Compsci 201Binary Trees

Dna Linked Assignment

Owen Astrachan ola@cs.duke.eduOctober 19, 2018

10/17/2018 Compsci 201, Fall 2018, Recursion + Binary Trees 1

N is for …

• new• Allocating memory from the heap

• null• Value when nothing has been allocated

• next• Iterating if hasNext

10/18/17 Compsci 201, Fall 2017, Linked 2

Plan for Today

• Binary Trees, Binary Search Trees• Best of arrays and linked lists?• O(1) insert, O(log n) search

• Recursion will be indispensable

• DNA Linked Assignment• Conceptual overview

• Guest Speaker: Ge Wang

10/17/2018 Compsci 201, Fall 2018, Recursion + Binary Trees 3

Best of Both Worlds

• With arrays we can use binary search• This is O(log N), that’s really, really fast• Remember that 210 = 1024 so …

• With linked lists we can add/remove quickly• Cannot search, cannot index, can relink

• Can we get fast search and fast add/remove?

10/17/2018 Compsci 201, Fall 2018, Recursion + Binary Trees 4

Binary Search Trees

• Nodes have left/right references: similar prev/next• At each node: <= goes left, > goes right

• How do we search?• How do we insert?

• Insert: “koala”

�llama�

�tiger�

�monkey��jaguar��elephant�

�giraffe�

�pig��hippo� �leopard�

�koala�

�koala�

�koala�

�koala�

�koala�

10/17/2018 Compsci 201, Fall 2018, Recursion + Binary Trees 5

Tree Terminology

• Root: "top node", has no parent

• "macaque". Subtrees also have a root

• Leaf: bottom nodes, have no children

• "baboon", "lemur", "organutan"

• Path: sequence of parent-child nodes

• "macaque", "chimp", "lemur"

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees6

A TreeNode by any other name…• What does this look like? Doubly linked list?

public class TreeNode{

TreeNode left;TreeNode right;String info;TreeNode(String s,

TreeNode llink, TreeNode rlink){info = s;left = llink;right = rlink;

}}

�llama�

�tiger��giraffe�

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees7

Trees: Concepts and Code

• In a search tree: property holds at every node

• Nodes in left subtree are < (or <=)

• Nodes in right subtree are >

• To search or add: if not found?

• Look left if <=

• Look right if >

• Iterative or recursive

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees8

all values < 7

all values > 7

7

Tree Performance

• Seasrch for any value. Compare to root and …• Similar to binary search. O(log N) if tree "good"

• Trees are generally well-behaved, but !!!• Guarantee? Balanced tree: AVL or Red-Black

• We get O(log N) search and …• No shifting to add, find leaf

10/17/2018 Compsci 201, Fall 2018, Recursion + Binary Trees 9

all values < 7

all values > 7

7

Tree Algorithms/Methods

• Think of search trees as recursive/hierarchical

• Node with two subtrees

• What do we know about subtrees? Also tree!

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees10

Height of a tree• Longest root-to-leaf path (# nodes): 5,4,3 below

10/17/2018 Compsci 201, Fall 2018, Recursion + Binary Trees 11

Tree function: Tree height

• Compute tree height (longest root-to-leaf path)

int height(Tree root) {if (root == null) return 0;else {return 1 + Math.max(height(root.left),

height(root.right));}

}

• Find height of left subtree, height of right subtree

• Use results to determine height of tree

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees12

Interfaces and Inheritance

• EfficientMarkov extends BaseMarkov• Inherits method getRandomText()• This works the same in both classes!

• Method .getRandomText() uses myRandom• Must be accessible in BaseMarkov!

• Don't shadow state/instance variables

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees13

EfficientMarkov em = new EfficientMarkov();em.setTraining("hello new world");String st = em.getRandomText();// what getFollows() is called

Interfaces

• Specify method headers/signatures

• See MarkovInterface for examples

• BaseMarkov implements MarkovInterface

• Can also inherit default implementations

• Cannot have state in an interface

• myRandom and myText in Markov Assignment

• Thus use BaseMarkov.getRandomText()

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees14

From Links to …

11/1/17 Compsci 201, Fall 2017, Tree, Tries, Tradoffs 15

• What is the DNA/LinkStrand assignment about?• Why do we study linked lists• How do you work in a group?

From PCR to linked lists

• Polymerase Chain Reaction

• Make copies of a specific DNA segment

• Recombinant DNA

• Insert DNA using restriction enzymes

• Loosely forms basis for DNA/Linked assignment

• Big gains in efficiency using Linked Lists

• Compare to array of chars, e.g. Strings

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees16

Basics of cutAndSplice

• Find enzyme like ‘gat’

• Replace with splicee like ‘gggtttaaa’

• Strings and StringBuilder for creating new strings

• Complexity of “hello” + “world”, or A+B

• String: A + B, StringBuilder: B

11/1/17Compsci 201, Fall 2017, Tree, Tries,

Tradoffs17

What do linked lists get us?

• Faster run-time, much better use of memory

• We splice in constant time? Re-use strings

• Same as previous slide: sequential char view

11/1/17Compsci 201, Fall 2017, Tree, Tries,

Tradoffs18

String Concatenation Examined

• See StringPlay.java• https://github.com/astrachano/classcode201fall18

• Runtime of stringConcat(“hello”,N)• Depends on size of ret, 5, 10, 15, … 5*N

• 5(1 + 2 + … + N) which is O(N2)

11/1/17Compsci 201, Fall 2017, Tree, Tries,

Tradoffs19

public String stringConcat(String s, int reps) {String ret = "";for(int k=0; k < reps; k++) {

ret += s;}return ret;

}

StringBuilder Examined

• Just say no to quadratic, use StringBuilder

• String is immutable, StringBuilder is not

• Runtime of builderConcat(“hello”,N)• 5 + 5 + 5 + … + 5 a total of N times: O(N)

11/1/17Compsci 201, Fall 2017, Tree, Tries,

Tradoffs20

public String builderConcat(String s, int reps) {StringBuilder ret = new StringBuilder();for(int k=0; k < reps; k++) {

ret.append(s);}return ret.toString();

}

linked list improvement: memory

• Suppose we have B "gat" (blue), in strand size N

• Inserting size S "gggtttaaa" (green) splicees

• For String/StringBuilder: memory: B*S (+ N)

• For LinkedList: memory: S (re-use green!) (+ N)

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees21

linked list improvement: time

• Suppose we have B "gat" (blue), in strand size N

• Inserting size S "gggtttaaa" (green) splicees

• For String: time: B2S + N, builder: BS + N

• For LinkedList: B + N

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees22

Theory and Practice

• The JVM can sometimes optimize your code• Don’t optimize what you don’t have to …• http://www.pellegrino.link/2015/08/22/string-

concatenation-with-java-8.html

• Timings with System.nanoTime() are suspect• Other things going on in computer• JVM can go into garbage-collection mode• Other considerations

11/1/17 Compsci 201, Fall 2017, Tree, Tries, Tradoffs 23

WOTO

http://bit.ly/201fall18-oct19-1

11/1/17 Compsci 201, Fall 2017, Tree, Tries, Tradoffs 24

Guest Speaker

10/17/2018Compsci 201, Fall 2018, Recursion +

Binary Trees25

https://en.wikipedia.org/wiki/Ge_Wang