23.7. Inductive Solution Approach

Try these first

1. 1.

   What is an inductive definition?

   Hint

   Think about how factorial is defined.

2. 2.

   What does the base case of a recursive function provide?

   Hint

   Consider what happens when n=0 in factorial.

3. 3.

   What does an inductive definition allow?

   • Defining functions iteratively
   • Defining functions based on smaller cases
   • Neither

   Hint

   Think of how factorial is structured.

4. 4.

   True or False: The optimal substructure property means a problem can be solved by combining solutions of subproblems.

   • True
   • False

   Hint

   Recall the definitions of optimal substructure.

5. 5.

   Using dynamic programming, calculate the number of ways to reach the nth Fibonacci number without recalculating each intermediate step.

   Hint

   Remember how Fibonacci builds on previous results.

6. 6.

   Devise an optimal solution for a modified interval scheduling problem where each request has a different weight based on the value of the request.

   Hint

   Think about prioritizing requests based on weight versus duration.