23.1. Inductive Definitions

Try these first

1. 1.

   Define the factorial of 4 using the inductive definition.

   Hint

   Start by breaking down 4! step by step.

2. 2.

   What is the base case for the factorial function?

   Hint

   Think about what happens when you have zero items.

3. 3.

   What is the base case for the inductive definition of factorial?

   Hint

   Consider what factorial means for zero.

4. 4.

   True or False: Greedy algorithms always guarantee an optimal solution.

   • True
   • False

   Hint

   Consider scenarios like weighted interval scheduling.

5. 5.

   Prove that the recursive definition of factorial is correct through induction.

   Hint

   Start with simple values to show it holds.

6. 6.

   Given the interval scheduling problem with weights, design an efficient algorithm using dynamic programming.

   Hint

   Consider maintaining an array of best weights to avoid overlaps.