java.util

Class TreeMap<K,V>

Implemented Interfaces:
Cloneable, Map<K,V>, NavigableMap<K,V>, Serializable, SortedMap<K,V>

public class TreeMap<K,V>
extends AbstractMap<K,V>
implements NavigableMap<K,V>, Cloneable, Serializable

This class provides a red-black tree implementation of the SortedMap interface. Elements in the Map will be sorted by either a user-provided Comparator object, or by the natural ordering of the keys. The algorithms are adopted from Corman, Leiserson, and Rivest's Introduction to Algorithms. TreeMap guarantees O(log n) insertion and deletion of elements. That being said, there is a large enough constant coefficient in front of that "log n" (overhead involved in keeping the tree balanced), that TreeMap may not be the best choice for small collections. If something is already sorted, you may want to just use a LinkedHashMap to maintain the order while providing O(1) access. TreeMap is a part of the JDK1.2 Collections API. Null keys are allowed only if a Comparator is used which can deal with them; natural ordering cannot cope with null. Null values are always allowed. Note that the ordering must be consistent with equals to correctly implement the Map interface. If this condition is violated, the map is still well-behaved, but you may have suprising results when comparing it to other maps.

This implementation is not synchronized. If you need to share this between multiple threads, do something like:
SortedMap m = Collections.synchronizedSortedMap(new TreeMap(...));

The iterators are fail-fast, meaning that any structural modification, except for remove() called on the iterator itself, cause the iterator to throw a ConcurrentModificationException rather than exhibit non-deterministic behavior.

Since:
1.2
See Also:
Map, HashMap, Hashtable, LinkedHashMap, Comparable, Comparator, Collection, Collections.synchronizedSortedMap(SortedMap), Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class java.util.AbstractMap<K,V>

AbstractMap.SimpleEntry, AbstractMap.SimpleImmutableEntry

Constructor Summary

TreeMap()
Instantiate a new TreeMap with no elements, using the keys' natural ordering to sort.
TreeMap(K> c)
Instantiate a new TreeMap with no elements, using the provided comparator to sort.
TreeMap(SortedMap sm)
Instantiate a new TreeMap, initializing it with all of the elements in the provided SortedMap.
TreeMap(extends K, V> map)
Instantiate a new TreeMap, initializing it with all of the elements in the provided Map.

Method Summary

SortedMap
V> headMap(K toKey)
Returns a view of this Map including all entries with keys less than toKey.
NavigableMap
V> headMap(K toKey, boolean inclusive)
Returns a view of this Map including all entries with keys less than (or equal to, if inclusive is true) toKey.
SortedMap
V> subMap(K fromKey, K toKey)
Returns a view of this Map including all entries with keys greater or equal to fromKey and less than toKey (a half-open interval).
NavigableMap
V> subMap(K fromKey, boolean fromInclusive, K toKey, boolean toInclusive)
Returns a view of this Map including all entries with keys greater (or equal to, if fromInclusive is true) fromKey and less than (or equal to, if toInclusive is true) toKey.
SortedMap
V> tailMap(K fromKey)
Returns a view of this Map including all entries with keys greater or equal to fromKey.
NavigableMap
V> tailMap(K fromKey, boolean inclusive)
Returns a view of this Map including all entries with keys greater or equal to fromKey.
Entry
ceilingEntry(K key)
Returns the entry associated with the least or lowest key that is greater than or equal to the specified key, or null if there is no such key.
K
ceilingKey(K key)
Returns the the least or lowest key that is greater than or equal to the specified key, or null if there is no such key.
void
clear()
Clears the Map so it has no keys.
Object
clone()
Returns a shallow clone of this TreeMap.
boolean
containsKey(Object key)
Returns true if the map contains a mapping for the given key.
boolean
containsValue(Object value)
Returns true if the map contains at least one mapping to the given value.
NavigableSet
descendingKeySet()
Returns a reverse ordered NavigableSet view of this map's keys.
NavigableMap
descendingMap()
Returns a view of the map in reverse order.
Set>
entrySet()
Returns a "set view" of this TreeMap's entries.
Entry
firstEntry()
Returns the entry associated with the least or lowest key in the map, or null if the map is empty.
K
firstKey()
Returns the first (lowest) key in the map.
Entry
floorEntry(K key)
Returns the entry associated with the greatest or highest key that is less than or equal to the specified key, or null if there is no such key.
K
floorKey(K key)
Returns the the greatest or highest key that is less than or equal to the specified key, or null if there is no such key.
V
get(Object key)
Return the value in this TreeMap associated with the supplied key, or null if the key maps to nothing.
Entry
higherEntry(K key)
Returns the entry associated with the least or lowest key that is strictly greater than the specified key, or null if there is no such key.
K
higherKey(K key)
Returns the the least or lowest key that is strictly greater than the specified key, or null if there is no such key.
Set
keySet()
Returns a "set view" of this TreeMap's keys.
Entry
lastEntry()
Returns the entry associated with the greatest or highest key in the map, or null if the map is empty.
K
lastKey()
Returns the last (highest) key in the map.
Entry
lowerEntry(K key)
Returns the entry associated with the greatest or highest key that is strictly less than the specified key, or null if there is no such key.
K
lowerKey(K key)
Returns the the greatest or highest key that is strictly less than the specified key, or null if there is no such key.
NavigableSet
navigableKeySet()
Returns a NavigableSet view of this map's keys.
Entry
pollFirstEntry()
Removes and returns the entry associated with the least or lowest key in the map, or null if the map is empty.
Entry
pollLastEntry()
Removes and returns the entry associated with the greatest or highest key in the map, or null if the map is empty.
V
put(K key, V value)
Puts the supplied value into the Map, mapped by the supplied key.
void
putAll(extends K, V> m)
Copies all elements of the given map into this TreeMap.
V
remove(Object key)
Removes from the TreeMap and returns the value which is mapped by the supplied key.
int
size()
Returns the number of key-value mappings currently in this Map.
Comparator
super K> comparator()
Return the comparator used to sort this map, or null if it is by natural order.
Collection
values()
Returns a "collection view" (or "bag view") of this TreeMap's values.

Methods inherited from class java.util.AbstractMap<K,V>

V>> entrySet, clear, clone, containsKey, containsValue, equals, get, hashCode, isEmpty, keySet, put, putAll, remove, size, toString, values

Methods inherited from class java.lang.Object

clone, equals, extends Object> getClass, finalize, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

TreeMap

public TreeMap()
Instantiate a new TreeMap with no elements, using the keys' natural ordering to sort. All entries in the map must have a key which implements Comparable, and which are mutually comparable, otherwise map operations may throw a ClassCastException. Attempts to use a null key will throw a NullPointerException.
See Also:
Comparable

TreeMap

public TreeMap(K> c)
Instantiate a new TreeMap with no elements, using the provided comparator to sort. All entries in the map must have keys which are mutually comparable by the Comparator, otherwise map operations may throw a ClassCastException.
Parameters:
c - the sort order for the keys of this map, or null for the natural order

TreeMap

public TreeMap(SortedMap sm)
Instantiate a new TreeMap, initializing it with all of the elements in the provided SortedMap. The elements will be sorted using the same comparator as in the provided SortedMap. This runs in linear time.
Parameters:
sm - a SortedMap, whose entries will be put into this TreeMap
Throws:
NullPointerException - if sm is null

TreeMap

public TreeMap(extends K,
               V> map)
Instantiate a new TreeMap, initializing it with all of the elements in the provided Map. The elements will be sorted using the natural ordering of the keys. This algorithm runs in n*log(n) time. All entries in the map must have keys which implement Comparable and are mutually comparable, otherwise map operations may throw a ClassCastException.
Parameters:
map - a Map, whose entries will be put into this TreeMap
Throws:
ClassCastException - if the keys in the provided Map are not comparable
NullPointerException - if map is null
See Also:
Comparable

Method Details

V> headMap

public SortedMapV> headMap(K toKey)
Returns a view of this Map including all entries with keys less than toKey. The returned map is backed by the original, so changes in one appear in the other. The submap will throw an IllegalArgumentException for any attempt to access or add an element beyond the specified cutoff. The returned map does not include the endpoint; if you want inclusion, pass the successor element or call headMap(toKey, true). This is equivalent to calling headMap(toKey, false).
Specified by:
V> headMap in interface SortedMap<K,V>
Parameters:
toKey - the (exclusive) cutoff point
Returns:
a view of the map less than the cutoff
Throws:
ClassCastException - if toKey is not compatible with the comparator (or is not Comparable, for natural ordering)
NullPointerException - if toKey is null, but the comparator does not tolerate null elements

V> headMap

public NavigableMapV> headMap(K toKey,
                                  boolean inclusive)
Returns a view of this Map including all entries with keys less than (or equal to, if inclusive is true) toKey. The returned map is backed by the original, so changes in one appear in the other. The submap will throw an IllegalArgumentException for any attempt to access or add an element beyond the specified cutoff.
Parameters:
toKey - the cutoff point
inclusive - true if the cutoff point should be included.
Returns:
a view of the map less than (or equal to, if inclusive is true) the cutoff.
Throws:
ClassCastException - if toKey is not compatible with the comparator (or is not Comparable, for natural ordering)
NullPointerException - if toKey is null, but the comparator does not tolerate null elements

V> subMap

public SortedMapV> subMap(K fromKey,
                              K toKey)
Returns a view of this Map including all entries with keys greater or equal to fromKey and less than toKey (a half-open interval). The returned map is backed by the original, so changes in one appear in the other. The submap will throw an IllegalArgumentException for any attempt to access or add an element beyond the specified cutoffs. The returned map includes the low endpoint but not the high; if you want to reverse this behavior on either end, pass in the successor element or call subMap(K,boolean,K,boolean). This call is equivalent to subMap(fromKey, true, toKey, false).
Specified by:
V> subMap in interface SortedMap<K,V>
Parameters:
fromKey - the (inclusive) low cutoff point
toKey - the (exclusive) high cutoff point
Returns:
a view of the map between the cutoffs
Throws:
ClassCastException - if either cutoff is not compatible with the comparator (or is not Comparable, for natural ordering)
NullPointerException - if fromKey or toKey is null, but the comparator does not tolerate null elements
IllegalArgumentException - if fromKey is greater than toKey

V> subMap

public NavigableMapV> subMap(K fromKey,
                                 boolean fromInclusive,
                                 K toKey,
                                 boolean toInclusive)
Returns a view of this Map including all entries with keys greater (or equal to, if fromInclusive is true) fromKey and less than (or equal to, if toInclusive is true) toKey. The returned map is backed by the original, so changes in one appear in the other. The submap will throw an IllegalArgumentException for any attempt to access or add an element beyond the specified cutoffs.
Parameters:
fromKey - the low cutoff point
fromInclusive - true if the low cutoff point should be included.
toKey - the high cutoff point
toInclusive - true if the high cutoff point should be included.
Returns:
a view of the map for the specified range.
Throws:
ClassCastException - if either cutoff is not compatible with the comparator (or is not Comparable, for natural ordering)
NullPointerException - if fromKey or toKey is null, but the comparator does not tolerate null elements
IllegalArgumentException - if fromKey is greater than toKey

V> tailMap

public SortedMapV> tailMap(K fromKey)
Returns a view of this Map including all entries with keys greater or equal to fromKey. The returned map is backed by the original, so changes in one appear in the other. The submap will throw an IllegalArgumentException for any attempt to access or add an element beyond the specified cutoff. The returned map includes the endpoint; if you want to exclude it, pass in the successor element. This is equivalent to calling tailMap(fromKey, true).
Specified by:
V> tailMap in interface SortedMap<K,V>
Parameters:
fromKey - the (inclusive) low cutoff point
Returns:
a view of the map above the cutoff
Throws:
ClassCastException - if fromKey is not compatible with the comparator (or is not Comparable, for natural ordering)
NullPointerException - if fromKey is null, but the comparator does not tolerate null elements

V> tailMap

public NavigableMapV> tailMap(K fromKey,
                                  boolean inclusive)
Returns a view of this Map including all entries with keys greater or equal to fromKey. The returned map is backed by the original, so changes in one appear in the other. The submap will throw an IllegalArgumentException for any attempt to access or add an element beyond the specified cutoff. The returned map includes the endpoint; if you want to exclude it, pass in the successor element.
Parameters:
fromKey - the low cutoff point
inclusive - true if the cutoff point should be included.
Returns:
a view of the map above the cutoff
Throws:
ClassCastException - if fromKey is not compatible with the comparator (or is not Comparable, for natural ordering)
NullPointerException - if fromKey is null, but the comparator does not tolerate null elements

ceilingEntry

public Entry ceilingEntry(K key)
Returns the entry associated with the least or lowest key that is greater than or equal to the specified key, or null if there is no such key.
Specified by:
ceilingEntry in interface NavigableMap<K,V>
Parameters:
key - the key relative to the returned entry.
Returns:
the entry with the least key greater than or equal to the given key, or null if there is no such key.
Throws:
ClassCastException - if the specified key can not be compared with those in the map.
NullPointerException - if the key is null and this map either uses natural ordering or a comparator that does not permit null keys.
Since:
1.6

ceilingKey

public K ceilingKey(K key)
Returns the the least or lowest key that is greater than or equal to the specified key, or null if there is no such key.
Specified by:
ceilingKey in interface NavigableMap<K,V>
Parameters:
key - the key relative to the returned entry.
Returns:
the least key greater than or equal to the given key, or null if there is no such key.
Throws:
ClassCastException - if the specified key can not be compared with those in the map.
NullPointerException - if the key is null and this map either uses natural ordering or a comparator that does not permit null keys.
Since:
1.6

clear

public void clear()
Clears the Map so it has no keys. This is O(1).
Specified by:
clear in interface Map<K,V>
Overrides:
clear in interface AbstractMap<K,V>

clone

public Object clone()
Returns a shallow clone of this TreeMap. The Map itself is cloned, but its contents are not.
Overrides:
clone in interface AbstractMap<K,V>
Returns:
the clone

containsKey

public boolean containsKey(Object key)
Returns true if the map contains a mapping for the given key.
Specified by:
containsKey in interface Map<K,V>
Overrides:
containsKey in interface AbstractMap<K,V>
Parameters:
key - the key to look for
Returns:
true if the key has a mapping
Throws:
ClassCastException - if key is not comparable to map elements
NullPointerException - if key is null and the comparator is not tolerant of nulls

containsValue

public boolean containsValue(Object value)
Returns true if the map contains at least one mapping to the given value. This requires linear time.
Specified by:
containsValue in interface Map<K,V>
Overrides:
containsValue in interface AbstractMap<K,V>
Parameters:
value - the value to look for
Returns:
true if the value appears in a mapping

descendingKeySet

public NavigableSet descendingKeySet()
Returns a reverse ordered NavigableSet view of this map's keys. The set is backed by the TreeMap, so changes in one show up in the other. The set supports element removal, but not element addition.
Specified by:
descendingKeySet in interface NavigableMap<K,V>
Returns:
a reverse ordered set view of the keys.
Since:
1.6

descendingMap

public NavigableMap descendingMap()
Returns a view of the map in reverse order. The descending map is backed by the original map, so that changes affect both maps. Any changes occurring to either map while an iteration is taking place (with the exception of a Iterator.remove() operation) result in undefined behaviour from the iteration. The ordering of the descending map is the same as for a map with a Comparator given by Collections.reverseOrder(), and calling descendingMap() on the descending map itself results in a view equivalent to the original map.
Specified by:
descendingMap in interface NavigableMap<K,V>
Returns:
a reverse order view of the map.
Since:
1.6

entrySet

public Set> entrySet()
Returns a "set view" of this TreeMap's entries. The set is backed by the TreeMap, so changes in one show up in the other. The set supports element removal, but not element addition.

Note that the iterators for all three views, from keySet(), entrySet(), and values(), traverse the TreeMap in sorted sequence.

Returns:
a set view of the entries

firstEntry

public Entry firstEntry()
Returns the entry associated with the least or lowest key in the map, or null if the map is empty.
Specified by:
firstEntry in interface NavigableMap<K,V>
Returns:
the lowest entry, or null if the map is empty.
Since:
1.6

firstKey

public K firstKey()
Returns the first (lowest) key in the map.
Specified by:
firstKey in interface SortedMap<K,V>
Returns:
the first key
Throws:
NoSuchElementException - if the map is empty

floorEntry

public Entry floorEntry(K key)
Returns the entry associated with the greatest or highest key that is less than or equal to the specified key, or null if there is no such key.
Specified by:
floorEntry in interface NavigableMap<K,V>
Parameters:
key - the key relative to the returned entry.
Returns:
the entry with the greatest key less than or equal to the given key, or null if there is no such key.
Throws:
ClassCastException - if the specified key can not be compared with those in the map.
NullPointerException - if the key is null and this map either uses natural ordering or a comparator that does not permit null keys.
Since:
1.6

floorKey

public K floorKey(K key)
Returns the the greatest or highest key that is less than or equal to the specified key, or null if there is no such key.
Specified by:
floorKey in interface NavigableMap<K,V>
Parameters:
key - the key relative to the returned entry.
Returns:
the greatest key less than or equal to the given key, or null if there is no such key.
Throws:
ClassCastException - if the specified key can not be compared with those in the map.
NullPointerException - if the key is null and this map either uses natural ordering or a comparator that does not permit null keys.
Since:
1.6

get

public V get(Object key)
Return the value in this TreeMap associated with the supplied key, or null if the key maps to nothing. NOTE: Since the value could also be null, you must use containsKey to see if this key actually maps to something.
Specified by:
get in interface Map<K,V>
Overrides:
get in interface AbstractMap<K,V>
Parameters:
key - the key for which to fetch an associated value
Returns:
what the key maps to, if present
Throws:
ClassCastException - if key is not comparable to elements in the map
NullPointerException - if key is null but the comparator does not tolerate nulls
See Also:
put(Object, Object), containsKey(Object)

higherEntry

public Entry higherEntry(K key)
Returns the entry associated with the least or lowest key that is strictly greater than the specified key, or null if there is no such key.
Specified by:
higherEntry in interface NavigableMap<K,V>
Parameters:
key - the key relative to the returned entry.
Returns:
the entry with the least key greater than the given key, or null if there is no such key.
Throws:
ClassCastException - if the specified key can not be compared with those in the map.
NullPointerException - if the key is null and this map either uses natural ordering or a comparator that does not permit null keys.
Since:
1.6

higherKey

public K higherKey(K key)
Returns the the least or lowest key that is strictly greater than the specified key, or null if there is no such key.
Specified by:
higherKey in interface NavigableMap<K,V>
Parameters:
key - the key relative to the returned entry.
Returns:
the least key greater than the given key, or null if there is no such key.
Throws:
ClassCastException - if the specified key can not be compared with those in the map.
NullPointerException - if the key is null and this map either uses natural ordering or a comparator that does not permit null keys.
Since:
1.6

keySet

public Set keySet()
Returns a "set view" of this TreeMap's keys. The set is backed by the TreeMap, so changes in one show up in the other. The set supports element removal, but not element addition.
Specified by:
keySet in interface Map<K,V>
Overrides:
keySet in interface AbstractMap<K,V>
Returns:
a set view of the keys

lastEntry

public Entry lastEntry()
Returns the entry associated with the greatest or highest key in the map, or null if the map is empty.
Specified by:
lastEntry in interface NavigableMap<K,V>
Returns:
the highest entry, or null if the map is empty.
Since:
1.6

lastKey

public K lastKey()
Returns the last (highest) key in the map.
Specified by:
lastKey in interface SortedMap<K,V>
Returns:
the last key
Throws:
NoSuchElementException - if the map is empty

lowerEntry

public Entry lowerEntry(K key)
Returns the entry associated with the greatest or highest key that is strictly less than the specified key, or null if there is no such key.
Specified by:
lowerEntry in interface NavigableMap<K,V>
Parameters:
key - the key relative to the returned entry.
Returns:
the entry with the greatest key less than the given key, or null if there is no such key.
Throws:
ClassCastException - if the specified key can not be compared with those in the map.
NullPointerException - if the key is null and this map either uses natural ordering or a comparator that does not permit null keys.
Since:
1.6

lowerKey

public K lowerKey(K key)
Returns the the greatest or highest key that is strictly less than the specified key, or null if there is no such key.
Specified by:
lowerKey in interface NavigableMap<K,V>
Parameters:
key - the key relative to the returned entry.
Returns:
the greatest key less than the given key, or null if there is no such key.
Throws:
ClassCastException - if the specified key can not be compared with those in the map.
NullPointerException - if the key is null and this map either uses natural ordering or a comparator that does not permit null keys.
Since:
1.6

navigableKeySet

public NavigableSet navigableKeySet()
Returns a NavigableSet view of this map's keys. The set is backed by the TreeMap, so changes in one show up in the other. Any changes occurring to either while an iteration is taking place (with the exception of a Iterator.remove() operation) result in undefined behaviour from the iteration. The ordering The set supports element removal, but not element addition.
Specified by:
navigableKeySet in interface NavigableMap<K,V>
Returns:
a NavigableSet view of the keys.
Since:
1.6

pollFirstEntry

public Entry pollFirstEntry()
Removes and returns the entry associated with the least or lowest key in the map, or null if the map is empty.
Specified by:
pollFirstEntry in interface NavigableMap<K,V>
Returns:
the removed first entry, or null if the map is empty.
Since:
1.6

pollLastEntry

public Entry pollLastEntry()
Removes and returns the entry associated with the greatest or highest key in the map, or null if the map is empty.
Specified by:
pollLastEntry in interface NavigableMap<K,V>
Returns:
the removed last entry, or null if the map is empty.
Since:
1.6

put

public V put(K key,
             V value)
Puts the supplied value into the Map, mapped by the supplied key. The value may be retrieved by any object which equals() this key. NOTE: Since the prior value could also be null, you must first use containsKey if you want to see if you are replacing the key's mapping.
Specified by:
put in interface Map<K,V>
Overrides:
put in interface AbstractMap<K,V>
Parameters:
key - the key used to locate the value
value - the value to be stored in the Map
Returns:
the prior mapping of the key, or null if there was none
Throws:
ClassCastException - if key is not comparable to current map keys
NullPointerException - if key is null, but the comparator does not tolerate nulls

putAll

public void putAll(extends K,
                   V> m)
Copies all elements of the given map into this TreeMap. If this map already has a mapping for a key, the new mapping replaces the current one.
Specified by:
putAll in interface Map<K,V>
Overrides:
putAll in interface AbstractMap<K,V>
Parameters:
m - the map to be added
Throws:
ClassCastException - if a key in m is not comparable with keys in the map
NullPointerException - if a key in m is null, and the comparator does not tolerate nulls

remove

public V remove(Object key)
Removes from the TreeMap and returns the value which is mapped by the supplied key. If the key maps to nothing, then the TreeMap remains unchanged, and null is returned. NOTE: Since the value could also be null, you must use containsKey to see if you are actually removing a mapping.
Specified by:
remove in interface Map<K,V>
Overrides:
remove in interface AbstractMap<K,V>
Parameters:
key - the key used to locate the value to remove
Returns:
whatever the key mapped to, if present
Throws:
ClassCastException - if key is not comparable to current map keys
NullPointerException - if key is null, but the comparator does not tolerate nulls

size

public int size()
Returns the number of key-value mappings currently in this Map.
Specified by:
size in interface Map<K,V>
Overrides:
size in interface AbstractMap<K,V>
Returns:
the size

super K> comparator

public Comparatorsuper K> comparator()
Return the comparator used to sort this map, or null if it is by natural order.
Specified by:
super K> comparator in interface SortedMap<K,V>
Returns:
the map's comparator

values

public Collection values()
Returns a "collection view" (or "bag view") of this TreeMap's values. The collection is backed by the TreeMap, so changes in one show up in the other. The collection supports element removal, but not element addition.
Specified by:
values in interface Map<K,V>
Overrides:
values in interface AbstractMap<K,V>
Returns:
a bag view of the values

TreeMap.java -- a class providing a basic Red-Black Tree data structure, mapping Object --> Object Copyright (C) 1998, 1999, 2000, 2001, 2002, 2004, 2005, 2006 Free Software Foundation, Inc. This file is part of GNU Classpath. GNU Classpath is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version. GNU Classpath is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with GNU Classpath; see the file COPYING. If not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. Linking this library statically or dynamically with other modules is making a combined work based on this library. Thus, the terms and conditions of the GNU General Public License cover the whole combination. As a special exception, the copyright holders of this library give you permission to link this library with independent modules to produce an executable, regardless of the license terms of these independent modules, and to copy and distribute the resulting executable under terms of your choice, provided that you also meet, for each linked independent module, the terms and conditions of the license of that module. An independent module is a module which is not derived from or based on this library. If you modify this library, you may extend this exception to your version of the library, but you are not obligated to do so. If you do not wish to do so, delete this exception statement from your version.