What is the base case for the Padovan sequence P(n)?

<p>P(0) = P(1) = P(2) = 1. (C)</p> Signup and view all the answers

How does the factorial function utilize named-let according to the pattern described?

<p>It binds the name factorial to a lambda that processes the factorial calculation. (B)</p> Signup and view all the answers

What is the purpose of the parameters (m 2), (fm 1), and (fm-1 1) in the Fibonacci named-let?

<p>They set the initial state needed to compute Fibonacci numbers. (C)</p> Signup and view all the answers

What will the expression (if (= m n) fm ...) in the Fibonacci named-let do when m equals n?

<p>It will return the value of fm. (C)</p> Signup and view all the answers

Study Notes

Parabola Function

  • Parabola is defined by the quadratic function: ( y = ax^2 + bx + c ).
  • Scheme function structure: ( (define parabola (lambda (x)...)) ) needs completion.

Functional Programming and Recursion

  • Iterations often involve mutable variables, leading to side effects, which are undesirable in functional programming.
  • Recursion can replace loops, maintaining immutability.

Recursion Fundamentals

  • Establish a function with base cases to terminate and recursive cases to move closer to base.
  • Recursive functions call themselves with modified parameters to progress toward base case.

Factorial Function

  • Factorial defined as:
    • ( n! = 1 ) if ( n == 0 )
    • ( n! = n \times (n-1)! ) if ( n > 0 ).
  • Needs completion for the Scheme definition: ( (define factorial (lambda (n)...)) ).

Stack Overflow and Recursion

  • Evaluating ( (factorial 1000) ) causes StackOverflowError due to recursion depth.
  • Each recursive call produces a unique stack frame, consuming stack space.

Tail Recursion

  • Recursive calls that perform their last action as another recursive call are called tail-recursive.
  • Tail recursion allows stack frames to be reused, simulating loops in recursion.

Improving the Factorial Function

  • The traditional factorial function lacks tail recursion.
  • Proposed solution involves a helper function to implement tail recursion.
  • Example structure:
    • ( (define fact-helper (lambda (n m fm)...)) )
    • ( (define factorial (lambda (n) (if (< n 0) 1 (fact-helper n 1 1)))) ).

Local Binding with let

  • let allows variable bindings for expressions, isolating names within the expression context.
  • Variables must remain independent.

Fibonacci Function with let

  • Structure for Fibonacci can be completed using let:
    • ( (define fibonacci (lambda (n) (if (< n 2) n (let ((fn-1...) (fn-2...))...)))) ).

Named let

  • Named let allows recursive evaluations without cluttering the variable namespace.
  • Format:
    • ( (let name ((name1 expr1) (name2 expr2)...) expression) )
  • Inside the expression, name can refer to the recursive call.

Final Fibonacci Implementation

  • An optimized Fibonacci function using named let:
    • If ( n < 2 ), return ( n ); otherwise, define f to compute based on the recurrence relation.

Exercise on Factorial with Named let

  • A different approach using named let for factorial is suggested.

Padovan Sequence

  • Defined by:
    • ( P(0) = P(1) = P(2) = 1 )
    • Recurrence relation: ( P(n) = P(n-2) + P(n-3) ).
  • Complete the definition: ( (define padovan (lambda (n)...)) ).

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

06 - Recursion in Scheme.pdf

Description

This quiz covers the concepts of recursion and functional programming in Scheme, particularly focusing on defining parabolic functions. You will work on completing a function definition and understand the challenges of iterative structures in functional programming.

More Like This

Recursion Quiz
9 questions

Recursion Quiz

VigilantRooster avatar
VigilantRooster
Recursion in Java
5 questions
Recursion, Stacks, and Queues Data Structures
5 questions
Use Quizgecko on...
Browser
Browser