6.1.2. Examples of Input Sizes

Try these first

1. 1.

   What does input size refer to in the context of algorithms?

   Hint

   Think about how different problems might require different types of data.

2. 2.

   Can you name a problem where the worst-case analysis is particularly relevant?

   Hint

   Consider scenarios of searching in lists.

3. 3.

   What does input size primarily represent in algorithm analysis?

   • The value of numbers
   • The amount of space needed to represent data
   • The speed of execution

   Hint

   Think about how the representation of data can impact processing.

4. 4.

   True or False: In primality checking algorithms, the size of the input is based on the numeric value of the number being checked.

   • True
   • False

   Hint

   What do we focus on when analyzing digits versus values?

5. 5.

   Design an algorithm to find the largest prime number less than a given number n. Discuss the impact of input size on the efficiency of your algorithm.

   Hint

   Consider how prime checking scales with larger n.

6. 6.

   Analyze a sorting algorithm of your choice, identifying how different input sizes affect its performance in worst-case scenarios.

   Hint

   Think about pivot selection strategies and their impacts.