Recursive Definitions and Factorials

The video introduces recursion in computer science, explaining it as a method where a function calls itself to solve problems. It uses factorials as an example, detailing how to calculate them and write a recursive function. The video also discusses the complete definition of factorials, including the special case of zero factorial, and demonstrates how to apply this definition.

What is recursion in computer science?

• A method of solving problems by repeating a process

• A way of solving problems by calling a function within itself

• A technique to solve problems by using loops

• A method to solve problems by using arrays

What is the factorial of a positive integer n?

• The sum of all integers from 1 to n

• The product of all integers from 1 to n

• The difference of all integers from n to 1

• The division of n by all integers from 1 to n

What is the value of 4 factorial (4!)?

• 12

• 16

• 24

• 32

How is zero factorial (0!) defined?

• Undefined

• One

• Negative one

• Zero

What is the purpose of writing a function using recursion?

• To make the function run faster

• To reduce the number of lines of code

• To solve problems by calling the function within itself

• To avoid using loops

In the recursive definition of factorials, what does n factorial equal?

• n plus n minus one factorial

• n times n minus one factorial

• n divided by n minus one factorial

• n times n factorial

Why does the recursive definition of factorials break for zero?

• Because it results in an infinite loop

• Because it results in a negative factorial

• Because zero factorial is not defined

• Because it results in a division by zero

What is the complete recursive definition of factorials for all integers?

• n factorial is n times n minus one factorial for all n

• n factorial is n plus n minus one factorial for all n

• n factorial is n times n minus one factorial if n is greater than or equal to one, otherwise one

• n factorial is n divided by n minus one factorial for all n

How can the recursive definition be used to find the factorial of 3?

• By multiplying 3 by 2 factorial

• By subtracting 3 from 2 factorial

• By dividing 3 by 2 factorial

• By adding 3 to 2 factorial