Recursion Techniques Quiz

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What is recursion?

A technique where a function calls another function during execution

A method for breaking down problems into smaller sub-problems

A technique by which a function makes one or more calls to itself during execution (correct)

A method for achieving parallel processing in computer programs

Which problem-solving technique provides an elegant and powerful alternative for performing repetitive tasks?

Iteration

Divide and conquer

Recursion (correct)

Dynamic programming

What is the factorial of a positive integer n?

$n! = n^2$

$n! = n * (n+1) * (n+2) * ... * 1$

$n! = n * (n-1) * (n-2) * ... * 1$ (correct)

$n! = n * (n-1) * (n-2)$

Which of the following is an example of a fractal structure?

The recursive pattern of an English ruler Signup and view all the answers

What problem can binary search efficiently solve?

Locating a desired value in a data set with billions of entries Signup and view all the answers

What is the recursive definition of the factorial function when n=0?

$0! = 1$ Signup and view all the answers

What is the base case for the factorial function?

n == 0 Signup and view all the answers

In the English ruler pattern, what happens to the tick length as the size of the interval decreases by half?

It decreases by one Signup and view all the answers

What is a common real-world application of binary search?

Searching for a word in a dictionary Signup and view all the answers

What is the purpose of the draw_line method in the Python code for drawing an English ruler?

To draw a line with a specified tick length Signup and view all the answers

What does the recursive trace closely mirror in a programming language's execution of recursion?

The language's execution of the recursion Signup and view all the answers

What is the interval with a central tick length L ≥ 1 composed of?

An interval with a central tick length L−1, a single tick of length L, and an interval with a central tick length L−1 Signup and view all the answers

What is the purpose of the binary_search function?

To find the position of a target value within a sorted array Signup and view all the answers

What happens if the target value is not found in the indicated portion of a Python list in binary search?

The function returns False Signup and view all the answers

What is the role of 'mid' in the binary search algorithm?

To store the mid-point location of the search interval Signup and view all the answers

What does the draw_ruler method do in the Python code for drawing an English ruler?

It draws both major and minor ticks for each inch on the ruler Signup and view all the answers

In the context of recursion, what is the main characteristic of a data structure that relies upon smaller instances of the same type of structure in its representation?

It has a self-referential function call Signup and view all the answers

What type of recursion involves more than one function calling one another mutually?

Indirect recursion Signup and view all the answers

In the given C code, what is the purpose of the 'if' statement in the 'factorial' function?

It checks for the base case of the recursion Signup and view all the answers

What does the 'factorial' function return when the input 'i' is less than or equal to 1?

1 Signup and view all the answers

What is the output of the given C code when 'i' is 12?

479001600 Signup and view all the answers

Which type of recursion involves a function calling itself from within itself?

Direct recursion Signup and view all the answers

In the function 'fun' mentioned in the text, what type of recursion is demonstrated?

Tail Recursion Signup and view all the answers

What type of recursion is demonstrated in the 'fun' function in the second example provided in the text?

Head Recursion Signup and view all the answers

Which type of recursion is exemplified by the 'fun' function in the third example given in the text?

Tree Recursion Signup and view all the answers

What type of recursion is illustrated by the 'fun' function in the fourth example provided in the text?

Nested Recursion Signup and view all the answers

In the context of recursion, what type of call occurs when a function calls itself and that recursive call is the last statement in the function?