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Diffstat (limited to 'src/main/java/org/apache/commons/math3/geometry/partitioning/utilities/AVLTree.java')
| -rw-r--r-- | src/main/java/org/apache/commons/math3/geometry/partitioning/utilities/AVLTree.java | 634 |
1 files changed, 634 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/geometry/partitioning/utilities/AVLTree.java b/src/main/java/org/apache/commons/math3/geometry/partitioning/utilities/AVLTree.java new file mode 100644 index 0000000..00c9d3e --- /dev/null +++ b/src/main/java/org/apache/commons/math3/geometry/partitioning/utilities/AVLTree.java @@ -0,0 +1,634 @@ +/* + * 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. + * + * <p>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.</p> + * + * <p>Since the {@code equals} method is not sufficient to + * differentiate elements, the {@link #delete delete} method is + * implemented using the equality operator.</p> + * + * <p>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semantics as the ones specified in the + * {@code SortedSet} interface, different names are used + * ({@code add} has been replaced by {@link #insert insert} and + * {@code remove} has been replaced by {@link #delete + * delete}).</p> + * + * <p>This class is based on the C implementation Georg Kraml has put + * in the public domain. Unfortunately, his <a + * href="www.purists.org/georg/avltree/index.html">page</a> seems not + * to exist any more.</p> + * + * @param <T> 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<T extends Comparable<T>> { + + /** 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. + * <p>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 + * <em>different</em> 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).</p> + * @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. + * <p>AVL tree nodes implement all the logical structure of the + * tree. Nodes are created by the {@link AVLTree AVLTree} class.</p> + * <p>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.</p> + * @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. + * <p>The skew factor are not updated by this method, they + * <em>must</em> be updated by the caller</p> + */ + 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. + * <p>The skew factor are not updated by this method, they + * <em>must</em> be updated by the caller</p> + */ + 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; + } + + } + + } + +} |