Lecture 8

Learning objectives

After this class, you should be able to:

1. Given an input to a sorting algorithm, give the permutation corresponding to it.
2. Given a sorting algorithm and n, give the decision tree for sorting all permutations of 1, ..., n.
3. Derive a lower bound on comparison based sorting, and other variants of this problem.
4. Given a data structure, some operation on it, and a time complexity, show that no algorithm exists to perform that operation with the specified time complexity.

Reading assignment

1. Lectures 6-9 slides.
2. CLR: Section 8.1.

Exercises and review questions

• Questions on current lecture's material
  1. Exercise 8.1-2.
  2. Exercise 8.1-3.
  3. Prove that there is no algorithm (based on comparisons) which, when given an array of data, will create a binary search tree containing that data in linear time (analogous to the BuildMaxHeap function for heaps).

• Questions on next lecture's material
  1. None.