Podcast
Questions and Answers
What is the base case for the factorial function defined recursively?
What is the base case for the factorial function defined recursively?
- n ≤ 1 (correct)
- n > 1
- n = 1
- n = 0
The factorial of a number n is defined as n! = (n - 1)! · n for all n > 0.
The factorial of a number n is defined as n! = (n - 1)! · n for all n > 0.
True (A)
What is the result of 3!?
What is the result of 3!?
6
The factorial function is denoted as _____ (use the symbol).
The factorial function is denoted as _____ (use the symbol).
Which of the following statements is true about the recursive definition of factorial?
Which of the following statements is true about the recursive definition of factorial?
Match the following numbers with their factorial value:
Match the following numbers with their factorial value:
What is the recursive step in the definition of the factorial function?
What is the recursive step in the definition of the factorial function?
The factorial of a number increases significantly as the number increases.
The factorial of a number increases significantly as the number increases.
Which of the following is a standard library type for representing text in C++?
Which of the following is a standard library type for representing text in C++?
The size of a std::string is always equal to the number of characters it contains.
The size of a std::string is always equal to the number of characters it contains.
What is the purpose of the at() function in std::string?
What is the purpose of the at() function in std::string?
The _______ code is a method of encoding text where each character is shifted by a fixed number of positions.
The _______ code is a method of encoding text where each character is shifted by a fixed number of positions.
Match the following string operations with their descriptions:
Match the following string operations with their descriptions:
How can you initialize a std::string with multiple characters?
How can you initialize a std::string with multiple characters?
You can read the first character of a std::string using the expression text[0].
You can read the first character of a std::string using the expression text[0].
What will the condition if (text == 'a') check?
What will the condition if (text == 'a') check?
To shift input text by a specific number, you would use the _______ function.
To shift input text by a specific number, you would use the _______ function.
Which encoding system uses a variable number of bytes to represent characters?
Which encoding system uses a variable number of bytes to represent characters?
Which of the following represents a string literal in C++?
Which of the following represents a string literal in C++?
A char can easily be converted to an int using its ASCII value.
A char can easily be converted to an int using its ASCII value.
What header file is required to use the std::string type in C++?
What header file is required to use the std::string type in C++?
To concatenate two strings in C++, you would use the _____ operator.
To concatenate two strings in C++, you would use the _____ operator.
Match the following data types with their descriptions:
Match the following data types with their descriptions:
What function can be used to get the length of a std::string?
What function can be used to get the length of a std::string?
Flashcards
Recursion
Recursion
A way to define a function in terms of itself. It breaks down a problem into smaller, similar subproblems.
Factorial
Factorial
A mathematical function that calculates the product of all positive integers less than or equal to a given number.
If statement
If statement
A statement that checks a condition and executes different code blocks based on whether the condition is true or false.
Recursive factorial function
Recursive factorial function
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Base case
Base case
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Infinite recursion
Infinite recursion
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Recursive function steps
Recursive function steps
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Non-recursive function
Non-recursive function
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What is a text string?
What is a text string?
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Character
Character
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ASCII Encoding
ASCII Encoding
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UTF-8 Encoding
UTF-8 Encoding
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Caesar Code
Caesar Code
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std::string
std::string
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string.size()
string.size()
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string.at(index)
string.at(index)
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caesar(string)
caesar(string)
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Iterating over String Characters
Iterating over String Characters
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What is a character?
What is a character?
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What is std::string?
What is std::string?
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string.size() function
string.size() function
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string.at(index) function
string.at(index) function
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How are chars converted into ints?
How are chars converted into ints?
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Study Notes
Introduction to Computer Science
- Course offered: 252-0032, 252-0047, 252-0058
- Authors: Manuela Fischer and Felix Friedrich
- Department: Computer Science, ETH Zurich
- Semester: Fall 2024
Recursion
- Recursion is a method where function definitions contain calls to the same function.
- Factorial example: n! = 1 if n ≤ 1; (n - 1)! * n otherwise
- Recursive functions need both a base case (to stop the recursion) and a recursive case (calls itself for a smaller problem toward the base case).
- Termination is crucial; a recursive case must make progress towards the base case (e.g., reducing the input).
- Stack overflow can occur if the recursion depth (number of function calls) becomes too large.
Call Stack
- The call stack manages function calls.
- Each function call gets a frame in memory, storing local variables and the return address.
- When a base case is reached, the frame is popped off the stack, returning to the calling function.
- Return values are passed upward.
- Recursion can exhaust the stack space, possibly causing a segmentation fault.
Example: Greatest Common Divisor
- Euclid's algorithm finds the greatest common divisor (gcd) of two numbers.
- Defined recursively: gcd(a, b) = a if b = 0, else gcd(b, a % b).
- Termination is guaranteed because each recursive call results in a smaller value for 'b' which ultimately reaches zero.
Example: Bit Strings
- Generating all bit strings of a specified length.
- Recursive approach: Start with an empty string, recursively append either '0' or '1', until the target length is reached.
General Recursive Problem-Solving Strategies
- Decrease and Conquer: Successively reducing the problem size until a base case is reached.
- Divide and Conquer: Breaking down the problem into smaller subproblems of approximately equal size, solving them recursively, and combining results to solve the whole problem.
Recursion and Iteration
- Recursion is potentially elegant but can be less efficient than iteration.
- Recursion can be slower because of repeated calculations.
- Fibonacci sequence shows the potential for inefficiency in recursive approaches. (In some applications, repeated calculations of the same values can slow down the recursion significantly).
- An iterative or loop-based approach solves the Fibonacci sequence far more efficiently, avoiding redundant calculations.
- Recursive solutions can sometimes be easier to understand and implement but can have less efficient performance. Iteration often provides a more direct and potentially faster solution to a problem.
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Description
This quiz covers key concepts in recursion and the call stack within computer science. It explores how recursive functions operate, including base and recursive cases, and discusses the management of function calls through the call stack. Additionally, it provides an example of finding the greatest common divisor using Euclid's algorithm.
