Class 27: Trees and Logs

cs1120: Introduction to Computing
Explorations in Language, Logic, and Machine
University of Virginia, Spring 2016

http://xplorecs.org/class27

Class 27:
The Search Problem
Complexity of FindMatch
Introducing Trees

Transcript

1. Class 27: Trees and Logs Introduction to Computing: Explorations in Language, Logic, and Machines cs1120 Spring 2016 David Evans University of Virginia
2. Course Update 10 people have now passed the Blue Belt Level 7 qualified to (re-)take Blue Belt exam If you are stuck, not making progress, or unsure what you should be doing, make sure to check in with me today or at office hours tomorrow.
3. Plan Searching Trees Cost in Theory and Practice
4. What is the “search” problem?
5. FindMatch Problem Inputs: lst, a list of N elements of type T, ftest, a test function T → Bool Output:
6. FindMatch Problem Inputs: lst, a list of N elements of type T, ftest, a test function T → Bool Output: an element, e, of lst such that ftest(e) is True, or None if no such element exists What is the complexity of the FindMatch problem?
10. FindMatch Complexity Inputs: lst, a list of N elements of type T, ftest, a test function T → Bool Output: an element, e, of lst such that ftest(e) is True, or None if no such element exists Complexity: Running time is in ϴ(N) - We know an algorithm, find_match, with running time in ϴ(N) - We know no asymptotically faster solution exists since it is necessary to look at all elements for a possible match.
11. FindMatch Complexity Inputs: lst, a list of N elements of type T, ftest, a test function T → Bool Output: an element, e, of lst such that ftest(e) is True, or None if no such element exists Complexity: Running time is in ϴ(N) - We know an algorithm, find_match, with running time in ϴ(N) - We know no asymptotically faster solution exists since it is necessary to look at all elements for a possible match. How can we do better?
12. Doing Better: Adding Restrictions 1. Input must be organized according to some comparison function. 2. The matching function must be restricted in a way that enables one comparison to eliminate a fraction of the input.
13. Binary Tree
14. Charge • Next class: implementing Trees, searching in a binary tree, faster searching If you are stuck, not making progress, or unsure what you should be doing, make sure to check in with me today or at office hours tomorrow.