! Insert a key with specified value. ! Given a key, search for the corresponding value. ! Insert URL with specified IP address.

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1 Symbol Table 4.4 Symbol Tables Symbol table. Keyvalue pair abstraction.! Insert a key with specified value.! Given a key, search for the corresponding value. Ex. [DS lookup]! Insert URL with specified IP address.! Given URL, find corresponding IP address. URL IP address key value Introduction to Computer Science Robert Sedgewick and Kevin Wayne Copyright Symbol Table API Symbol Table Applicions public class ST<Key key, Val val> (symbol table da type) void Val boolean void Iteror<Key> ST() put(key key, Val val) get(key key) contains(key key) remove(key key) iteror() cree an empty symbol table insert a keyvalue pair return value associed with given key is the given key present? delete the key and associed value return an iteror over the keys public stic void main(string[] args) { ST<String, String> st = new ST<String, String>(); st.put(" " "); st.put(" " "); st.put(" " "); st[" = " " StdOut.println(st.get(" StdOut.println(st.get(" StdOut.println(st.get(" st[" null Applicion Purpose Key Value Phone book Look up phone number ame Phone number Bank Process transaction Account number Transaction details File share Find song to download ame of song Computer ID File system Find file on disk Filename Locion on disk Dictionary Look up word Word Definition Web search Find relevant documents Keyword List of documents Book index Find relevant pages Keyword List of pages Web cache Download Filename File contents Gemics Find markers DA string Kwn positions DS Find IP address given URL URL IP address Reverse DS Find URL given IP address IP address URL Compiler Find properties of variable Variable name Value and type Routing table Route Internet packets Destinion Best route 3 4

2 Symbol Table Client: Frequency Counter Dasets Frequency counter. [e.g., web traffic analysis, linguistic analysis]! Read in a key.! If key is in symbol table, increment counter by one; If key is t in symbol table, insert it with count = 1. Linguistic analysis. Compute word frequencies in a corpus of text. File Description Words Distinct public class FrequencyCounter { public stic void main(string[] args) { ST<String, Integer> st = new ST<String, Integer>(); mobydict.txt leipzig100k.txt Melville's Moby Dick 100K random sentences 210,028 2,121,054 16, ,256 while (!StdIn.isEmpty()) { String key = StdIn.readString(); if (st.contains(key)) st.put(key, st.get(key) + 1); else st.put(key, 1); calcule frequencies leipzig200k.txt leipzig1m.txt 200K random sentences 1M random sentences 4,238,435 21,191, , ,580 enhanced for loop for (String s : st) StdOut.println(st.get(s) + " " + s); print results Reference: Wortschz corpus, Univesität Leipzig Zipf's Law Zipf's Law Linguistic analysis. Compute word frequencies in a piece of text. Linguistic analysis. Compute word frequencies in a piece of text. % java Freq < mobydick.txt 4583 a 2 aback 2 abaft 3 abandon 7 abandoned 1 abandonedly 2 abandonment 2 abased 1 abasement 2 abashed 1 abe % java Freq < mobydick.txt sort rn the 6415 of 6247 and 4583 a 4508 to 4037 in 2911 th 2481 his 2370 it 1940 i 1793 but % java Freq < leipzig1m.txt sort rn the of to a and in for The th is said Zipf's law. In nural language, frequency of i th most common word is proportional to i. e.g., most frequent word occurs about twice as often as second most frequent one Zipf's law. In nural language, frequency of i th most common word is proportional to i. e.g., most frequent word occurs about twice as often as second most frequent one 7 8

3 Symbol Table: Brute Force Implementions Symbol Table: Implementions Cost Summary Unsorted array.! Put: add key to the end (if t already there).! Get: scan through all keys to find desired value. Urdered array. Hopelessly slow for large inputs. Ordered array. Acceptable if many more searches than inserts; too slow if many inserts Running Time Frequency Count Sorted array.! Put: find insertion point, and shift all larger keys right.! Get: binary search to find desired key. Implemention Search Insert Moby 100K 200K 1M Urdered array 170 sec 4.1 hr Ordered array log 5.8 sec 5.8 min 15 min 2.1 hr insert 28 Challenge. Make all ops logarithmic Binary Search Trees Binary Search Trees Def. A binary search tree is a binary tree in symmetric order. Binary tree is either:! Empty.! A keyvalue pair and two binary trees. hi (values hidden) do if pi be go me of we Symmetric order.! Keys in left subtree are smaller than parent.! Keys in right subtree are larger than parent. de x A smaller keys B larger keys Reference: Knuth, The Art of Computer Programming 11 12

4 Binary Tree: Java Implemention BST: Skeleton To implement: use two links per ode. A ode is comprised of:! A key.! A value! A reference to the left subtree.! A reference to the right subtree. prive class ode { prive Key key; prive Val val; prive ode left; prive ode right; root BST. Allow generic keys and values. public class BST<Key extends Comparable, Val> { prive ode root; prive class ode { prive Key key; prive Val val; prive ode left, right; // root of the BST prive ode(key key, Val val) { this.key = key; this.val = val; allows String and Integer keys; see book for details (values hidden again) public void put(key key, Val val) { public Val get(key key) { public boolean contains(key key) { BST: Search BST: Insert Get. Return val corresponding to given key, or null if such key. public Val get(key key) { return get(root, key); prive Val get(ode x, Key key) { if (x == null) return null; int cmp = key.compareto(x.key); if (cmp < 0) return get(x.left, key); else if (cmp > 0) return get(x.right, key); else if (cmp > 0) return x.val; public boolean contains(key key) { return (get(key)!= null); negive if less, zero if equal, positive if greer Put. Associe val with key.! Search, then insert.! Concise (but tricky) recursive code. public void put(key key, Val val) { root = insert(root, key, val); prive ode insert(ode x, Key key, Val val) { if (x == null) return new ode(key, val); int cmp = key.compareto(x.key); ifse if (cmp < 0) x.left = insert(x.left, key, val); else if (cmp > 0) x.right = insert(x.right, key, val); else x.val = val; return x; overwrite old value with new value 15 16

5 BST Insertion Example BST Implemention: Practice BST insert. A S E R C H I G X M P L Bottom line. Difference between a practical solution and solution. Running Time Frequency Count Implemention Search Insert Moby 100K 200K 1M Urdered array 170 sec 4.1 hr Ordered array log 5.8 sec 5.8 min 15 min 2.1 hr BST??.95 sec 7.1 sec 14 sec 69 sec BST: Analysis BST: Analysis Running time per put/get.! There are many BSTs th correspond to same set of keys.! Cost is proportional to depth of de. number of des on ph from root to de Fact. If keys are inserted in random order, average depth! 2 ln and expected height! 4.31 ln. maximum depth Corollary. Search and insert take logarithmic time on average. depth = 1 hi be unbalanced (height = 9) balanced (height = 5) depth = 2 depth = 3 do if pi go pi depth = 4 be go me of we do if of we depth = 5 hi me 19 20

6 Symbol Table: Implementions Cost Summary RedBlack Tree BST. Logarithmic time ops if keys inserted in random order. Redblack tree. A clever BST variant th guarantees height " 2 lg. see COS 226 Running Time Frequency Count Running Time Frequency Count Implemention Search Insert Moby 100K 200K 1M Implemention Search Insert Moby 100K 200K 1M Urdered array 170 sec 4.1 hr Urdered array 170 sec 4.1 hr Ordered array log 5.8 sec 5.8 min 15 min 2.1 hr Ordered array log 5.8 sec 5.8 min 15 min 2.1 hr BST log log.95 sec 7.1 sec 14 sec 69 sec BST log log.95 sec 7.1 sec 14 sec 69 sec Redblack log log.95 sec 7.0 sec 14 sec 74 sec assumes keys inserted in random order assumes keys inserted in random order Q. Can we guarantee logarithmic performance? Symbol Table: Summary Symbol table. Quintessential dabase lookup da type. Iterion Choices. Ordered array, urdered array, BST, redblack, hash,.! Different implementions have different performance characteristics.! Java libraries: TreeMap, HashMap. Remark. Better symbol table implemention improves all clients

7 Irder Traversal Preorder Traversal Irder traversal. hi Preorder traversal. hi! Recursively visit left subtree.! Visit de.! Visit de.! Recursively visit left subtree.! Recursively visit right subtree. do if pi! Recursively visit right subtree. do if pi be go me of we be go me of we irder: be do go hi if me of pi we preorder: hi do be go if me pi of we public irder() { irder(root); prive void irder(ode x) { if (x == null) return; irder(x.left); StdOut.println(x.key); irder(x.right); public preorder() { preorder(root); prive void preorder(ode x) { if (x == null) return; preorder(x.left); StdOut.println(x.key); preorder(x.right); Postorder Traversal Enhanced For Loop Postorder traversal. hi Enhanced for loop. Enable client to itere over items in a collection.! Recursively visit left subtree.! Recursively visit right subtree.! Visit de. do if pi be go me of we public postorder() { postorder(root); postorder: be go do me if of we pi hi ST<String, Integer> st = new ST<String, Integer>(); for (String s : st) { StdOut.println(st.get(s) + " " + s); prive void postorder(ode x) { if (x == null) return; postorder(x.left); postorder(x.right); StdOut.println(x.key); 27 28

Enhanced For Loop with BST BST. Add following code to make compible with enhanced for loop. see COS 226 for details Inverted Index import java.util.

osuchelementexception; public class BST<Key extends Comparable, Val> implements Iterable<Key> { prive ode root; prive class ode { public void put(key key, Val val) { public Val get(key key) { public

8 Enhanced For Loop with BST BST. Add following code to make compible with enhanced for loop. see COS 226 for details Inverted Index import java.util.iteror; import java.util.osuchelementexception; public class BST<Key extends Comparable, Val> implements Iterable<Key> { prive ode root; prive class ode { public void put(key key, Val val) { public Val get(key key) { public boolean contains(key key) { public Iteror<Key> iteror() { return new Irder(); prive class Irder implements Iteror<Key> { prive Stack<ode> stack = new Stack<ode>(); Irder() { ode x = root; while (x!= null) { stack.push(x); x = x.left; public boolean hasext() { return!stack.isempty(); public Key next() { if (!hasext()) throw new osuchelementexception(); ode x = stack.pop(); Key key = x.key; x = x.right; while (x!= null) { stack.push(x); x = x.left; return key; 29 Introduction to Computer Science Robert Sedgewick and Kevin Wayne Copyright Inverted Index Set API Inverted index. Given a list of pages, preprocess them so th you can quickly find all pages containing a given query word. Ex 1. Book index. Ex 2. Web search engine index. Ex 3. File index (e.g, Spotlight). Symbol table.! Key = query word.! Value = set of pages. duplices Set. Urdered collection of distinct keys. public class SET<Key key> (set da type) SET() cree an empty set void add(key key) add a key to the set boolean contains(key key) is the given key in the set? void remove(key key) delete the key from the set Iteror<Key> iteror() return an iteror over the keys Efficient implemention. Same as symbol table, but igre value

9 Inverted Index: Java Implemention Inverted Index: Example public class InvertedIndex { public stic void main(string[] args) { ST<String, SET<String>> st = new ST<String, SET<String>>(); for (String filename : args) { In in = new In(filename); while (!in.isempty()) { String word = in.readstring(); if (!st.contains(word)) st.put(word, new SET<String>()); st.get(word).add(filename); build inverted index Ex. Index all your.java files. % java InvertedIndex *.java set DeDup.java ExceptionFilter.java InvertedIndex.java SET.java vector SparseVector.java SparseMrix.java spotlight OT FOUD while (!Stdin.isEmpty()) { String query = StdIn.readString(); System.out.println(st.get(query)); process queries Inverted Index Extensions.! Igre case.! Igre stopwords: the, on, of,! Boolean queries: set intersection (AD), set union (OR).! Proximity search: multiple words must appear nearby.! Record position and number of occurrences of word in document. Other Types of Trees 35 Introduction to Computer Science Robert Sedgewick and Kevin Wayne Copyright

10 Other Types of Trees Other Types of Trees root Charles! Parse tree: represents the syntactic structure of a stement, sentence, or expression. dad mom + Philip Elizabeth II * 7 Andrew Alice George VI Elizabeth George I Olga Louis Victoria George V Mary Claude Celia (10 * 12) Other Types of Trees Other Types of Trees! Parse tree.! Unix file hierarchy. bin lib etc u /! Parse tree.! Unix file hierarchy.! Phylogeny tree. aaclarke cos126 zrnye files grades submit sequence dsp tsp Point.java TSP.java tsp13509.txt 39 40

Other Types of Trees Other Types of Trees! Parse tree.! Unix file hierarchy.! Phylogeny tree.! GUI containment hierarchy.! Parse tree.! Unix file hierarchy.! Phylogeny tree.! GUI containment hierarchy.! Tournament trees.

11 Other Types of Trees Other Types of Trees! Parse tree.! Unix file hierarchy.! Phylogeny tree.! GUI containment hierarchy.! Parse tree.! Unix file hierarchy.! Phylogeny tree.! GUI containment hierarchy.! Tournament trees. Italien 1 Italien 1 iederlande 3 Argentinien 2 Italien 1 iederlande 3 Spanien 4 Argentinien 2 Deutschland 5 Frankreich 6 Italien 1 iederlande 3 Polen 7 Spanien 4 USA 8 Reference: Reference: Tobias Lauer 41 42

! Insert a key with specified value. ! Given a key, search for the corresponding value. ! Insert URL with specified IP address.

! Insert a key with specified value. ! Given a key, search for the corresponding value. ! Insert URL with specified IP address. Symbol Table 4.4 Symbol Tables Symbol table. Key-value pair abstraction.! Insert a key with specied value.! Given a key, search for the corresponding value. Ex. [DS lookup]! Insert URL with specied IP