java.util
Class TreeMap

java.lang.Object
  |
  +--java.util.AbstractMap
        |
        +--java.util.TreeMap

All Implemented Interfaces:

Cloneable, Map, Serializable, SortedMap

public class TreeMap

extends AbstractMap

implements SortedMap, Cloneable, Serializable

Untamed:

See Also:

Serialized Form

Field Summary

private static boolean	BLACK
private Comparator	comparator The Comparator used to maintain order in this TreeMap, or null if this TreeMap uses its elements natural ordering.
private Set	entrySet This field is initialized to contain an instance of the entry set view the first time this view is requested.
private int	modCount The number of structural modifications to the tree.
private static boolean	RED
private java.util.TreeMap.Entry	root
private static long	serialVersionUID
private int	size The number of entries in the tree

Fields inherited from class java.util.AbstractMap

keySet, values

Constructor Summary

TreeMap()
Enabled: Constructs a new, empty map, sorted according to the keys' natural order.

TreeMap(Comparator c)
Enabled: Constructs a new, empty map, sorted according to the given comparator.

TreeMap(Map m)
Enabled: Constructs a new map containing the same mappings as the given map, sorted according to the keys' natural order.

TreeMap(SortedMap m)
Enabled: Constructs a new map containing the same mappings as the given SortedMap, sorted according to the same ordering.

Method Summary

(package private) void	addAllForTreeSet(SortedSet set, Object defaultVal) Intended to be called only from TreeSet.addAll
private static java.util.TreeMap.Entry	buildFromSorted(int level, int lo, int hi, int redLevel, Iterator it, ObjectInputStream str, Object defaultVal) Recursive "helper method" that does the real work of the of the previous method.
private void	buildFromSorted(int size, Iterator it, ObjectInputStream str, Object defaultVal) Linear time tree building algorithm from sorted data.
void	clear() Enabled: Removes all mappings from this TreeMap.
Object	clone() Suppressed: Returns a shallow copy of this TreeMap instance.
private static boolean	colorOf(java.util.TreeMap.Entry p) Balancing operations.
Comparator	comparator() Enabled: Returns the comparator used to order this map, or null if this map uses its keys' natural order.
private int	compare(Object k1, Object k2) Compares two keys using the correct comparison method for this TreeMap.
private static int	computeRedLevel(int sz) Find the level down to which to assign all nodes BLACK.
boolean	containsKey(Object key) Enabled: Returns true if this map contains a mapping for the specified key.
boolean	containsValue(Object value) Enabled: Returns true if this map maps one or more keys to the specified value.
private void	decrementSize()
private void	deleteEntry(java.util.TreeMap.Entry p) Delete node p, and then rebalance the tree.
Set	entrySet() Enabled: Returns a set view of the mappings contained in this map.
private java.util.TreeMap.Entry	firstEntry() Returns the first Entry in the TreeMap (according to the TreeMap's key-sort function).
Object	firstKey() Enabled: Returns the first (lowest) key currently in this sorted map.
private void	fixAfterDeletion(java.util.TreeMap.Entry x) From CLR
private void	fixAfterInsertion(java.util.TreeMap.Entry x) From CLR
Object	get(Object key) Enabled: Returns the value to which this map maps the specified key.
private java.util.TreeMap.Entry	getCeilEntry(Object key) Gets the entry corresponding to the specified key; if no such entry exists, returns the entry for the least key greater than the specified key; if no such entry exists (i.e., the greatest key in the Tree is less than the specified key), returns null.
private java.util.TreeMap.Entry	getEntry(Object key) Returns this map's entry for the given key, or null if the map does not contain an entry for the key.
private java.util.TreeMap.Entry	getPrecedingEntry(Object key) Returns the entry for the greatest key less than the specified key; if no such entry exists (i.e., the least key in the Tree is greater than the specified key), returns null.
SortedMap	headMap(Object toKey) Enabled: Returns a view of the portion of this map whose keys are strictly less than toKey.
private void	incrementSize()
private static Object	key(java.util.TreeMap.Entry e) Returns the key corresonding to the specified Entry.
Set	keySet() Enabled: Returns a Set view of the keys contained in this map.
private java.util.TreeMap.Entry	lastEntry() Returns the last Entry in the TreeMap (according to the TreeMap's key-sort function).
Object	lastKey() Enabled: Returns the last (highest) key currently in this sorted map.
private static java.util.TreeMap.Entry	leftOf(java.util.TreeMap.Entry p)
private static java.util.TreeMap.Entry	parentOf(java.util.TreeMap.Entry p)
Object	put(Object key, Object value) Enabled: Associates the specified value with the specified key in this map.
void	putAll(Map map) Enabled: Copies all of the mappings from the specified map to this map.
private void	readObject(ObjectInputStream s) Reconstitute the TreeMap instance from a stream (i.e., deserialize it).
(package private) void	readTreeSet(int size, ObjectInputStream s, Object defaultVal) Intended to be called only from TreeSet.readObject
Object	remove(Object key) Enabled: Removes the mapping for this key from this TreeMap if present.
private static java.util.TreeMap.Entry	rightOf(java.util.TreeMap.Entry p)
private void	rotateLeft(java.util.TreeMap.Entry p) From CLR
private void	rotateRight(java.util.TreeMap.Entry p) From CLR
private static void	setColor(java.util.TreeMap.Entry p, boolean c)
int	size() Enabled: Returns the number of key-value mappings in this map.
SortedMap	subMap(Object fromKey, Object toKey) Enabled: Returns a view of the portion of this map whose keys range from fromKey, inclusive, to toKey, exclusive.
private java.util.TreeMap.Entry	successor(java.util.TreeMap.Entry t) Returns the successor of the specified Entry, or null if no such.
SortedMap	tailMap(Object fromKey) Enabled: Returns a view of the portion of this map whose keys are greater than or equal to fromKey.
private static boolean	valEquals(Object o1, Object o2) Test two values for equality.
Collection	values() Enabled: Returns a collection view of the values contained in this map.
private boolean	valueSearchNonNull(java.util.TreeMap.Entry n, Object value)
private boolean	valueSearchNull(java.util.TreeMap.Entry n)
private void	writeObject(ObjectOutputStream s) Save the state of the TreeMap instance to a stream (i.e., serialize it).

Methods inherited from class java.util.AbstractMap

equals, hashCode, isEmpty, toString

Methods inherited from class java.lang.Object

finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.util.Map

equals, hashCode, isEmpty

Field Detail

comparator

private Comparator comparator

The Comparator used to maintain order in this TreeMap, or null if this TreeMap uses its elements natural ordering.

root

private transient java.util.TreeMap.Entry root

size

private transient int size

The number of entries in the tree

modCount

private transient int modCount

The number of structural modifications to the tree.

entrySet

private transient volatile Set entrySet

This field is initialized to contain an instance of the entry set view the first time this view is requested. The view is stateless, so there's no reason to create more than one.

RED

private static final boolean RED

BLACK

private static final boolean BLACK

serialVersionUID

private static final long serialVersionUID

Constructor Detail

TreeMap

public TreeMap()

Enabled: Constructs a new, empty map, sorted according to the keys' natural order. All keys inserted into the map must implement the Comparable interface. Furthermore, all such keys must be mutually comparable: k1.compareTo(k2) must not throw a ClassCastException for any elements k1 and k2 in the map. If the user attempts to put a key into the map that violates this constraint (for example, the user attempts to put a string key into a map whose keys are integers), the put(Object key, Object value) call will throw a ClassCastException.

See Also:

Comparable

TreeMap

public TreeMap(Comparator c)

Enabled: Constructs a new, empty map, sorted according to the given comparator. All keys inserted into the map must be mutually comparable by the given comparator: comparator.compare(k1, k2) must not throw a ClassCastException for any keys k1 and k2 in the map. If the user attempts to put a key into the map that violates this constraint, the put(Object key, Object value) call will throw a ClassCastException.

Parameters:

c - the comparator that will be used to sort this map. A null value indicates that the keys' natural ordering should be used.

TreeMap

public TreeMap(Map m)

Enabled: Constructs a new map containing the same mappings as the given map, sorted according to the keys' natural order. All keys inserted into the new map must implement the Comparable interface. Furthermore, all such keys must be mutually comparable: k1.compareTo(k2) must not throw a ClassCastException for any elements k1 and k2 in the map. This method runs in n*log(n) time.

Parameters:

m - the map whose mappings are to be placed in this map.

Throws:

ClassCastException - the keys in t are not Comparable, or are not mutually comparable.

NullPointerException - if the specified map is null.

TreeMap

public TreeMap(SortedMap m)

Enabled: Constructs a new map containing the same mappings as the given SortedMap, sorted according to the same ordering. This method runs in linear time.

Parameters:

m - the sorted map whose mappings are to be placed in this map, and whose comparator is to be used to sort this map.

Throws:

NullPointerException - if the specified sorted map is null.

Method Detail

incrementSize

private void incrementSize()

decrementSize

private void decrementSize()

size

public int size()

Enabled: Returns the number of key-value mappings in this map.

Specified by:

size in interface Map

Overrides:

size in class AbstractMap

Returns:

the number of key-value mappings in this map.

containsKey

public boolean containsKey(Object key)

Enabled: Returns true if this map contains a mapping for the specified key.

Specified by:

containsKey in interface Map

Overrides:

containsKey in class AbstractMap

Parameters:

key - key whose presence in this map is to be tested.

Returns:

true if this map contains a mapping for the specified key.

Throws:

ClassCastException - if the key cannot be compared with the keys currently in the map.

NullPointerException - key is null and this map uses natural ordering, or its comparator does not tolerate null keys.

containsValue

public boolean containsValue(Object value)

Enabled: Returns true if this map maps one or more keys to the specified value. More formally, returns true if and only if this map contains at least one mapping to a value v such that (value==null ? v==null : value.equals(v)). This operation will probably require time linear in the Map size for most implementations of Map.

Specified by:

containsValue in interface Map

Overrides:

containsValue in class AbstractMap

Parameters:

value - value whose presence in this Map is to be tested.

Returns:

true if a mapping to value exists; false otherwise.

Since:

1.2

valueSearchNull

private boolean valueSearchNull(java.util.TreeMap.Entry n)

valueSearchNonNull

private boolean valueSearchNonNull(java.util.TreeMap.Entry n,
                                   Object value)

get

public Object get(Object key)

Enabled: Returns the value to which this map maps the specified key. Returns null if the map contains no mapping for this key. A return value of null does not necessarily indicate that the map contains no mapping for the key; it's also possible that the map explicitly maps the key to null. The containsKey operation may be used to distinguish these two cases.

Specified by:

get in interface Map

Overrides:

get in class AbstractMap

Parameters:

key - key whose associated value is to be returned.

Returns:

the value to which this map maps the specified key, or null if the map contains no mapping for the key.

Throws:

ClassCastException - key cannot be compared with the keys currently in the map.

NullPointerException - key is null and this map uses natural ordering, or its comparator does not tolerate null keys.

See Also:

containsKey(Object)

comparator

public Comparator comparator()

Enabled: Returns the comparator used to order this map, or null if this map uses its keys' natural order.

Specified by:

comparator in interface SortedMap

Returns:

the comparator associated with this sorted map, or null if it uses its keys' natural sort method.

firstKey

public Object firstKey()

Enabled: Returns the first (lowest) key currently in this sorted map.

Specified by:

firstKey in interface SortedMap

Returns:

the first (lowest) key currently in this sorted map.

Throws:

NoSuchElementException - Map is empty.

lastKey

public Object lastKey()

Enabled: Returns the last (highest) key currently in this sorted map.

Specified by:

lastKey in interface SortedMap

Returns:

the last (highest) key currently in this sorted map.

Throws:

NoSuchElementException - Map is empty.

putAll

public void putAll(Map map)

Enabled: Copies all of the mappings from the specified map to this map. These mappings replace any mappings that this map had for any of the keys currently in the specified map.

Specified by:

putAll in interface Map

Overrides:

putAll in class AbstractMap

Parameters:

map - mappings to be stored in this map.

Throws:

ClassCastException - class of a key or value in the specified map prevents it from being stored in this map.

NullPointerException - if the given map is null or this map does not permit null keys and a key in the specified map is null.

getEntry

private java.util.TreeMap.Entry getEntry(Object key)

Returns this map's entry for the given key, or null if the map does not contain an entry for the key.

Returns:

this map's entry for the given key, or null if the map does not contain an entry for the key.

Throws:

ClassCastException - if the key cannot be compared with the keys currently in the map.

NullPointerException - key is null and this map uses natural order, or its comparator does not tolerate * null keys.

getCeilEntry

private java.util.TreeMap.Entry getCeilEntry(Object key)

Gets the entry corresponding to the specified key; if no such entry exists, returns the entry for the least key greater than the specified key; if no such entry exists (i.e., the greatest key in the Tree is less than the specified key), returns null.

getPrecedingEntry

private java.util.TreeMap.Entry getPrecedingEntry(Object key)

Returns the entry for the greatest key less than the specified key; if no such entry exists (i.e., the least key in the Tree is greater than the specified key), returns null.

key

private static Object key(java.util.TreeMap.Entry e)

Returns the key corresonding to the specified Entry. Throw NoSuchElementException if the Entry is null.

put

public Object put(Object key,
                  Object value)

Enabled: Associates the specified value with the specified key in this map. If the map previously contained a mapping for this key, the old value is replaced.

Specified by:

put in interface Map

Overrides:

put in class AbstractMap

Parameters:

key - key with which the specified value is to be associated.

value - value to be associated with the specified key.

Returns:

previous value associated with specified key, or null if there was no mapping for key. A null return can also indicate that the map previously associated null with the specified key.

Throws:

ClassCastException - key cannot be compared with the keys currently in the map.

NullPointerException - key is null and this map uses natural order, or its comparator does not tolerate null keys.

remove

public Object remove(Object key)

Enabled: Removes the mapping for this key from this TreeMap if present.

Specified by:

remove in interface Map

Overrides:

remove in class AbstractMap

Parameters:

key - key for which mapping should be removed

Returns:

previous value associated with specified key, or null if there was no mapping for key. A null return can also indicate that the map previously associated null with the specified key.

Throws:

ClassCastException - key cannot be compared with the keys currently in the map.

NullPointerException - key is null and this map uses natural order, or its comparator does not tolerate null keys.

clear

public void clear()

Enabled: Removes all mappings from this TreeMap.

Specified by:

clear in interface Map

Overrides:

clear in class AbstractMap

clone

public Object clone()

Suppressed: Returns a shallow copy of this TreeMap instance. (The keys and values themselves are not cloned.)

Overrides:

clone in class AbstractMap

Returns:

a shallow copy of this Map.

keySet

public Set keySet()

Enabled: Returns a Set view of the keys contained in this map. The set's iterator will return the keys in ascending order. The map is backed by this TreeMap instance, so changes to this map are reflected in the Set, and vice-versa. The Set supports element removal, which removes the corresponding mapping from the map, via the Iterator.remove, Set.remove, removeAll, retainAll, and clear operations. It does not support the add or addAll operations.

Specified by:

keySet in interface Map

Overrides:

keySet in class AbstractMap

Returns:

a set view of the keys contained in this TreeMap.

values

public Collection values()

Enabled: Returns a collection view of the values contained in this map. The collection's iterator will return the values in the order that their corresponding keys appear in the tree. The collection is backed by this TreeMap instance, so changes to this map are reflected in the collection, and vice-versa. The collection supports element removal, which removes the corresponding mapping from the map through the Iterator.remove, Collection.remove, removeAll, retainAll, and clear operations. It does not support the add or addAll operations.

Specified by:

values in interface Map

Overrides:

values in class AbstractMap

Returns:

a collection view of the values contained in this map.

entrySet

public Set entrySet()

Enabled: Returns a set view of the mappings contained in this map. The set's iterator returns the mappings in ascending key order. Each element in the returned set is a Map.Entry. The set is backed by this map, so changes to this map are reflected in the set, and vice-versa. The set supports element removal, which removes the corresponding mapping from the TreeMap, through the Iterator.remove, Set.remove, removeAll, retainAll and clear operations. It does not support the add or addAll operations.

Specified by:

entrySet in interface Map

Specified by:

entrySet in class AbstractMap

Returns:

a set view of the mappings contained in this map.

See Also:

Map.Entry

subMap

public SortedMap subMap(Object fromKey,
                        Object toKey)

Enabled: Returns a view of the portion of this map whose keys range from fromKey, inclusive, to toKey, exclusive. (If fromKey and toKey are equal, the returned sorted map is empty.) The returned sorted map is backed by this map, so changes in the returned sorted map are reflected in this map, and vice-versa. The returned sorted map supports all optional map operations.

The sorted map returned by this method will throw an IllegalArgumentException if the user attempts to insert a key less than fromKey or greater than or equal to toKey.

Note: this method always returns a half-open range (which includes its low endpoint but not its high endpoint). If you need a closed range (which includes both endpoints), and the key type allows for calculation of the successor a given key, merely request the subrange from lowEndpoint to successor(highEndpoint). For example, suppose that m is a sorted map whose keys are strings. The following idiom obtains a view containing all of the key-value mappings in m whose keys are between low and high, inclusive:

    SortedMap sub = m.submap(low, high+"\0");

A similar technique can be used to generate an open range (which contains neither endpoint). The following idiom obtains a view containing all of the key-value mappings in m whose keys are between low and high, exclusive:

    SortedMap sub = m.subMap(low+"\0", high);

Specified by:

subMap in interface SortedMap

Parameters:

fromKey - low endpoint (inclusive) of the subMap.

toKey - high endpoint (exclusive) of the subMap.

Returns:

a view of the portion of this map whose keys range from fromKey, inclusive, to toKey, exclusive.

Throws:

ClassCastException - if fromKey and toKey cannot be compared to one another using this map's comparator (or, if the map has no comparator, using natural ordering).

IllegalArgumentException - if fromKey is greater than toKey.

NullPointerException - if fromKey or toKey is null and this map uses natural order, or its comparator does not tolerate null keys.

headMap

public SortedMap headMap(Object toKey)

Enabled: Returns a view of the portion of this map whose keys are strictly less than toKey. The returned sorted map is backed by this map, so changes in the returned sorted map are reflected in this map, and vice-versa. The returned sorted map supports all optional map operations.

The sorted map returned by this method will throw an IllegalArgumentException if the user attempts to insert a key greater than or equal to toKey.

Note: this method always returns a view that does not contain its (high) endpoint. If you need a view that does contain this endpoint, and the key type allows for calculation of the successor a given key, merely request a headMap bounded by successor(highEndpoint). For example, suppose that suppose that m is a sorted map whose keys are strings. The following idiom obtains a view containing all of the key-value mappings in m whose keys are less than or equal to high:

     SortedMap head = m.headMap(high+"\0");
 

Specified by:

headMap in interface SortedMap

Parameters:

toKey - high endpoint (exclusive) of the headMap.

Returns:

a view of the portion of this map whose keys are strictly less than toKey.

Throws:

ClassCastException - if toKey is not compatible with this map's comparator (or, if the map has no comparator, if toKey does not implement Comparable).

IllegalArgumentException - if this map is itself a subMap, headMap, or tailMap, and toKey is not within the specified range of the subMap, headMap, or tailMap.

NullPointerException - if toKey is null and this map uses natural order, or its comparator does not tolerate null keys.

tailMap

public SortedMap tailMap(Object fromKey)

Enabled: Returns a view of the portion of this map whose keys are greater than or equal to fromKey. The returned sorted map is backed by this map, so changes in the returned sorted map are reflected in this map, and vice-versa. The returned sorted map supports all optional map operations.

The sorted map returned by this method will throw an IllegalArgumentException if the user attempts to insert a key less than fromKey.

Note: this method always returns a view that contains its (low) endpoint. If you need a view that does not contain this endpoint, and the element type allows for calculation of the successor a given value, merely request a tailMap bounded by successor(lowEndpoint). For For example, suppose that suppose that m is a sorted map whose keys are strings. The following idiom obtains a view containing all of the key-value mappings in m whose keys are strictly greater than low:

     SortedMap tail = m.tailMap(low+"\0");
 

Specified by:

tailMap in interface SortedMap

Parameters:

fromKey - low endpoint (inclusive) of the tailMap.

Returns:

a view of the portion of this map whose keys are greater than or equal to fromKey.

Throws:

ClassCastException - if fromKey is not compatible with this map's comparator (or, if the map has no comparator, if fromKey does not implement Comparable).

IllegalArgumentException - if this map is itself a subMap, headMap, or tailMap, and fromKey is not within the specified range of the subMap, headMap, or tailMap.

NullPointerException - if fromKey is null and this map uses natural order, or its comparator does not tolerate null keys.

compare

private int compare(Object k1,
                    Object k2)

Compares two keys using the correct comparison method for this TreeMap.

valEquals

private static boolean valEquals(Object o1,
                                 Object o2)

Test two values for equality. Differs from o1.equals(o2) only in that it copes with with null o1 properly.

firstEntry

private java.util.TreeMap.Entry firstEntry()

Returns the first Entry in the TreeMap (according to the TreeMap's key-sort function). Returns null if the TreeMap is empty.

lastEntry

private java.util.TreeMap.Entry lastEntry()

Returns the last Entry in the TreeMap (according to the TreeMap's key-sort function). Returns null if the TreeMap is empty.

successor

private java.util.TreeMap.Entry successor(java.util.TreeMap.Entry t)

Returns the successor of the specified Entry, or null if no such.

colorOf

private static boolean colorOf(java.util.TreeMap.Entry p)

Balancing operations. Implementations of rebalancings during insertion and deletion are slightly different than the CLR version. Rather than using dummy nilnodes, we use a set of accessors that deal properly with null. They are used to avoid messiness surrounding nullness checks in the main algorithms.

parentOf

private static java.util.TreeMap.Entry parentOf(java.util.TreeMap.Entry p)

setColor

private static void setColor(java.util.TreeMap.Entry p,
                             boolean c)

leftOf

private static java.util.TreeMap.Entry leftOf(java.util.TreeMap.Entry p)

rightOf

private static java.util.TreeMap.Entry rightOf(java.util.TreeMap.Entry p)

rotateLeft

private void rotateLeft(java.util.TreeMap.Entry p)

From CLR

rotateRight

private void rotateRight(java.util.TreeMap.Entry p)

From CLR

fixAfterInsertion

private void fixAfterInsertion(java.util.TreeMap.Entry x)

From CLR

deleteEntry

private void deleteEntry(java.util.TreeMap.Entry p)

Delete node p, and then rebalance the tree.

fixAfterDeletion

private void fixAfterDeletion(java.util.TreeMap.Entry x)

From CLR

writeObject

private void writeObject(ObjectOutputStream s)
                  throws IOException

Save the state of the TreeMap instance to a stream (i.e., serialize it).

IOException

readObject

private void readObject(ObjectInputStream s)
                 throws IOException,
                        ClassNotFoundException

Reconstitute the TreeMap instance from a stream (i.e., deserialize it).

IOException

ClassNotFoundException

readTreeSet

void readTreeSet(int size,
                 ObjectInputStream s,
                 Object defaultVal)
           throws IOException,
                  ClassNotFoundException

Intended to be called only from TreeSet.readObject

IOException

ClassNotFoundException

addAllForTreeSet

void addAllForTreeSet(SortedSet set,
                      Object defaultVal)

Intended to be called only from TreeSet.addAll

buildFromSorted

private void buildFromSorted(int size,
                             Iterator it,
                             ObjectInputStream str,
                             Object defaultVal)
                      throws IOException,
                             ClassNotFoundException

Linear time tree building algorithm from sorted data. Can accept keys and/or values from iterator or stream. This leads to too many parameters, but seems better than alternatives. The four formats that this method accepts are: 1) An iterator of Map.Entries. (it != null, defaultVal == null). 2) An iterator of keys. (it != null, defaultVal != null). 3) A stream of alternating serialized keys and values. (it == null, defaultVal == null). 4) A stream of serialized keys. (it == null, defaultVal != null). It is assumed that the comparator of the TreeMap is already set prior to calling this method.

Parameters:

size - the number of keys (or key-value pairs) to be read from the iterator or stream.

it - If non-null, new entries are created from entries or keys read from this iterator.

defaultVal - if non-null, this default value is used for each value in the map. If null, each value is read from iterator or stream, as described above.

Throws:

IOException - propagated from stream reads. This cannot occur if str is null.

ClassNotFoundException - propagated from readObject. This cannot occur if str is null.

buildFromSorted

private static java.util.TreeMap.Entry buildFromSorted(int level,
                                                       int lo,
                                                       int hi,
                                                       int redLevel,
                                                       Iterator it,
                                                       ObjectInputStream str,
                                                       Object defaultVal)
                                                throws IOException,
                                                       ClassNotFoundException

Recursive "helper method" that does the real work of the of the previous method. Identically named parameters have identical definitions. Additional parameters are documented below. It is assumed that the comparator and size fields of the TreeMap are already set prior to calling this method. (It ignores both fields.)

Parameters:

level - the current level of tree. Initial call should be 0.

lo - the first element index of this subtree. Initial should be 0.

hi - the last element index of this subtree. Initial should be size-1.

redLevel - the level at which nodes should be red. Must be equal to computeRedLevel for tree of this size.

IOException

ClassNotFoundException

computeRedLevel

private static int computeRedLevel(int sz)

Find the level down to which to assign all nodes BLACK. This is the last `full' level of the complete binary tree produced by buildTree. The remaining nodes are colored RED. (This makes a `nice' set of color assignments wrt future insertions.) This level number is computed by finding the number of splits needed to reach the zeroeth node. (The answer is ~lg(N), but in any case must be computed by same quick O(lg(N)) loop.)