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Additions:
**Tree.java**
%%(java)
import java.util.ArrayList;
import java.util.Comparator;
import java.util.TreeSet;
/*
* Created on 08.07.2005
*
*/
public class Tree {
final private int minDegree;
final private Comparator comp;
private Node root;
public Tree(final int minDegree, final Comparator comp) {
this.minDegree = minDegree;
this.comp = comp;
this.root = new Node(minDegree);
}
public boolean insert(final Object key) {
if (this.root.isFull()) { // root is full and will be split
final Node oldRoot = this.root;
final Node newRoot = new Node(this.minDegree); // create a new root
this.root = newRoot;
newRoot.setLeaf(false);
newRoot.setSubNode(0, oldRoot); // add old root as a child to the new root
newRoot.splitFullChild(oldRoot, 0); // split the old (full) root into two nodes
return insertNonFull(newRoot, key); // insert into the (not anymore full) root
} else {
return insertNonFull(this.root, key); // insert into a non-full root
}
}
private boolean insertNonFull(final Node node, final Object key) {
assert !node.isFull();
if (node.isLeaf()) { // node is a leaf
return node.insertKey(key, this.comp); // since the node is not full, we can simply insert
} else { // node is an inner node
int i = node.findInsertionPosition(key, this.comp); // find the position where to insert
if (i >= 0) { // the node doesn't contain the key, we insert at the found insertion position
final Node child = node.getSubNode(i); // get the child where we continue our insertion
if (child.isFull()) {
node.splitFullChild(child, i); // split the full child
final int comp = this.comp.compare(key, node.getKey(i));
if (comp > 0) {
i++;
} else if (comp == 0) {
return false;
}
}
return insertNonFull(node.getSubNode(i), key);
} else { // the node already contained the key
return false;
}
}
}
public boolean delete(final Object key) {
return delete(this.root, key);
}
private boolean delete(final Node node, final Object key) {
final NodeSearchResult search = node.search(key, this.comp);
if (search.isFound()) {
deleteFromNode(node, search.getKeyIndex());
return true;
} else {
if (node.isLeaf()) return false; // key not in tree
final Node child = ensureFullEnoughChild(node, search.getKeyIndex());
return delete(child, key);
}
}
private Node ensureFullEnoughChild(final Node node, final int index) {
Node child = node.getSubNode(index);
Node leftSibling = null;
Node rightSibling = null;
if (!child.isFullEnough()) {
if (index > 0) { // check left sibling
leftSibling = node.getSubNode(index - 1);
if (leftSibling.isFullEnough()) {
//System.out.println("case 3a left");
final Object pushdownKey = node.getKey(index - 1);
child.shiftAllRight();
child.setKey(0, pushdownKey);
child.setSubNode(0, leftSibling.getSubNode(leftSibling.getNumKeys()));
leftSibling.setSubNode(leftSibling.getNumKeys(), null); // not necessary
final Object pushupKey = leftSibling.getKey(leftSibling.getNumKeys() - 1);
leftSibling.removeKey(leftSibling.getNumKeys() - 1);
node.setKey(index - 1, pushupKey);
}
}
}
if (!child.isFullEnough()) {
if (index < node.getNumKeys()) { // check right sibling
rightSibling = node.getSubNode(index + 1);
if (rightSibling.isFullEnough()) {
//System.out.println("case 3a right");
final Object pushdownKey = node.getKey(index);
child.insertKey(pushdownKey, this.comp);
child.setSubNode(child.getNumKeys(), rightSibling.getSubNode(0));
final Object pushupKey = rightSibling.getKey(0);
rightSibling.shiftAllLeft();
node.setKey(index, pushupKey);
}
}
}
if (!child.isFullEnough()) {
if (leftSibling != null) {
//System.out.println("case 3b left");
node.mergeRightIntoLeftChild(leftSibling, index - 1, child);
child = leftSibling;
} else if (rightSibling != null) {
//System.out.println("case 3b right");
node.mergeRightIntoLeftChild(child, index, rightSibling);
} else {
assert false;
}
if (node == this.root && node.getNumKeys() == 0) {
this.root = child;
}
}
assert child.isFullEnough();
return child;
}
private void deleteFromNode(final Node node, final int index) {
if (node.isLeaf()) {
//System.out.println("case 1");
node.removeKey(index);
} else {
// delete key in non-leaf-node
final Node leftChild = node.getSubNode(index);
if (leftChild.isFullEnough()) {
//System.out.println("case 2a");
final TreeSearchResult maxSearch = this.findMax(leftChild);
final Node maxNode = maxSearch.getNode();
final Object maxKey = maxNode.getKey(maxSearch.getKeyIndex());
node.setKey(index, maxKey);
delete(leftChild, maxKey);
} else {
final Node rightChild = node.getSubNode(index + 1);
if (rightChild.isFullEnough()) {
//System.out.println("case 2b");
final TreeSearchResult minSearch = this.findMin(rightChild);
final Node minNode = minSearch.getNode();
final Object minKey = minNode.getKey(minSearch.getKeyIndex());
node.setKey(index, minKey);
delete(rightChild, minKey);
} else {
//System.out.println("case 2c");
final Object key = node.getKey(index);
node.mergeRightIntoLeftChild(leftChild, index, rightChild);
// delete right child
delete(leftChild, key);
}
}
}
}
private TreeSearchResult findMax(final Node node) {
if (node.isLeaf()) {
return new TreeSearchResult(true, node, node.getNumKeys() - 1);
} else {
return findMax(node.getSubNode(node.getNumKeys()));
}
}
private TreeSearchResult findMin(final Node node) {
if (node.isLeaf()) {
return new TreeSearchResult(true, node, 0);
} else {
return findMin(node.getSubNode(0));
}
}
public void print() {
this.root.print();
System.out.println();
}
public Object[] getAll() {
ArrayList list = new ArrayList();
this.root.inOrder(list);
return list.toArray();
}
}
**Node.java**
%%(java)
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
/*
* Created on 08.07.2005
*
*/
class Node {
private final int minDegree; // the minimum number of sub-nodes
private final int maxSize; // the maximum number of keys
private int numKeys; // the current number of keys
private Object[] keys; // the keys
private Node[] subNodes; // the subnodes
private boolean leaf;
Node(final int minDegree) {
this.minDegree = minDegree;
this.maxSize = minDegree * 2 - 1;
this.keys = new Object[this.maxSize];
this.subNodes = new Node[this.maxSize + 1];
this.numKeys = 0;
this.leaf = true;
}
NodeSearchResult search(final Object key, final Comparator comp) {
final int i = Node.binarySearch(this.keys, key, this.numKeys - 1, comp);
if (i >= 0) {
return new NodeSearchResult(true, i);
} else {
return new NodeSearchResult(false, -(i + 1));
}
}
void setLeaf(final boolean leaf) {
this.leaf = leaf;
}
boolean isLeaf() {
return this.leaf;
}
boolean isFull() {
return (this.numKeys == this.maxSize);
}
boolean isFullEnough() {
return (this.numKeys >= this.minDegree);
}
void setSubNode(final int i, final Node node) {
this.subNodes[i] = node;
}
void setKey(final int i, final Object key) {
this.keys[i] = key;
}
/**
* Splits the i-th sub-node of this node into two nodes and moves the median of the i-th sub-node up into this node
* @param i
*/
void splitFullChild(final Node fullChildNode, final int i) {
final Node newNode = new Node(this.minDegree);
newNode.leaf = fullChildNode.leaf;
newNode.numKeys = this.minDegree - 1;
/* move upper half of the keys and possible subnodes from the full child to the new node */
System.arraycopy(fullChildNode.keys, this.minDegree, newNode.keys, 0, this.minDegree - 1);
Arrays.fill(fullChildNode.keys, this.minDegree, this.maxSize, null); // not necessary, note: the end index is not included!!
if (!fullChildNode.leaf) {
System.arraycopy(fullChildNode.subNodes, this.minDegree, newNode.subNodes, 0, this.minDegree);
Arrays.fill(fullChildNode.subNodes, this.minDegree, this.maxSize, null); // not necessary
}
fullChildNode.numKeys = this.minDegree - 1;
/* make space in this node for the new child node and add it */
System.arraycopy(this.subNodes, i, this.subNodes, i + 1, this.numKeys + 1 - i);
this.subNodes[i + 1] = newNode;
System.arraycopy(this.keys, i, this.keys, i + 1, this.numKeys - i);
this.keys[i] = fullChildNode.keys[this.minDegree - 1];
fullChildNode.keys[this.minDegree - 1] = null; // not necessary
this.numKeys++;
}
/**
* Merges the right child (the one right of keyIndex) with the left child (left of keyIndex). The keys and subnodes
* of the right child are copied into the left child. The current nodes key at the keyIndex position drops down to the
* left child as well. The right child is removed from the tree.
*/
void mergeRightIntoLeftChild(final Node leftChild, final int keyIndex, final Node rightChild) {
leftChild.keys[leftChild.numKeys] = this.keys[keyIndex];
leftChild.numKeys++;
System.arraycopy(this.keys, keyIndex + 1, this.keys, keyIndex, this.numKeys - 1 - keyIndex);
System.arraycopy(this.subNodes, keyIndex + 2, this.subNodes, keyIndex + 1, this.numKeys - 1 - keyIndex);
this.keys[this.numKeys - 1] = null; // not necessary
this.subNodes[this.numKeys] = null; // not necessary
this.numKeys--;
System.arraycopy(rightChild.keys, 0, leftChild.keys, leftChild.numKeys, rightChild.numKeys);
System.arraycopy(rightChild.subNodes, 0, leftChild.subNodes, leftChild.numKeys, rightChild.numKeys);
leftChild.numKeys += rightChild.numKeys;
leftChild.subNodes[leftChild.numKeys] = rightChild.subNodes[rightChild.numKeys];
}
int findInsertionPosition(final Object key, final Comparator comp) {
return -(Node.binarySearch(this.keys, key, this.numKeys - 1, comp) + 1);
}
boolean insertKey(final Object key, final Comparator comp) {
final int i = this.findInsertionPosition(key, comp);
if (i >= 0) {
System.arraycopy(this.keys, i, this.keys, i + 1, this.numKeys - i);
this.keys[i] = key;
this.numKeys++;
return true;
} else {
return false;
}
}
void shiftAllRight() {
System.arraycopy(this.keys, 0, this.keys, 1, this.numKeys);
System.arraycopy(this.subNodes, 0, this.subNodes, 1, this.numKeys + 1);
this.subNodes[0] = null; // not necessary
this.keys[0] = null; // not necessary
this.numKeys++;
}
void shiftAllLeft() {
System.arraycopy(this.keys, 1, this.keys, 0, this.numKeys - 1);
System.arraycopy(this.subNodes, 1, this.subNodes, 0, this.numKeys);
this.keys[this.numKeys - 1] = null; // not necessary
this.subNodes[this.numKeys] = null; // not necessary
this.numKeys--;
}
/**
* Removes a key (and only the key) from the node. If this is not a leaf care has to be taken of the subNodes.
*
* @param keyIndex the index of the key to delete
*/
void removeKey(final int keyIndex) {
System.arraycopy(this.keys, keyIndex + 1, this.keys, keyIndex, this.numKeys - 1 - keyIndex);
this.keys[this.numKeys - 1] = null; // not necessary
this.numKeys--;
}
Object getKey(final int i) {
return this.keys[i];
}
Node getSubNode(final int i) {
return this.subNodes[i];
}
int getNumKeys() {
return this.numKeys;
}
public static int binarySearch(final Object[] a, final Object key, int high, final Comparator c) {
int low = 0;
while (low <= high) {
final int mid = (low + high) >> 1;
final Object midVal = a[mid];
final int cmp = c.compare(midVal, key);
if (cmp < 0) {
low = mid + 1;
} else if (cmp > 0) {
high = mid - 1;
} else {
return mid; // key found
}
}
return -(low + 1); // key not found.
}
}
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%%(java)
import java.util.ArrayList;
import java.util.Comparator;
import java.util.TreeSet;
/*
* Created on 08.07.2005
*
*/
public class Tree {
final private int minDegree;
final private Comparator comp;
private Node root;
public Tree(final int minDegree, final Comparator comp) {
this.minDegree = minDegree;
this.comp = comp;
this.root = new Node(minDegree);
}
public boolean insert(final Object key) {
if (this.root.isFull()) { // root is full and will be split
final Node oldRoot = this.root;
final Node newRoot = new Node(this.minDegree); // create a new root
this.root = newRoot;
newRoot.setLeaf(false);
newRoot.setSubNode(0, oldRoot); // add old root as a child to the new root
newRoot.splitFullChild(oldRoot, 0); // split the old (full) root into two nodes
return insertNonFull(newRoot, key); // insert into the (not anymore full) root
} else {
return insertNonFull(this.root, key); // insert into a non-full root
}
}
private boolean insertNonFull(final Node node, final Object key) {
assert !node.isFull();
if (node.isLeaf()) { // node is a leaf
return node.insertKey(key, this.comp); // since the node is not full, we can simply insert
} else { // node is an inner node
int i = node.findInsertionPosition(key, this.comp); // find the position where to insert
if (i >= 0) { // the node doesn't contain the key, we insert at the found insertion position
final Node child = node.getSubNode(i); // get the child where we continue our insertion
if (child.isFull()) {
node.splitFullChild(child, i); // split the full child
final int comp = this.comp.compare(key, node.getKey(i));
if (comp > 0) {
i++;
} else if (comp == 0) {
return false;
}
}
return insertNonFull(node.getSubNode(i), key);
} else { // the node already contained the key
return false;
}
}
}
public boolean delete(final Object key) {
return delete(this.root, key);
}
private boolean delete(final Node node, final Object key) {
final NodeSearchResult search = node.search(key, this.comp);
if (search.isFound()) {
deleteFromNode(node, search.getKeyIndex());
return true;
} else {
if (node.isLeaf()) return false; // key not in tree
final Node child = ensureFullEnoughChild(node, search.getKeyIndex());
return delete(child, key);
}
}
private Node ensureFullEnoughChild(final Node node, final int index) {
Node child = node.getSubNode(index);
Node leftSibling = null;
Node rightSibling = null;
if (!child.isFullEnough()) {
if (index > 0) { // check left sibling
leftSibling = node.getSubNode(index - 1);
if (leftSibling.isFullEnough()) {
//System.out.println("case 3a left");
final Object pushdownKey = node.getKey(index - 1);
child.shiftAllRight();
child.setKey(0, pushdownKey);
child.setSubNode(0, leftSibling.getSubNode(leftSibling.getNumKeys()));
leftSibling.setSubNode(leftSibling.getNumKeys(), null); // not necessary
final Object pushupKey = leftSibling.getKey(leftSibling.getNumKeys() - 1);
leftSibling.removeKey(leftSibling.getNumKeys() - 1);
node.setKey(index - 1, pushupKey);
}
}
}
if (!child.isFullEnough()) {
if (index < node.getNumKeys()) { // check right sibling
rightSibling = node.getSubNode(index + 1);
if (rightSibling.isFullEnough()) {
//System.out.println("case 3a right");
final Object pushdownKey = node.getKey(index);
child.insertKey(pushdownKey, this.comp);
child.setSubNode(child.getNumKeys(), rightSibling.getSubNode(0));
final Object pushupKey = rightSibling.getKey(0);
rightSibling.shiftAllLeft();
node.setKey(index, pushupKey);
}
}
}
if (!child.isFullEnough()) {
if (leftSibling != null) {
//System.out.println("case 3b left");
node.mergeRightIntoLeftChild(leftSibling, index - 1, child);
child = leftSibling;
} else if (rightSibling != null) {
//System.out.println("case 3b right");
node.mergeRightIntoLeftChild(child, index, rightSibling);
} else {
assert false;
}
if (node == this.root && node.getNumKeys() == 0) {
this.root = child;
}
}
assert child.isFullEnough();
return child;
}
private void deleteFromNode(final Node node, final int index) {
if (node.isLeaf()) {
//System.out.println("case 1");
node.removeKey(index);
} else {
// delete key in non-leaf-node
final Node leftChild = node.getSubNode(index);
if (leftChild.isFullEnough()) {
//System.out.println("case 2a");
final TreeSearchResult maxSearch = this.findMax(leftChild);
final Node maxNode = maxSearch.getNode();
final Object maxKey = maxNode.getKey(maxSearch.getKeyIndex());
node.setKey(index, maxKey);
delete(leftChild, maxKey);
} else {
final Node rightChild = node.getSubNode(index + 1);
if (rightChild.isFullEnough()) {
//System.out.println("case 2b");
final TreeSearchResult minSearch = this.findMin(rightChild);
final Node minNode = minSearch.getNode();
final Object minKey = minNode.getKey(minSearch.getKeyIndex());
node.setKey(index, minKey);
delete(rightChild, minKey);
} else {
//System.out.println("case 2c");
final Object key = node.getKey(index);
node.mergeRightIntoLeftChild(leftChild, index, rightChild);
// delete right child
delete(leftChild, key);
}
}
}
}
private TreeSearchResult findMax(final Node node) {
if (node.isLeaf()) {
return new TreeSearchResult(true, node, node.getNumKeys() - 1);
} else {
return findMax(node.getSubNode(node.getNumKeys()));
}
}
private TreeSearchResult findMin(final Node node) {
if (node.isLeaf()) {
return new TreeSearchResult(true, node, 0);
} else {
return findMin(node.getSubNode(0));
}
}
public void print() {
this.root.print();
System.out.println();
}
public Object[] getAll() {
ArrayList list = new ArrayList();
this.root.inOrder(list);
return list.toArray();
}
}
**Node.java**
%%(java)
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
/*
* Created on 08.07.2005
*
*/
class Node {
private final int minDegree; // the minimum number of sub-nodes
private final int maxSize; // the maximum number of keys
private int numKeys; // the current number of keys
private Object[] keys; // the keys
private Node[] subNodes; // the subnodes
private boolean leaf;
Node(final int minDegree) {
this.minDegree = minDegree;
this.maxSize = minDegree * 2 - 1;
this.keys = new Object[this.maxSize];
this.subNodes = new Node[this.maxSize + 1];
this.numKeys = 0;
this.leaf = true;
}
NodeSearchResult search(final Object key, final Comparator comp) {
final int i = Node.binarySearch(this.keys, key, this.numKeys - 1, comp);
if (i >= 0) {
return new NodeSearchResult(true, i);
} else {
return new NodeSearchResult(false, -(i + 1));
}
}
void setLeaf(final boolean leaf) {
this.leaf = leaf;
}
boolean isLeaf() {
return this.leaf;
}
boolean isFull() {
return (this.numKeys == this.maxSize);
}
boolean isFullEnough() {
return (this.numKeys >= this.minDegree);
}
void setSubNode(final int i, final Node node) {
this.subNodes[i] = node;
}
void setKey(final int i, final Object key) {
this.keys[i] = key;
}
/**
* Splits the i-th sub-node of this node into two nodes and moves the median of the i-th sub-node up into this node
* @param i
*/
void splitFullChild(final Node fullChildNode, final int i) {
final Node newNode = new Node(this.minDegree);
newNode.leaf = fullChildNode.leaf;
newNode.numKeys = this.minDegree - 1;
/* move upper half of the keys and possible subnodes from the full child to the new node */
System.arraycopy(fullChildNode.keys, this.minDegree, newNode.keys, 0, this.minDegree - 1);
Arrays.fill(fullChildNode.keys, this.minDegree, this.maxSize, null); // not necessary, note: the end index is not included!!
if (!fullChildNode.leaf) {
System.arraycopy(fullChildNode.subNodes, this.minDegree, newNode.subNodes, 0, this.minDegree);
Arrays.fill(fullChildNode.subNodes, this.minDegree, this.maxSize, null); // not necessary
}
fullChildNode.numKeys = this.minDegree - 1;
/* make space in this node for the new child node and add it */
System.arraycopy(this.subNodes, i, this.subNodes, i + 1, this.numKeys + 1 - i);
this.subNodes[i + 1] = newNode;
System.arraycopy(this.keys, i, this.keys, i + 1, this.numKeys - i);
this.keys[i] = fullChildNode.keys[this.minDegree - 1];
fullChildNode.keys[this.minDegree - 1] = null; // not necessary
this.numKeys++;
}
/**
* Merges the right child (the one right of keyIndex) with the left child (left of keyIndex). The keys and subnodes
* of the right child are copied into the left child. The current nodes key at the keyIndex position drops down to the
* left child as well. The right child is removed from the tree.
*/
void mergeRightIntoLeftChild(final Node leftChild, final int keyIndex, final Node rightChild) {
leftChild.keys[leftChild.numKeys] = this.keys[keyIndex];
leftChild.numKeys++;
System.arraycopy(this.keys, keyIndex + 1, this.keys, keyIndex, this.numKeys - 1 - keyIndex);
System.arraycopy(this.subNodes, keyIndex + 2, this.subNodes, keyIndex + 1, this.numKeys - 1 - keyIndex);
this.keys[this.numKeys - 1] = null; // not necessary
this.subNodes[this.numKeys] = null; // not necessary
this.numKeys--;
System.arraycopy(rightChild.keys, 0, leftChild.keys, leftChild.numKeys, rightChild.numKeys);
System.arraycopy(rightChild.subNodes, 0, leftChild.subNodes, leftChild.numKeys, rightChild.numKeys);
leftChild.numKeys += rightChild.numKeys;
leftChild.subNodes[leftChild.numKeys] = rightChild.subNodes[rightChild.numKeys];
}
int findInsertionPosition(final Object key, final Comparator comp) {
return -(Node.binarySearch(this.keys, key, this.numKeys - 1, comp) + 1);
}
boolean insertKey(final Object key, final Comparator comp) {
final int i = this.findInsertionPosition(key, comp);
if (i >= 0) {
System.arraycopy(this.keys, i, this.keys, i + 1, this.numKeys - i);
this.keys[i] = key;
this.numKeys++;
return true;
} else {
return false;
}
}
void shiftAllRight() {
System.arraycopy(this.keys, 0, this.keys, 1, this.numKeys);
System.arraycopy(this.subNodes, 0, this.subNodes, 1, this.numKeys + 1);
this.subNodes[0] = null; // not necessary
this.keys[0] = null; // not necessary
this.numKeys++;
}
void shiftAllLeft() {
System.arraycopy(this.keys, 1, this.keys, 0, this.numKeys - 1);
System.arraycopy(this.subNodes, 1, this.subNodes, 0, this.numKeys);
this.keys[this.numKeys - 1] = null; // not necessary
this.subNodes[this.numKeys] = null; // not necessary
this.numKeys--;
}
/**
* Removes a key (and only the key) from the node. If this is not a leaf care has to be taken of the subNodes.
*
* @param keyIndex the index of the key to delete
*/
void removeKey(final int keyIndex) {
System.arraycopy(this.keys, keyIndex + 1, this.keys, keyIndex, this.numKeys - 1 - keyIndex);
this.keys[this.numKeys - 1] = null; // not necessary
this.numKeys--;
}
Object getKey(final int i) {
return this.keys[i];
}
Node getSubNode(final int i) {
return this.subNodes[i];
}
int getNumKeys() {
return this.numKeys;
}
public static int binarySearch(final Object[] a, final Object key, int high, final Comparator c) {
int low = 0;
while (low <= high) {
final int mid = (low + high) >> 1;
final Object midVal = a[mid];
final int cmp = c.compare(midVal, key);
if (cmp < 0) {
low = mid + 1;
} else if (cmp > 0) {
high = mid - 1;
} else {
return mid; // key found
}
}
return -(low + 1); // key not found.
}
}
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Deletions:
%%(java)
import java.util.ArrayList;
import java.util.Comparator;
import java.util.TreeSet;
/*
* Created on 08.07.2005
*
*/
public class Tree {
final private int minDegree;
final private Comparator comp;
private Node root;
public Tree(final int minDegree, final Comparator comp) {
this.minDegree = minDegree;
this.comp = comp;
this.root = new Node(minDegree);
}
public boolean insert(final Object key) {
if (this.root.isFull()) { // root is full and will be split
final Node oldRoot = this.root;
final Node newRoot = new Node(this.minDegree); // create a new root
this.root = newRoot;
newRoot.setLeaf(false);
newRoot.setSubNode(0, oldRoot); // add old root as a child to the new root
newRoot.splitFullChild(oldRoot, 0); // split the old (full) root into two nodes
return insertNonFull(newRoot, key); // insert into the (not anymore full) root
} else {
return insertNonFull(this.root, key); // insert into a non-full root
}
}
private boolean insertNonFull(final Node node, final Object key) {
assert !node.isFull();
if (node.isLeaf()) { // node is a leaf
return node.insertKey(key, this.comp); // since the node is not full, we can simply insert
} else { // node is an inner node
int i = node.findInsertionPosition(key, this.comp); // find the position where to insert
if (i >= 0) { // the node doesn't contain the key, we insert at the found insertion position
final Node child = node.getSubNode(i); // get the child where we continue our insertion
if (child.isFull()) {
node.splitFullChild(child, i); // split the full child
final int comp = this.comp.compare(key, node.getKey(i));
if (comp > 0) {
i++;
} else if (comp == 0) {
return false;
}
}
return insertNonFull(node.getSubNode(i), key);
} else { // the node already contained the key
return false;
}
}
}
public boolean delete(final Object key) {
return delete(this.root, key);
}
private boolean delete(final Node node, final Object key) {
final NodeSearchResult search = node.search(key, this.comp);
if (search.isFound()) {
deleteFromNode(node, search.getKeyIndex());
return true;
} else {
if (node.isLeaf()) return false; // key not in tree
final Node child = ensureFullEnoughChild(node, search.getKeyIndex());
return delete(child, key);
}
}
private Node ensureFullEnoughChild(final Node node, final int index) {
Node child = node.getSubNode(index);
Node leftSibling = null;
Node rightSibling = null;
if (!child.isFullEnough()) {
if (index > 0) { // check left sibling
leftSibling = node.getSubNode(index - 1);
if (leftSibling.isFullEnough()) {
//System.out.println("case 3a left");
final Object pushdownKey = node.getKey(index - 1);
child.shiftAllRight();
child.setKey(0, pushdownKey);
child.setSubNode(0, leftSibling.getSubNode(leftSibling.getNumKeys()));
leftSibling.setSubNode(leftSibling.getNumKeys(), null); // not necessary
final Object pushupKey = leftSibling.getKey(leftSibling.getNumKeys() - 1);
leftSibling.removeKey(leftSibling.getNumKeys() - 1);
node.setKey(index - 1, pushupKey);
}
}
}
if (!child.isFullEnough()) {
if (index < node.getNumKeys()) { // check right sibling
rightSibling = node.getSubNode(index + 1);
if (rightSibling.isFullEnough()) {
//System.out.println("case 3a right");
final Object pushdownKey = node.getKey(index);
child.insertKey(pushdownKey, this.comp);
child.setSubNode(child.getNumKeys(), rightSibling.getSubNode(0));
final Object pushupKey = rightSibling.getKey(0);
rightSibling.shiftAllLeft();
node.setKey(index, pushupKey);
}
}
}
if (!child.isFullEnough()) {
if (leftSibling != null) {
//System.out.println("case 3b left");
node.mergeRightIntoLeftChild(leftSibling, index - 1, child);
child = leftSibling;
} else if (rightSibling != null) {
//System.out.println("case 3b right");
node.mergeRightIntoLeftChild(child, index, rightSibling);
} else {
assert false;
}
if (node == this.root && node.getNumKeys() == 0) {
this.root = child;
}
}
assert child.isFullEnough();
return child;
}
private void deleteFromNode(final Node node, final int index) {
if (node.isLeaf()) {
//System.out.println("case 1");
node.removeKey(index);
} else {
// delete key in non-leaf-node
final Node leftChild = node.getSubNode(index);
if (leftChild.isFullEnough()) {
//System.out.println("case 2a");
final TreeSearchResult maxSearch = this.findMax(leftChild);
final Node maxNode = maxSearch.getNode();
final Object maxKey = maxNode.getKey(maxSearch.getKeyIndex());
node.setKey(index, maxKey);
delete(leftChild, maxKey);
} else {
final Node rightChild = node.getSubNode(index + 1);
if (rightChild.isFullEnough()) {
//System.out.println("case 2b");
final TreeSearchResult minSearch = this.findMin(rightChild);
final Node minNode = minSearch.getNode();
final Object minKey = minNode.getKey(minSearch.getKeyIndex());
node.setKey(index, minKey);
delete(rightChild, minKey);
} else {
//System.out.println("case 2c");
final Object key = node.getKey(index);
node.mergeRightIntoLeftChild(leftChild, index, rightChild);
// delete right child
delete(leftChild, key);
}
}
}
}
private TreeSearchResult findMax(final Node node) {
if (node.isLeaf()) {
return new TreeSearchResult(true, node, node.getNumKeys() - 1);
} else {
return findMax(node.getSubNode(node.getNumKeys()));
}
}
private TreeSearchResult findMin(final Node node) {
if (node.isLeaf()) {
return new TreeSearchResult(true, node, 0);
} else {
return findMin(node.getSubNode(0));
}
}
public void print() {
this.root.print();
System.out.println();
}
public Object[] getAll() {
ArrayList list = new ArrayList();
this.root.inOrder(list);
return list.toArray();
}
}
%%
**Node.java**
%%(java)
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
/*
* Created on 08.07.2005
*
*/
class Node {
private final int minDegree; // the minimum number of sub-nodes
private final int maxSize; // the maximum number of keys
private int numKeys; // the current number of keys
private Object[] keys; // the keys
private Node[] subNodes; // the subnodes
private boolean leaf;
Node(final int minDegree) {
this.minDegree = minDegree;
this.maxSize = minDegree * 2 - 1;
this.keys = new Object[this.maxSize];
this.subNodes = new Node[this.maxSize + 1];
this.numKeys = 0;
this.leaf = true;
}
NodeSearchResult search(final Object key, final Comparator comp) {
final int i = Node.binarySearch(this.keys, key, this.numKeys - 1, comp);
if (i >= 0) {
return new NodeSearchResult(true, i);
} else {
return new NodeSearchResult(false, -(i + 1));
}
}
void setLeaf(final boolean leaf) {
this.leaf = leaf;
}
boolean isLeaf() {
return this.leaf;
}
boolean isFull() {
return (this.numKeys == this.maxSize);
}
boolean isFullEnough() {
return (this.numKeys >= this.minDegree);
}
void setSubNode(final int i, final Node node) {
this.subNodes[i] = node;
}
void setKey(final int i, final Object key) {
this.keys[i] = key;
}
/**
* Splits the i-th sub-node of this node into two nodes and moves the median of the i-th sub-node up into this node
* @param i
*/
void splitFullChild(final Node fullChildNode, final int i) {
final Node newNode = new Node(this.minDegree);
newNode.leaf = fullChildNode.leaf;
newNode.numKeys = this.minDegree - 1;
/* move upper half of the keys and possible subnodes from the full child to the new node */
System.arraycopy(fullChildNode.keys, this.minDegree, newNode.keys, 0, this.minDegree - 1);
Arrays.fill(fullChildNode.keys, this.minDegree, this.maxSize, null); // not necessary, note: the end index is not included!!
if (!fullChildNode.leaf) {
System.arraycopy(fullChildNode.subNodes, this.minDegree, newNode.subNodes, 0, this.minDegree);
Arrays.fill(fullChildNode.subNodes, this.minDegree, this.maxSize, null); // not necessary
}
fullChildNode.numKeys = this.minDegree - 1;
/* make space in this node for the new child node and add it */
System.arraycopy(this.subNodes, i, this.subNodes, i + 1, this.numKeys + 1 - i);
this.subNodes[i + 1] = newNode;
System.arraycopy(this.keys, i, this.keys, i + 1, this.numKeys - i);
this.keys[i] = fullChildNode.keys[this.minDegree - 1];
fullChildNode.keys[this.minDegree - 1] = null; // not necessary
this.numKeys++;
}
/**
* Merges the right child (the one right of keyIndex) with the left child (left of keyIndex). The keys and subnodes
* of the right child are copied into the left child. The current nodes key at the keyIndex position drops down to the
* left child as well. The right child is removed from the tree.
*/
void mergeRightIntoLeftChild(final Node leftChild, final int keyIndex, final Node rightChild) {
leftChild.keys[leftChild.numKeys] = this.keys[keyIndex];
leftChild.numKeys++;
System.arraycopy(this.keys, keyIndex + 1, this.keys, keyIndex, this.numKeys - 1 - keyIndex);
System.arraycopy(this.subNodes, keyIndex + 2, this.subNodes, keyIndex + 1, this.numKeys - 1 - keyIndex);
this.keys[this.numKeys - 1] = null; // not necessary
this.subNodes[this.numKeys] = null; // not necessary
this.numKeys--;
System.arraycopy(rightChild.keys, 0, leftChild.keys, leftChild.numKeys, rightChild.numKeys);
System.arraycopy(rightChild.subNodes, 0, leftChild.subNodes, leftChild.numKeys, rightChild.numKeys);
leftChild.numKeys += rightChild.numKeys;
leftChild.subNodes[leftChild.numKeys] = rightChild.subNodes[rightChild.numKeys];
}
int findInsertionPosition(final Object key, final Comparator comp) {
return -(Node.binarySearch(this.keys, key, this.numKeys - 1, comp) + 1);
}
boolean insertKey(final Object key, final Comparator comp) {
final int i = this.findInsertionPosition(key, comp);
if (i >= 0) {
System.arraycopy(this.keys, i, this.keys, i + 1, this.numKeys - i);
this.keys[i] = key;
this.numKeys++;
return true;
} else {
return false;
}
}
void shiftAllRight() {
System.arraycopy(this.keys, 0, this.keys, 1, this.numKeys);
System.arraycopy(this.subNodes, 0, this.subNodes, 1, this.numKeys + 1);
this.subNodes[0] = null; // not necessary
this.keys[0] = null; // not necessary
this.numKeys++;
}
void shiftAllLeft() {
System.arraycopy(this.keys, 1, this.keys, 0, this.numKeys - 1);
System.arraycopy(this.subNodes, 1, this.subNodes, 0, this.numKeys);
this.keys[this.numKeys - 1] = null; // not necessary
this.subNodes[this.numKeys] = null; // not necessary
this.numKeys--;
}
/**
* Removes a key (and only the key) from the node. If this is not a leaf care has to be taken of the subNodes.
*
* @param keyIndex the index of the key to delete
*/
void removeKey(final int keyIndex) {
System.arraycopy(this.keys, keyIndex + 1, this.keys, keyIndex, this.numKeys - 1 - keyIndex);
this.keys[this.numKeys - 1] = null; // not necessary
this.numKeys--;
}
Object getKey(final int i) {
return this.keys[i];
}
Node getSubNode(final int i) {
return this.subNodes[i];
}
int getNumKeys() {
return this.numKeys;
}
public static int binarySearch(final Object[] a, final Object key, int high, final Comparator c) {
int low = 0;
while (low <= high) {
final int mid = (low + high) >> 1;
final Object midVal = a[mid];
final int cmp = c.compare(midVal, key);
if (cmp < 0) {
low = mid + 1;
} else if (cmp > 0) {
high = mid - 1;
} else {
return mid; // key found
}
}
return -(low + 1); // key not found.
}
}
