SET

java.lang.Object
- SET<Key>

Type Parameters:

Key - the generic type of a key in this set

All Implemented Interfaces:

java.lang.Iterable<Key>
```
public class SET<Key extends java.lang.Comparable<Key>>
extends java.lang.Object
implements java.lang.Iterable<Key>
```
The SET class represents an ordered set of comparable keys. It supports the usual add, contains, and delete methods. It also provides ordered methods for finding the minimum, maximum, floor, and ceiling and set methods for union, intersection, and equality.
Even though this implementation include the method equals(), it does not support the method hashCode() because sets are mutable.
This implementation uses a balanced binary search tree. It requires that the key type implements the Comparable interface and calls the compareTo() and method to compare two keys. It does not call either equals() or hashCode(). The add, contains, delete, minimum, maximum, ceiling, and floor methods take logarithmic time in the worst case. The size, and is-empty operations take constant time. Construction takes constant time.
This implementation uses a balanced binary search tree. It requires that For additional documentation, see Section 4.4 of Introduction to Programming in Java: An Interdisciplinary Approach by Robert Sedgewick and Kevin Wayne.

Constructor Summary

Constructors
Constructor and Description

SET()
Initializes an empty set.

SET(SET<Key> x)
Initializes a new set that is an independent copy of the specified set.

Constructors
Constructor and Description
`SET()` Initializes an empty set.
`SET(SET<Key> x)` Initializes a new set that is an independent copy of the specified set.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`add(Key key)` Adds the key to this set (if it is not already present).
`Key`	`ceiling(Key key)` Returns the smallest key in this set greater than or equal to `key`.
`boolean`	`contains(Key key)` Returns true if this set contains the given key.
`void`	`delete(Key key)` Removes the specified key from this set (if the set contains the specified key).
`boolean`	`equals(java.lang.Object other)` Compares this set to the specified set.
`Key`	`floor(Key key)` Returns the largest key in this set less than or equal to `key`.
`int`	`hashCode()` This operation is not supported because sets are mutable.
`SET<Key>`	`intersects(SET<Key> that)` Returns the intersection of this set and that set.
`boolean`	`isEmpty()` Returns true if this set is empty.
`java.util.Iterator<Key>`	`iterator()` Returns all of the keys in this set, as an iterator.
`static void`	`main(java.lang.String[] args)` Unit tests the `SET` data type.
`Key`	`max()` Returns the largest key in this set.
`Key`	`min()` Returns the smallest key in this set.
`int`	`size()` Returns the number of keys in this set.
`java.lang.String`	`toString()` Returns a string representation of this set.
`SET<Key>`	`union(SET<Key> that)` Returns the union of this set and that set.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.lang.Iterable
forEach, spliterator

- Constructor Detail
  - SET
```
public SET()
```
    Initializes an empty set.
  - SET
```
public SET(SET<Key> x)
```
    Initializes a new set that is an independent copy of the specified set.
- Method Detail
  - add
```
public void add(Key key)
```
    Adds the key to this set (if it is not already present).
    
    Parameters:
    
    key - the key to add
    
    Throws:
    
    java.lang.NullPointerException - if key is null
  - contains
```
public boolean contains(Key key)
```
    Returns true if this set contains the given key.
    
    Parameters:
    
    key - the key
    
    Returns:
    
    true if this set contains key; false otherwise
    
    Throws:
    
    java.lang.NullPointerException - if key is null
  - delete
```
public void delete(Key key)
```
    Removes the specified key from this set (if the set contains the specified key).
    
    Parameters:
    
    key - the key
    
    Throws:
    
    java.lang.NullPointerException - if key is null
  - size
```
public int size()
```
    Returns the number of keys in this set.
    
    Returns:
    
    the number of keys in this set
  - isEmpty
```
public boolean isEmpty()
```
    Returns true if this set is empty.
    
    Returns:
    
    true if this set is empty; false otherwise
  - iterator
```
public java.util.Iterator<Key> iterator()
```
    Returns all of the keys in this set, as an iterator. To iterate over all of the keys in a set named set, use the foreach notation: for (Key key : set).
    
    Specified by:
    
    iterator in interface java.lang.Iterable<Key extends java.lang.Comparable<Key>>
    
    Returns:
    
    an iterator to all of the keys in this set
  - max
```
public Key max()
```
    Returns the largest key in this set.
    
    Returns:
    
    the largest key in this set
    
    Throws:
    
    java.util.NoSuchElementException - if this set is empty
  - min
```
public Key min()
```
    Returns the smallest key in this set.
    
    Returns:
    
    the smallest key in this set
    
    Throws:
    
    java.util.NoSuchElementException - if this set is empty
  - ceiling
```
public Key ceiling(Key key)
```
    Returns the smallest key in this set greater than or equal to key.
    
    Parameters:
    
    key - the key
    
    Returns:
    
    the smallest key in this set greater than or equal to key
    
    Throws:
    
    java.lang.NullPointerException - if key is null
    
    java.util.NoSuchElementException - if there is no such key
  - floor
```
public Key floor(Key key)
```
    Returns the largest key in this set less than or equal to key.
    
    Parameters:
    
    key - the key
    
    Returns:
    
    the largest key in this set table less than or equal to key
    
    Throws:
    
    java.lang.NullPointerException - if key is null
    
    java.util.NoSuchElementException - if there is no such key
  - union
```
public SET<Key> union(SET<Key> that)
```
    Returns the union of this set and that set.
    
    Parameters:
    
    that - the other set
    
    Returns:
    
    the union of this set and that set
    
    Throws:
    
    java.lang.NullPointerException - if that is null
  - intersects
```
public SET<Key> intersects(SET<Key> that)
```
    Returns the intersection of this set and that set.
    
    Parameters:
    
    that - the other set
    
    Returns:
    
    the intersection of this set and that set
    
    Throws:
    
    java.lang.NullPointerException - if that is null
  - equals
```
public boolean equals(java.lang.Object other)
```
    Compares this set to the specified set.
    Note that this method declares two empty sets to be equal even if they are parameterized by different generic types. This is consistent with the behavior of equals() within Java's Collections framework.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Parameters:
    
    other - the other set
    
    Returns:
    
    true if this set equals other; false otherwise
  - hashCode
```
public int hashCode()
```
    This operation is not supported because sets are mutable.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    does not return a value
    
    Throws:
    
    java.lang.UnsupportedOperationException - if called
  - toString
```
public java.lang.String toString()
```
    Returns a string representation of this set.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    
    a string representation of this set, with the keys separated by single spaces
  - main
```
public static void main(java.lang.String[] args)
```
    Unit tests the SET data type.

Class SET<Key extends java.lang.Comparable<Key>>

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface java.lang.Iterable

Constructor Detail

SET

SET

Method Detail

add

contains

delete

size

isEmpty

iterator

max

min

ceiling

floor

union

intersects

equals

hashCode

toString

main