Sets and Maps

Ellen WalkerCPSC 201 Data Structures

Hiram College

Sets in the Collection Hierarchy

Set vs. List

• A list is a sequence of items– Order matters– Traversal makes sense– Duplicates are allowed in the list

• A set is a collection of items, without sequence– Order does not matter; traversal does not make

sense– No duplicates are allowed in the list

• Like ordered lists and binary search trees, sets are value-oriented

Mathematical Set Operations

• Element-of (x S) – Boolean: Is x a member of the set S?

• Subset (S T)– Boolean: Are all elements of S also elements of T?

• Union (S T)– Create a new set with all elements of S and all elements of T

• Intersection (S T)– Create a new set with all elements that are in both S and T

• Set-Difference (S – T)– Create a new set with all elements that are in S but not in T

Methods of Set<E>

Implementing Mathematical Operations

• Element-of (x S) – S.contains(x);

• Subset (S T)– T.containsAll(S);

• Union (S T)– S.addAll(T); or T.addAll(S);

• Intersection (S T)– S.retainAll(T) or T.retainAll(S);

• Set-Difference (S – T) – S.removeAll(T);

Create and Print a Set

HashSet<String> students201 = new HashSet<String>(); String[] names = {"ChrisK", "ChrisF", "Robin", "Tim", "Andrew",

"David", "Will", "Matt"}; for(int i=0;i<names.length;i++) students201.add(names[i]); System.out.println("Students in 201 are: ” +

students201);

Compute Union and Intersection

HashSet<String> inBoth = (HashSet<String>)students356.clone();

inBoth.retainAll(students201); //intersectionSystem.out.println("Students in both 201 and 356 are: " +

inBoth);

HashSet<String> inOne = (HashSet<String>)(students356.clone());

inOne.addAll(students201); //unionSystem.out.println("Students in one of the classes are: "

+ inOne);

Set Iteration

• Iterator presents elements of set in arbitrary order

• Because there is an iterator, we can use the foreach loop with sets:

for (String x : students201) System.out.println(x);

Maps

• A map is a set of ordered (key, value) pairs• Given the key, we should be able to find the

value• Example:

– { (CPSC, Computer Science), (MATH, Mathematics), (INTD, Interdisciplinary) (CS, Computer Science) }

Graphical View

• CPSC• CS• MATH• INTD

• Computer Science• Mathematics• Interdisciplinary

Arrows connect key to valueThis is a many-to-one mapping (vs. one-to-one)

Methods of Map < K, V >

Maps and Sets are Similar…

• In both, order doesn’t matter• For both, need to determine whether an

object is present (key, for a map)• Duplicates are not allowed (duplicate keys

not allowed for maps)• Maps are more complicated because the

association between key and value must be maintained

Corresponding Map and Set Methods

Map Methods• V get (Object key)

• V put(K key, V value)

• V remove (Object key)

Set Methods• boolean

contains(Object key)• boolean add (K key)

• boolean remove(K key)

Implementing Maps and Sets

• TreeMap and TreeSet– Implemented using Binary Search Tree (actually a

red-black tree)• HashMap and HashSet

– Implemented using Hash Table

Hash Codes in Java

• Object.hashCode()– Based on address in memory

• String.hashCode()– Multiply each character’s code by 31 raised to a

power depending on position– Example hash(“EAT”) = hash(‘E’)* 312+

hash(‘A’)*31 + hash(‘T’)– Hash(“EAT”) ≠ hash(“ATE”) ≠ hash(“TEA”)

.hashCode() and .equals()

• Java contract for .hashCode– If obj1.equals(obj2) then obj1.hashCode() ==

obj2.hashCode()

• Object’s .equals and .hashCode() depend on address• Many objects (e.g. Integer, String) override

both .equals() and .hashCode() to depend on value• If your class overrides .equals(), it should also

override .hashCode()