Introduction to Python Recursion
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Questions and Answers

What is a base case in recursion?

  • A type of iterative loop
  • Condition that stops recursion (correct)
  • A method to simplify code
  • A function that calls itself repeatedly
  • How is factorial represented mathematically?

  • n %
  • n*
  • n! (correct)
  • n#
  • Which of the following describes the recursive case?

  • Function calling itself on a smaller problem (correct)
  • Method to debug recursive errors
  • Stopping point for the recursion
  • Initial setup for the algorithm
  • What is the value of 0!?

    <p>1</p> Signup and view all the answers

    In the process of programming, what does the coding phase involve?

    <p>Implementing the solution in code</p> Signup and view all the answers

    Which of the following statements regarding recursive functions is false?

    <p>Every recursive function is also an iterative function.</p> Signup and view all the answers

    What is a possible output if the input to a factorial function is 3?

    <p>6</p> Signup and view all the answers

    What is the first step in the programming process?

    <p>Analysis</p> Signup and view all the answers

    What should happen if the first item in the list is a hashtag?

    <p>It should be added to the result list.</p> Signup and view all the answers

    Which statement correctly describes how the recursive case functions?

    <p>It uses list slicing to access the first item and count hashtags.</p> Signup and view all the answers

    What is the base case in the recursive function 'extract_hashtags'?

    <p>If the list is empty.</p> Signup and view all the answers

    When the first item in the list is not a hashtag, what should the function do?

    <p>Skip it and return the processed tail.</p> Signup and view all the answers

    Which of the following describes what the final return statement in the function does?

    <p>Concatenates the first hashtag with the list of remaining hashtags.</p> Signup and view all the answers

    What is the base case for the factorial function?

    <p>if n == 0 or n == 1:</p> Signup and view all the answers

    How does the recursive case of the factorial function operate?

    <p>It returns n multiplied by the factorial of n.</p> Signup and view all the answers

    What will the function return when factorial(0) is called?

    <p>1</p> Signup and view all the answers

    In the polished version of the factorial function, what condition indicates the recursive case?

    <p>if n &gt; 1:</p> Signup and view all the answers

    What is the purpose of including doctests in the function's docstring?

    <p>To provide examples of how the function should work.</p> Signup and view all the answers

    Which of the following is true about the return value of factorial(5)?

    <p>It returns 120.</p> Signup and view all the answers

    What type of value does the factorial function return?

    <p>Integer</p> Signup and view all the answers

    Which of the following statements about the recursive factorial function is incorrect?

    <p>The function calls itself for values of n less than 0.</p> Signup and view all the answers

    What is the base case in the recursive factorial implementation?

    <p>Both A and B</p> Signup and view all the answers

    Which statement best describes the recursive case for calculating factorial?

    <p>It uses the previous factorial value to calculate the next</p> Signup and view all the answers

    What is the first step in defining a recursive factorial function?

    <p>Define the function signature</p> Signup and view all the answers

    Why is the initial implementation of the recursive factorial impractical for large numbers?

    <p>It has a repetitive pattern without proper recursion</p> Signup and view all the answers

    In the correct recursive case implementation of factorial, what does 'else' indicate?

    <p>It defines how to calculate factorial for n &gt; 1</p> Signup and view all the answers

    Which of the following correctly describes the factorial of a number n?

    <p>A product of all positive integers from 1 to n</p> Signup and view all the answers

    What is the primary purpose of using recursion in the factorial function?

    <p>To reduce the complexity of the code</p> Signup and view all the answers

    What will occur when n = 0 in the factorial function?

    <p>It will return 1 based on the base case</p> Signup and view all the answers

    What is the base condition for the factorial function?

    <p>n == 1</p> Signup and view all the answers

    What is the output of the function call factorial(5)?

    <p>120</p> Signup and view all the answers

    What is the purpose of recursion in the factorial function?

    <p>To call the function itself with a reduced argument</p> Signup and view all the answers

    What would happen if the factorial function is called with a negative number?

    <p>It would throw an error</p> Signup and view all the answers

    What pattern does the Fibonacci sequence follow?

    <p>Each number is the sum of the two preceding numbers</p> Signup and view all the answers

    In the count_hashtags function, what parameter does it take?

    <p>A list of strings to search for hashtags</p> Signup and view all the answers

    What would be the result of F(4) in the Fibonacci sequence?

    <p>3</p> Signup and view all the answers

    What is a primary use of Python Tutor as suggested in the exercises?

    <p>To visualize the execution of Python code</p> Signup and view all the answers

    What is the primary structure of the Fibonacci spiral made up of?

    <p>Square tiles</p> Signup and view all the answers

    What does the orientation of tiles in the Fibonacci spiral depend on?

    <p>The rotation sequence</p> Signup and view all the answers

    What should you check to ensure proper functionality of the tile(...) function?

    <p>The implementation of the orient(...) function</p> Signup and view all the answers

    Why should base cases be ensured in recursive functions?

    <p>To avoid infinite loops</p> Signup and view all the answers

    Which technique can help optimize recursive implementations for large Fibonacci numbers?

    <p>Memoization</p> Signup and view all the answers

    Which of the following is NOT a concern with deep recursion in Python?

    <p>It can cause infinite loops</p> Signup and view all the answers

    What is a significant characteristic of the color produced for each tile in the spiral?

    <p>It is determined by the hsv_color(...) function</p> Signup and view all the answers

    In the Fibonacci spiral, what is a key reason for ensuring proper implementation of the fib_spiral(...) function?

    <p>To compute the size of new tiles accurately</p> Signup and view all the answers

    What graphical function is suggested to check the implementation of a sample tile?

    <p>show_graphic(tile(150, white, 5))</p> Signup and view all the answers

    What is the visual element that forms part of each tile in the Fibonacci spiral?

    <p>A quarter circle</p> Signup and view all the answers

    Study Notes

    Introduction to Programming in Python: Recursion

    • Recursion is a function calling itself to solve smaller problem instances.
    • It's a technique of divide and conquer, breaking problems into simpler, manageable parts.
    • Recursion mimics Russian nesting dolls, with a set of problem instances nested within another.
    • Recursion has a finite depth; it must have a base case to stop the chain of calls.
    • Main components of recursion:
      • Base case: A condition that terminates the recursion.
      • Recursive case: The function call itself on a smaller problem.

    Factorial

    • Factorial, denoted as n!, is the product of all positive integers less than or equal to n.
    • Examples:
      • 0! = 1 (no positive integers less than 1)
      • 1! = 1
      • 2! = 2 * 1 = 2
      • 3! = 3 * 2 * 1 = 6
      • 4! = 4 * 3 * 2 * 1 = 24

    Example Recursive Factorial

    • Implement a recursive function to compute the factorial of a number.

    Programming is a Process (Revisited)

    • Analysis: Problem analysis and specification.
    • Design: Breaking down problems into smaller sub-problems and formulating algorithms.
    • Coding: Implementing the solutions in code.
    • Testing: Testing code functionality.
    • Debugging: Identifying and fixing bugs.

    Example Recursive Factorial: Analysis

    • Ensure understanding of the mathematical definition of factorial (only for non-negative integers).
    • Determine the requirements:
      • Input data is a positive integer.
      • Output is an integer (the factorial).

    Example Recursive Factorial: Design

    • Determine a suitable function name (e.g., factorial).
    • Define the parameters (e.g., n, for the number).
    • Identify the base case (e.g., 0! or 1! equal 1).
    • Determine the recursive case (e.g., n! = n * (n-1)!).

    Example Recursive Factorial: Coding (Incorrect Approach)

    • A wrong approach is to manually enumerate the products for each case, an impractical method on large numbers.
    • This is a less elegant method of computing factorials recursively.

    Example Recursive Factorial: Coding (Correct Approach)

    • The recursive case includes:
      • elif n == 2: return 2 * factorial(2 - 1);
      • elif n == 3: return 3 * factorial(3 - 1);

    Example Recursive Factorial: Coding (Polishing Code)

    • Base case: if n == 0 or n == 1: return 1
    • Recursive case: else: return n * factorial(n-1)

    Example Recursive Factorial: Testing (by using doctest)

    • Include a docstring to clearly explain the function's purpose, input parameters, and return type.
    • Use doctests for testing different input values.

    Exercise 14.1: Python Tutor

    • Use Python Tutor to visualize the execution of the factorial function.

    Exercise 14.1: Python Tutor (Observer)

    • Observe how Python keeps track of recursive function calls.

    Fibonacci

    • A sequence where each number is the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3...).

    Exercise 14.2: Recursive Fibonacci

    • Implement the Fibonacci sequence recursively.

    Exercise 14.3: Counting Hashtags

    • Recursively count hashtags (strings starting with '#').

    Exercise 14.3: Counting Hashtags (Polished)

    • A polished and efficient recursive method for computing hashtags, with optimal considerations for base cases.

    Exercise 14.3: Counting Hashtags (Hack)

    • A concise recursive method for computing hashtags.

    Exercise 14.4: Extracting Hashtags

    • Recursively extract hashtags from a list of strings.

    Exercise 14.5: Fibonacci Spiral

    • Create a spiral visual representation of the Fibonacci sequence using tiles.

    Tile Orientation

    • Tiles rotate as they are added to the spiral (0°, 90°, 180°, 270°, then back to 0°, etc.)
    • The orient function handles these rotations.

    Best Practices about Recursion

    • Infinite Loops: Ensure a proper base case for recursion to terminate.
    • Deep Recursion: Be aware that Python has a limit on recursion depth.
    • Inefficient Fibonacci Computation: Recursively computing Fibonacci numbers can become very slow for large numbers; use memoization or iterative solutions.
    • Inefficient List Operations: Recursive operations on large lists can be much slower than using other Python techniques.

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    Description

    This quiz explores the concept of recursion in programming using Python. It covers definitions, main components, and the practical application of recursion in calculating factorials. Test your understanding of this essential programming technique!

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