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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.geometry.partitioning.utilities;
/** This class implements AVL trees.
*
* The purpose of this class is to sort elements while allowing
* duplicate elements (i.e. such that {@code a.equals(b)} is
* true). The {@code SortedSet} interface does not allow this, so
* a specific class is needed. Null elements are not allowed.
*
* Since the {@code equals} method is not sufficient to
* differentiate elements, the {@link #delete delete} method is
* implemented using the equality operator.
*
* In order to clearly mark the methods provided here do not have
* the same semantics as the ones specified in the
* {@code SortedSet} interface, different names are used
* ({@code add} has been replaced by {@link #insert insert} and
* {@code remove} has been replaced by {@link #delete
* delete}).
*
* This class is based on the C implementation Georg Kraml has put
* in the public domain. Unfortunately, his page seems not
* to exist any more.
*
* @param the type of the elements
*
* @since 3.0
* @deprecated as of 3.4, this class is not used anymore and considered
* to be out of scope of Apache Commons Math
*/
@Deprecated
public class AVLTree> {
/** Top level node. */
private Node top;
/** Build an empty tree.
*/
public AVLTree() {
top = null;
}
/** Insert an element in the tree.
* @param element element to insert (silently ignored if null)
*/
public void insert(final T element) {
if (element != null) {
if (top == null) {
top = new Node(element, null);
} else {
top.insert(element);
}
}
}
/** Delete an element from the tree.
* The element is deleted only if there is a node {@code n}
* containing exactly the element instance specified, i.e. for which
* {@code n.getElement() == element}. This is purposely
* different from the specification of the
* {@code java.util.Set} {@code remove} method (in fact,
* this is the reason why a specific class has been developed).
* @param element element to delete (silently ignored if null)
* @return true if the element was deleted from the tree
*/
public boolean delete(final T element) {
if (element != null) {
for (Node node = getNotSmaller(element); node != null; node = node.getNext()) {
// loop over all elements neither smaller nor larger
// than the specified one
if (node.element == element) {
node.delete();
return true;
} else if (node.element.compareTo(element) > 0) {
// all the remaining elements are known to be larger,
// the element is not in the tree
return false;
}
}
}
return false;
}
/** Check if the tree is empty.
* @return true if the tree is empty
*/
public boolean isEmpty() {
return top == null;
}
/** Get the number of elements of the tree.
* @return number of elements contained in the tree
*/
public int size() {
return (top == null) ? 0 : top.size();
}
/** Get the node whose element is the smallest one in the tree.
* @return the tree node containing the smallest element in the tree
* or null if the tree is empty
* @see #getLargest
* @see #getNotSmaller
* @see #getNotLarger
* @see Node#getPrevious
* @see Node#getNext
*/
public Node getSmallest() {
return (top == null) ? null : top.getSmallest();
}
/** Get the node whose element is the largest one in the tree.
* @return the tree node containing the largest element in the tree
* or null if the tree is empty
* @see #getSmallest
* @see #getNotSmaller
* @see #getNotLarger
* @see Node#getPrevious
* @see Node#getNext
*/
public Node getLargest() {
return (top == null) ? null : top.getLargest();
}
/** Get the node whose element is not smaller than the reference object.
* @param reference reference object (may not be in the tree)
* @return the tree node containing the smallest element not smaller
* than the reference object or null if either the tree is empty or
* all its elements are smaller than the reference object
* @see #getSmallest
* @see #getLargest
* @see #getNotLarger
* @see Node#getPrevious
* @see Node#getNext
*/
public Node getNotSmaller(final T reference) {
Node candidate = null;
for (Node node = top; node != null;) {
if (node.element.compareTo(reference) < 0) {
if (node.right == null) {
return candidate;
}
node = node.right;
} else {
candidate = node;
if (node.left == null) {
return candidate;
}
node = node.left;
}
}
return null;
}
/** Get the node whose element is not larger than the reference object.
* @param reference reference object (may not be in the tree)
* @return the tree node containing the largest element not larger
* than the reference object (in which case the node is guaranteed
* not to be empty) or null if either the tree is empty or all its
* elements are larger than the reference object
* @see #getSmallest
* @see #getLargest
* @see #getNotSmaller
* @see Node#getPrevious
* @see Node#getNext
*/
public Node getNotLarger(final T reference) {
Node candidate = null;
for (Node node = top; node != null;) {
if (node.element.compareTo(reference) > 0) {
if (node.left == null) {
return candidate;
}
node = node.left;
} else {
candidate = node;
if (node.right == null) {
return candidate;
}
node = node.right;
}
}
return null;
}
/** Enum for tree skew factor. */
private enum Skew {
/** Code for left high trees. */
LEFT_HIGH,
/** Code for right high trees. */
RIGHT_HIGH,
/** Code for Skew.BALANCED trees. */
BALANCED;
}
/** This class implements AVL trees nodes.
* AVL tree nodes implement all the logical structure of the
* tree. Nodes are created by the {@link AVLTree AVLTree} class.
* The nodes are not independant from each other but must obey
* specific balancing constraints and the tree structure is
* rearranged as elements are inserted or deleted from the tree. The
* creation, modification and tree-related navigation methods have
* therefore restricted access. Only the order-related navigation,
* reading and delete methods are public.
* @see AVLTree
*/
public class Node {
/** Element contained in the current node. */
private T element;
/** Left sub-tree. */
private Node left;
/** Right sub-tree. */
private Node right;
/** Parent tree. */
private Node parent;
/** Skew factor. */
private Skew skew;
/** Build a node for a specified element.
* @param element element
* @param parent parent node
*/
Node(final T element, final Node parent) {
this.element = element;
left = null;
right = null;
this.parent = parent;
skew = Skew.BALANCED;
}
/** Get the contained element.
* @return element contained in the node
*/
public T getElement() {
return element;
}
/** Get the number of elements of the tree rooted at this node.
* @return number of elements contained in the tree rooted at this node
*/
int size() {
return 1 + ((left == null) ? 0 : left.size()) + ((right == null) ? 0 : right.size());
}
/** Get the node whose element is the smallest one in the tree
* rooted at this node.
* @return the tree node containing the smallest element in the
* tree rooted at this node or null if the tree is empty
* @see #getLargest
*/
Node getSmallest() {
Node node = this;
while (node.left != null) {
node = node.left;
}
return node;
}
/** Get the node whose element is the largest one in the tree
* rooted at this node.
* @return the tree node containing the largest element in the
* tree rooted at this node or null if the tree is empty
* @see #getSmallest
*/
Node getLargest() {
Node node = this;
while (node.right != null) {
node = node.right;
}
return node;
}
/** Get the node containing the next smaller or equal element.
* @return node containing the next smaller or equal element or
* null if there is no smaller or equal element in the tree
* @see #getNext
*/
public Node getPrevious() {
if (left != null) {
final Node node = left.getLargest();
if (node != null) {
return node;
}
}
for (Node node = this; node.parent != null; node = node.parent) {
if (node != node.parent.left) {
return node.parent;
}
}
return null;
}
/** Get the node containing the next larger or equal element.
* @return node containing the next larger or equal element (in
* which case the node is guaranteed not to be empty) or null if
* there is no larger or equal element in the tree
* @see #getPrevious
*/
public Node getNext() {
if (right != null) {
final Node node = right.getSmallest();
if (node != null) {
return node;
}
}
for (Node node = this; node.parent != null; node = node.parent) {
if (node != node.parent.right) {
return node.parent;
}
}
return null;
}
/** Insert an element in a sub-tree.
* @param newElement element to insert
* @return true if the parent tree should be re-Skew.BALANCED
*/
boolean insert(final T newElement) {
if (newElement.compareTo(this.element) < 0) {
// the inserted element is smaller than the node
if (left == null) {
left = new Node(newElement, this);
return rebalanceLeftGrown();
}
return left.insert(newElement) ? rebalanceLeftGrown() : false;
}
// the inserted element is equal to or greater than the node
if (right == null) {
right = new Node(newElement, this);
return rebalanceRightGrown();
}
return right.insert(newElement) ? rebalanceRightGrown() : false;
}
/** Delete the node from the tree.
*/
public void delete() {
if ((parent == null) && (left == null) && (right == null)) {
// this was the last node, the tree is now empty
element = null;
top = null;
} else {
Node node;
Node child;
boolean leftShrunk;
if ((left == null) && (right == null)) {
node = this;
element = null;
leftShrunk = node == node.parent.left;
child = null;
} else {
node = (left != null) ? left.getLargest() : right.getSmallest();
element = node.element;
leftShrunk = node == node.parent.left;
child = (node.left != null) ? node.left : node.right;
}
node = node.parent;
if (leftShrunk) {
node.left = child;
} else {
node.right = child;
}
if (child != null) {
child.parent = node;
}
while (leftShrunk ? node.rebalanceLeftShrunk() : node.rebalanceRightShrunk()) {
if (node.parent == null) {
return;
}
leftShrunk = node == node.parent.left;
node = node.parent;
}
}
}
/** Re-balance the instance as left sub-tree has grown.
* @return true if the parent tree should be reSkew.BALANCED too
*/
private boolean rebalanceLeftGrown() {
switch (skew) {
case LEFT_HIGH:
if (left.skew == Skew.LEFT_HIGH) {
rotateCW();
skew = Skew.BALANCED;
right.skew = Skew.BALANCED;
} else {
final Skew s = left.right.skew;
left.rotateCCW();
rotateCW();
switch(s) {
case LEFT_HIGH:
left.skew = Skew.BALANCED;
right.skew = Skew.RIGHT_HIGH;
break;
case RIGHT_HIGH:
left.skew = Skew.LEFT_HIGH;
right.skew = Skew.BALANCED;
break;
default:
left.skew = Skew.BALANCED;
right.skew = Skew.BALANCED;
}
skew = Skew.BALANCED;
}
return false;
case RIGHT_HIGH:
skew = Skew.BALANCED;
return false;
default:
skew = Skew.LEFT_HIGH;
return true;
}
}
/** Re-balance the instance as right sub-tree has grown.
* @return true if the parent tree should be reSkew.BALANCED too
*/
private boolean rebalanceRightGrown() {
switch (skew) {
case LEFT_HIGH:
skew = Skew.BALANCED;
return false;
case RIGHT_HIGH:
if (right.skew == Skew.RIGHT_HIGH) {
rotateCCW();
skew = Skew.BALANCED;
left.skew = Skew.BALANCED;
} else {
final Skew s = right.left.skew;
right.rotateCW();
rotateCCW();
switch (s) {
case LEFT_HIGH:
left.skew = Skew.BALANCED;
right.skew = Skew.RIGHT_HIGH;
break;
case RIGHT_HIGH:
left.skew = Skew.LEFT_HIGH;
right.skew = Skew.BALANCED;
break;
default:
left.skew = Skew.BALANCED;
right.skew = Skew.BALANCED;
}
skew = Skew.BALANCED;
}
return false;
default:
skew = Skew.RIGHT_HIGH;
return true;
}
}
/** Re-balance the instance as left sub-tree has shrunk.
* @return true if the parent tree should be reSkew.BALANCED too
*/
private boolean rebalanceLeftShrunk() {
switch (skew) {
case LEFT_HIGH:
skew = Skew.BALANCED;
return true;
case RIGHT_HIGH:
if (right.skew == Skew.RIGHT_HIGH) {
rotateCCW();
skew = Skew.BALANCED;
left.skew = Skew.BALANCED;
return true;
} else if (right.skew == Skew.BALANCED) {
rotateCCW();
skew = Skew.LEFT_HIGH;
left.skew = Skew.RIGHT_HIGH;
return false;
} else {
final Skew s = right.left.skew;
right.rotateCW();
rotateCCW();
switch (s) {
case LEFT_HIGH:
left.skew = Skew.BALANCED;
right.skew = Skew.RIGHT_HIGH;
break;
case RIGHT_HIGH:
left.skew = Skew.LEFT_HIGH;
right.skew = Skew.BALANCED;
break;
default:
left.skew = Skew.BALANCED;
right.skew = Skew.BALANCED;
}
skew = Skew.BALANCED;
return true;
}
default:
skew = Skew.RIGHT_HIGH;
return false;
}
}
/** Re-balance the instance as right sub-tree has shrunk.
* @return true if the parent tree should be reSkew.BALANCED too
*/
private boolean rebalanceRightShrunk() {
switch (skew) {
case RIGHT_HIGH:
skew = Skew.BALANCED;
return true;
case LEFT_HIGH:
if (left.skew == Skew.LEFT_HIGH) {
rotateCW();
skew = Skew.BALANCED;
right.skew = Skew.BALANCED;
return true;
} else if (left.skew == Skew.BALANCED) {
rotateCW();
skew = Skew.RIGHT_HIGH;
right.skew = Skew.LEFT_HIGH;
return false;
} else {
final Skew s = left.right.skew;
left.rotateCCW();
rotateCW();
switch (s) {
case LEFT_HIGH:
left.skew = Skew.BALANCED;
right.skew = Skew.RIGHT_HIGH;
break;
case RIGHT_HIGH:
left.skew = Skew.LEFT_HIGH;
right.skew = Skew.BALANCED;
break;
default:
left.skew = Skew.BALANCED;
right.skew = Skew.BALANCED;
}
skew = Skew.BALANCED;
return true;
}
default:
skew = Skew.LEFT_HIGH;
return false;
}
}
/** Perform a clockwise rotation rooted at the instance.
* The skew factor are not updated by this method, they
* must be updated by the caller
*/
private void rotateCW() {
final T tmpElt = element;
element = left.element;
left.element = tmpElt;
final Node tmpNode = left;
left = tmpNode.left;
tmpNode.left = tmpNode.right;
tmpNode.right = right;
right = tmpNode;
if (left != null) {
left.parent = this;
}
if (right.right != null) {
right.right.parent = right;
}
}
/** Perform a counter-clockwise rotation rooted at the instance.
* The skew factor are not updated by this method, they
* must be updated by the caller
*/
private void rotateCCW() {
final T tmpElt = element;
element = right.element;
right.element = tmpElt;
final Node tmpNode = right;
right = tmpNode.right;
tmpNode.right = tmpNode.left;
tmpNode.left = left;
left = tmpNode;
if (right != null) {
right.parent = this;
}
if (left.left != null) {
left.left.parent = left;
}
}
}
}