CS 310: Maps and Sets and Trees

Transcription

1 CS 310: Maps and Sets and Trees Chris Kauman Week 8-2

2 Logistics Oce hours Wednesday normal: 4:30-5:30pm Thursday 2-3pm special oce hours Reading Weiss Ch. 6 (Java Library Classes/Interfaces) 6.7 Sets, 6.8 Maps Weiss Ch 18 (Trees) Ch 18.4: - Iterator classes for traversals Reading: Weiss Ch 19 Binary Search Trees Today Maps and Sets General Trees and Traversals

3 Map and Set Map: TreeMap and HashMap (key,value) pairs Insert value into a map according to its key Retrieve value using same key Same for removal Same key maps to same "place" in the data structure Set TreeSet and HashSet Maps where key is value Insert into set using value itself as key Retrieve using value itself as key Same for removal Same value maps to same "place" in data structure

4 Have Set, Build Map Sets and Maps share much functionality. Q: If I have Set, how would I build Map? Given: SimpleSet Build: SimpleMap Collection of distinct objects Can only contain one of each thing Uniqueness determined by equals() method Operations add(x), get(x), remove(x), contains(x) ArraySet implements SimpleSet Set of (key,value) pairs Compare pairs only on whether their key is equal (a,x) == (a,x) (a,x) == (a,y) (a,x)!= (b,y) (a,x)!= (b,x) Use the set to ensure no redundant keys enter Implement put(k,v), get(k), remove(k), contains(k)

5 Trick 1: Use an internal class public class MapFromSet<K, V>{ // Trick: Use a nested class // Class to carry around (key,val) pairs public static class KeyVal<K, V>{ public K key; public V value; public KeyVal(K key, V value){ this.key = key; this.value = value; } // Required for any set to work // Compare only based on key public boolean equals(object o); // Required for HashSet to work right public int hashcode(); // Required for TreeSet to work public int compareto(keyval<k,v> kv); }

6 Trick 2: Use a set of the key/val pairs public interface SimpleSet<T> { boolean contains(t x); boolean add(t x); boolean remove(t x); T get(t x); } public class MapFromSet<K, V>{ public static class KeyVal<K, V>{...} // Trick: Given a working Set class: use it! private SimpleSet< KeyVal<K,V> > theset; // Implement these using theset public MapFromSet(); public void put(k key, V value); public void remove(k key); public boolean contains(k key); public V get(k key); }

7 Have Map, Build Set A great exam question: build a Set from a Map Map TreeMap and HashMap (key,value) pairs Each key has exactly one value Insert value into a map according to its key Same key maps to same "place" in the data structure Supports put(k,v), remove(k), contains(k) Set TreeSet and HashSet Use an internal Map Dene Set operations void add(t x) void remove(t x) T get(t x) boolean contains(t x)

8 Java Does it In Java: Map Set java.util.treemap is a red-black tree java.util.treeset uses a TreeMap java.util.hashmap is a separate chained hash table java.util.hashset uses a HashMap In Weiss: Set Map weiss.util.treeset is an AA-tree (another balanced tree) weiss.util.treemap uses TreeSet Lesson Re-use when it makes sense Think hard about when it makes sense to re-use

9 Ordering List property There is a well dened ordering of rst, next, last objects in the data structure A property of the Data Structure being used Wide ranging uses Supported structurally in LinkedList, ArrayList Not supported in hash tables (why not?) Sorting property There is a well dened ordering relation over all possible data of a particular type A property of the Data being stored "bigger than" "less than" "equal to" are well dened A data structure can try to mirror the data ordering structurally Useful for searching, walking through stored data in order

10 Sorted Lists Denition is straight-forward "Smallest" things are structurally "rst", "Biggest" last Ordering on elements (Comparable/Comparator) add/insert put elements in proper place Question: For a sorted List L, what is the complexity of L.insert(x) which preserves sorting? L is an ArrayList How long to nd insertion location? complete insertion? traverse elements in order (e.g. for printing)? L is a LinkedList How long to nd insertion location? complete insertion? traverse elements in order (e.g. for printing)?

11 Alternatives Hash Tables Abandon list property Abandon sorting property O(1) insertion/retrieval O(N) traversal, not ordered Trees Abandon list property Preserve sorting property O(log N) insertion/retrieval O(N) traversal, ordered Commonly Binary Trees Other variants

12 Roots Next the 2 weeks we'll talk about roots For simplicity, we'll call them trees Source

13 Mutated Nodes Node Data Next (???) (node) Data 5 data Binary Tree Node Left Right next Linked Nodes aka Tree 8 Linked Nodes, aka List 22 data root 31 next data 20 next Node structures should be familiar for linked lists Singly linked: next/data Doubly linked: next/previous/data Trees use Nodes as well children, data, possibly parent Arbitrary Trees: List<Node> of children Binary Trees: left and right children

14 Tree Properties of Interest Root of tree Leaves Data at nodes Size (number of nodes) Height of tree Depth of a node

15 The Many Ways to Walk No list property: several orders to traverse tree (a) Pre-order traversal (parent, left, right) (b) Post-order traversal (left, right, parent) (c) In-order traversal (left, parent, right)

16 Next Time Binary Search Trees insert/remove findmin/findmax Order statistics Start start discussing balance Read Weiss Ch. 6 (Java Library Classes/Interfaces) 6.7 Sets, 6.8 Maps Weiss Ch 18 (Trees) Ch 18.4: - Iterator classes for traversals Reading: Weiss Ch 19 Binary Search Trees