Week 2. CS 400 Programming III. Read: Module 2 readings before lecture

Transcription

1 Week 2 Waitlisted Students: please come to front of class and sign by your name on waitlist. TopHat Join Code for my lecture: Announcements and Course Policies: Readings and Assignments: Assigned readings found in Modules for each Week on Canvas Get lecture outlines (pdfs) before lecture each week. Complete during lecture. Homework: h0 (quiz) on Reference and Review topics, due before 10pm 9/14 (Friday) Program: p1 available on Monday, due befor3e 10pm 9/17 (Monday) Lab Hours Start Monday 9/10 Read: Module 2 readings before lecture THIS WEEK in Lecture: (bring remaining pages from last week) Test Program Structure (review p1 TestPQ file) Linux: Copy, Compile and Run Java programs from command line BST Review o practice: insert and delete o implementation o complexity review classifications Balanced Search Trees Height-Balanced Practice: balancing NEXT WEEK X-Team Exercise (attendance and participation required) AVL Trees Red-Black Tree Properties Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 1

2 Run p1 on Linux Workstation Try this on your own before lecture CS 400 Programming III ssh cd private/cs400/programs/p1/ (may have to create dirs) cp /p/course/cs400-deppeler/public/html-s/assignments/p1/files/p1.zip. ls al unzip p1.zip ls al javac *.java ls al java TestPQ java TestPQ No PQ PQ01 PQ02 PQ03 MyPQ > results.txt ls al less results.txt Note: You will need to use q to quit the "less" view of the results file pico TestPQ.java Review TestPQ.java Program Structure Note: Ctrl-X to exit Pico editor TopHat suggestion: write questions what does > result.txt do? and about what does less results.txt do? Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 2

3 Practice - Inserting into a BST Insert 5, 27, 90, 73, 57 into the tree above. TopHat insert 27 TopHat insert 90 TopHat draw BST for 1,2,3,4,5 What can you conclude about the shape of a BST when values are inserted in sorted order? linear shape, O(N) for lookup, insert, and delete Will you get a bad shape only if values are inserted in sorted order? no, there are other insert orders that result in O(N) for example: 11,55,22,33,44,40,37 Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 3

4 Practice - Deleting from a BST Delete 90 from the tree above. Delete 40 and 65 from the tree above. Delete 10 and 70 from the tree above and redraw the tree. How do you delete 50 or 30 from the tree above? Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 4

5 Practice - Deleting from a BST Delete 30 from the tree above using the. Delete 50 from the tree above using the. Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 5

6 Implementing lookup Pseudo-Code Algorithm private boolean lookup(bstnode<k> n, K key) { if n is null, return false if n's key = key, return true if key < n's key, return lookup(left,key) return lookup(right,key) Implementing insert High-Level Algorithm throw DuplicateKeyException (user-defined or it is in Java EE) /** pre-cond: key is NOT null */ private BSTnode<K> insert(bstnode<k> n, K key) throws DuplicateKeyException { if n is null, return new node with this key if key equals n's key, throw DuplicateKeyException if key < n's key, assign insert(left,key) to n's left subtree else assign insert(right,key) to n's right subtree return current node if (null==n) return new BSTnode<K>(key,null,null); if ( key.compareto( n.key ) == 0 ) throw new DuplicateException(); if ( key.compareto( n.key ) < 0 ) { n.left = insert(n.left,key); else n.right = insert(n.right,key); return curr; Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 6

7 Implementing delete High-Level Algorithm /** pre-cond: key is not null */ private BSTnode<K> delete(bstnode<k> n, K key) { if n is null, return n // key not found if key equals n's key // key found, 3 cases to consider CASE #1: n has no children // "unlink N" by returning null // to appropriate child of parent CASE #2: n has one child // return n's other child to parent if (n.left==null) return n.right if (n.right==null) return n.left CASE #3: n has two children // find replacement value (v) for n // delete v from appropriate child of n 1. find replacement value largest value in left (in-order predecessor) smallest value in right (in-order successor) 2. copy v into n's key 3. recursively delete v from approp sub-tree KEY CONCEPT: AVOID LOTS OF RELINKING, FIND REPLACEMENT VALUE INSTEAD Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 7

8 Complexities of BST Methods Problem size: N = number of nodes (1 key per node) print: O(N) print each key exactly once lookup: want O(log2 N) insert: want O(log2 N) delete: want O(log2 N) get O(H) get O(H) get O(H) SHOW BUSHY (wide) VS STALKY TREES (tall) Classifying Binary Trees Full no missing nodes all leaf nodes at same level all interior nodes have 2 children H = log2(n+1), N=1,3,7,15,31,64,etc Complete Full to depth H-1 depth H filled from left to right (like heaps) H <= log2(n+1) + 1 Height-balanced "good enough" for each node: o the difference between height of left and height of right subtree is no more than 1 Balanced most relaxed, height growth rate function is O(log N) Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 8

9 Practice - Classifying Binary Trees Identify which trees below are full, complete and/or height balanced. Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 9

10 Balanced Search Trees Goal: keep height (H) at O(log2 N), where N is number of nodes Idea: insert and delete using BST algorithms and then fix it if it is not balanced (1) Detect out of balance (2) Fix balance How do we detect and fix? TOPHAT DISCUSSION count nodes and compare H to log2n? compute balance factor and when B.F. > 1, must rebalance Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 10

11 Height-Balanced Which of these trees is not height-balanced? What is the Balance Factor (BF) of each node? Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 11

12 Practice I - Balancing Draw BST for insert, have students re-draw as balanced DO all solution agree? Yes, then it's easy, just name and code A-B-C C-B-A A-C-B Answer this one on TopHat C-A-B Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 12

13 Practice II - Balancing insert increases height of sub-tree A right rotate at 10 insert increases height of sub-tree C left rotate at 30 Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 13

14 Practice III - Balancing insert increases height of sub-tree B left-right rotate at 10 insert increases height of sub-tree B right-left rotate at 30 Copyright 2018 Deb Deppeler CS 400 (S18): W2T - 14