Lecture 6

Learning objectives

After this class, you should be able to:

1. Given an algorithm, derive its asymptotic time complexity.
2. Prove properties of big-oh, big-omega, and big-theta.

Reading assignment

1. Chapter 2.
2. Class notes.
3. Lecture: Algorithm Analysis Examples.
4. Pages 74-76.

Exercises and review questions

• Exercises and review questions on current lecture's material
  1. Prove that high-low+1 decreases by a factor of at least 2 in each iteration of the binary search algorithm.
  2. Prove that n3 + n is O(n3) directly from the definition of big-O. Show constants c and n0 that satisfy the definition.

• Questions on next lecture's material
  1. Write a small piece of code that inserts a few numbers into a STL vector of floats and then output each number.
  2. Explain the operations on the STL list in the vlm.cpp from lecture 4.