29 Questions
What is recursion?
A technique by which a function calls itself during execution
Which type of recursion involves a function calling itself from within itself?
Direct recursion
In the illustrative examples, what is the output for the factorial of 12?
479001600
What is the base case in the recursive implementation of the factorial function?
i <= 1
Which technique often used for looking up words in the dictionary involves recursion?
Binary search
Which type of recursion involves more than one function calling one another mutually?
Mutual recursion
What type of recursion is exemplified by the 'fun' function in the first code snippet?
Tail recursion
In which type of recursion does the recursive call occur as the first statement in the function?
Head recursion
If a recursive function calls itself more than once, what type of recursion is it known as?
Tree recursion
What type of recursion is exemplified by the 'fun' function in the fourth code snippet?
Nested recursion
In nested recursion, what does the recursive function pass as a parameter?
A recursive call
What type of recursion involves multiple functions calling one another in a circular manner?
Indirect recursion
In indirect recursion, how do the functions call each other?
Recursively
What is the output of the factorial function when the input is 12?
479001600
Explain direct recursion and give an example from the text.
Direct recursion involves a function calling itself from within itself. An example from the text is the recursive implementation of the factorial function.
What is the difference between direct recursion and indirect recursion?
The difference lies in whether a function calls itself from within itself (direct) or more than one function call one another mutually (indirect).
Give an example of indirect recursion and explain how it differs from direct recursion.
An example of indirect recursion is not provided in the text. Indirect recursion differs from direct recursion as it involves multiple functions calling one another in a circular manner.
In which type of recursion does the recursive call occur as the first statement in the function?
In nested recursion, the recursive call occurs as the first statement in the function.
Explain the concept of recursion and provide an example from the text.
Recursion is a technique by which a function makes one or more calls to itself during execution, or by which a data structure relies upon smaller instances of the very same type of structure in its representation. An example from the text is the recursive implementation of the factorial function.
What is the difference between Tail Recursion and Head Recursion?
Tail Recursion: The recursive call is the last statement in the function and nothing is performed after the call. Head Recursion: The recursive call is the first statement in the function and all operations are done after the call.
Can you give an example of Tree Recursion?
void fun(int n) { if (n > 0) { printf("%d ", n); fun(n - 1); fun(n - 1); } }
What is Nested Recursion?
Nested Recursion involves a recursive function passing the parameter as a recursive call, creating recursion inside recursion.
In the context of recursion, what is Indirect Recursion?
Indirect Recursion involves more than one functions calling one another in a circular manner.
What is the main characteristic of Tail Recursion?
The main characteristic of Tail Recursion is that the recursive call is the last statement in the function and no operation is performed after the call.
Explain the concept of Head Recursion.
Head Recursion occurs when a recursive function calls itself and the recursive call is the first statement in the function, with no operations before the call.
What distinguishes Tree Recursion from Linear Recursion?
Tree Recursion occurs when a recursive function calls itself for more than one time within the function, while Linear Recursion involves a recursive function calling itself for only one time.
How is Nested Recursion different from other types of recursion?
Nested Recursion involves a recursive function passing the parameter as a recursive call, creating recursion inside recursion, whereas other types of recursion do not exhibit this nested behavior.
Explain the concept of Indirect Recursion.
Indirect Recursion involves more than one functions calling one another in a circular manner, creating a chain of function calls.
What are the defining features of Tail Recursion?
The defining features of Tail Recursion include the recursive call being the last statement in the function and no operation being performed after the call.
Study Notes
Recursion
- Recursion is a programming concept where a function calls itself from within itself.
Types of Recursion
-
Direct Recursion: a function calls itself directly.
- Example: a function calling itself from within itself.
-
Indirect Recursion: multiple functions call each other in a circular manner.
- Example: function A calls function B, which calls function C, which in turn calls function A.
- Tail Recursion: the recursive call occurs as the first statement in the function.
- Head Recursion: the recursive call occurs at the end of the function.
- Tree Recursion: a function calls itself multiple times, creating a tree-like structure.
- Nested Recursion: a function passes itself as a parameter to another function.
- Linear Recursion: a function calls itself once.
Examples and Illustrations
- The output of the factorial function for input 12 is 479,001,600.
- The base case in the recursive implementation of the factorial function is when the input is 0 or 1.
Real-World Applications
- Recursion is often used for looking up words in a dictionary, where each word is defined in terms of other words.
Explore the concept of recursion and its examples in Unit 1. Understand how a function makes calls to itself during execution and how data structures rely on smaller instances of the same type of structure. Discover real-life examples of recursion in art, nature, and everyday tasks like sorting documents and looking up words in the dictionary.
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