Lecture 17

Learning objectives

After this class, you should be able to:

1. Given a recursive code, draw a figure to show how the state of the run time stack changes with time.
2. Given a recursive definition of a formula or an algorithm, write code that computes the formula or implements the algorithm, and prove the correctness of your implementation.
3. Given a simple recursive algorithm, derive the time complexity for executing it.

Reading assignment

1. Section 5.1 - 5.8.
2. Page 216 and 217.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Chapter 5, exercise 2. (If group_number % 2 = 0)
  2. Let a singly linked list of ints be sorted in ascending order. Write a recursive function that outputs the list in descending order. (If group_number % 2 = 1)
  3. Implement the power function using a stack, instead of implementing it recursively. (All groups)
  4. Prove, using induction, that the iterative function power2, which we discussed in class, correctly computes the power of a number.
  5. Let a function f be defined such that f(0) = 1. f(n) = 2*f(n/2). Derive the time complexity of computing this function recursively.

• Questions on next lecture's material
  1. Draw any tree that you wish to, such as a family tree, or the tree of an organization for which you work. What is the height of your tree? Which node is the root of the tree.