The Implementation of A B Plus Tree

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import java.util.*;

public class BPlusTree<K extends Comparable<? super K>, V> {

/**
* The branching factor used when none specified in constructor.
*/
private static final int DEFAULT_BRANCHING_FACTOR = 128;
/**
* The branching factor for the B+ tree, that measures the capacity of nodes
* (i.e., the number of children nodes) for internal nodes in the tree.
*/
private int branchingFactor;
/**
* The root node of the B+ tree.
*/
private Node root;

public BPlusTree() {
this(DEFAULT_BRANCHING_FACTOR);
}

public BPlusTree(int branchingFactor) {
this.branchingFactor = branchingFactor;

// initially, root is a leaf node which is able to keep values. It will split when the
// value list is full. After that the root node only serves as a lookup table and becomes
// a internal node.
root = new LeafNode();
}

public static void main(String[] args) {
ArrayList<Integer> words = new ArrayList<>();

for (int i = 0; i < 10000; i++) {
words.add(i);
}

BPlusTree<Integer, Integer> tree = new BPlusTree<>();

for (Integer word : words) {
if (!tree.contains(word)) {
tree.insert(word, 0);
}

tree.set(word, tree.search(word).intValue() + 1);
}

System.out.println(tree);

System.out.println(tree.searchRange(10, RangePolicy.INCLUSIVE, 20, RangePolicy.INCLUSIVE));

for (int i = 0; i < 10000; i++) {
tree.delete(i);
}
System.out.println(tree);
}

/**
* Returns the value to which the specified key is associated, or
* {@code null} if this tree contains no association for the key.
* <p>
* <p>
* A return value of {@code null} does not <i>necessarily</i> indicate that
* the tree contains no association for the key; it's also possible that the
* tree explicitly associates the key to {@code null}.
*
* @param key the key whose associated value is to be returned
* @return the value to which the specified key is associated, or
* {@code null} if this tree contains no association for the key
*/
public V search(K key) {
return root.getValue(key);
}

public boolean contains(K key) {
return root.getValue(key) != null;
}

/**
* Returns the values associated with the keys specified by the range:
* {@code key1} and {@code key2}.
*
* @param key1 the start key of the range
* @param policy1 the range policy, {@link RangePolicy#EXCLUSIVE} or
* {@link RangePolicy#INCLUSIVE}
* @param key2 the end end of the range
* @param policy2 the range policy, {@link RangePolicy#EXCLUSIVE} or
* {@link RangePolicy#INCLUSIVE}
* @return the values associated with the keys specified by the range:
* {@code key1} and {@code key2}
*/
public List<V> searchRange(K key1, RangePolicy policy1, K key2, RangePolicy policy2) {
return root.getRange(key1, policy1, key2, policy2);
}

/**
* Associates the specified value with the specified key in this tree. If
* the tree previously contained a association for the key, the old value is
* replaced.
*
* @param key the key with which the specified value is to be associated
* @param value the value to be associated with the specified key
*/
public void insert(K key, V value) {
root.insertValue(key, value);
}

public void set(K key, V value) {
root.insertValue(key, value);
}

/**
* Removes the association for the specified key from this tree if present.
*
* @param key the key whose association is to be removed from the tree
*/
public void delete(K key) {
root.deleteValue(key);
}

public String toString() {

// This method helps you to better understand the structure of the B+ Tree.

Queue<List<Node>> queue = new LinkedList<>();

queue.add(Arrays.asList(root));

StringBuilder sb = new StringBuilder();

// BFS the tree
while (!queue.isEmpty()) {

Queue<List<Node>> nextQueue = new LinkedList<>();

// Traverse the nodes on a specific level
while (!queue.isEmpty()) {
List<Node> nodes = queue.remove();

sb.append('{');

Iterator<Node> it = nodes.iterator();

// Traverse a specific node
while (it.hasNext()) {
Node node = it.next();
sb.append(node.toString());

if (it.hasNext()) {
sb.append(", ");
}

// if current node is the Internal, walk through its children nodes in next traversal.
// for leaf nodes, they are at bottom without any children, no need to descend.
if (node instanceof BPlusTree.IndexNode) {
nextQueue.add(((IndexNode) node).children);
}
}

sb.append('}');

if (!queue.isEmpty()) {
sb.append(", ");
} else {
sb.append('\n');
}
}

queue = nextQueue;
}

return sb.toString();
}

enum RangePolicy {
EXCLUSIVE, INCLUSIVE
}

private abstract class Node {
List<K> keys;

int keyNumber() {
return keys.size();
}

abstract V getValue(K key);

abstract void deleteValue(K key);

abstract void insertValue(K key, V value);

abstract K getFirstLeafKey();

abstract List<V> getRange(K key1, RangePolicy policy1, K key2, RangePolicy policy2);

abstract void merge(Node sibling);

abstract Node split();

abstract boolean isOverflow();

abstract boolean isUnderflow();

public String toString() {
return keys.toString();
}
}

private class LeafNode extends Node {
List<V> values;
LeafNode next;

LeafNode() {
keys = new ArrayList<>();
values = new ArrayList<>();
}

@Override
V getValue(K key) {
int loc = Collections.binarySearch(keys, key);
return loc >= 0 ? values.get(loc) : null;
}

@Override
void deleteValue(K key) {
int loc = Collections.binarySearch(keys, key);

// not found, return directly.
if (loc < 0) {
return;
}

keys.remove(loc);
values.remove(loc);
}

@Override
void insertValue(K key, V value) {

// Collections.binarySearch() returns the index of the search key if present or the insertion point if
// not found.

int loc = Collections.binarySearch(keys, key);

// loc >= 0 node binding with the given key found, otherwise not found and -loc-1 is the insertion point.
int valueIndex = loc >= 0 ? loc : -loc - 1;

// key exists, update it
if (loc >= 0) {
values.set(valueIndex, value);
}
// key not exists, add a new node
else {

// For index node, children node is always 1 more than keys
// But leaf nodes are aways of same size about keys and values.

keys.add(valueIndex, key);
values.add(valueIndex, value);
}

// This happens only when root node is still a leaf node, or the tree just consists of one level.
if (this == root && root.isOverflow()) {
Node sibling = split();

IndexNode newRoot = new IndexNode();

newRoot.keys.add(sibling.getFirstLeafKey());
newRoot.children.add(this);
newRoot.children.add(sibling);

root = newRoot;
}
}

@Override
K getFirstLeafKey() {
return keys.get(0);
}

@Override
List<V> getRange(K key1, RangePolicy policy1, K key2, RangePolicy policy2) {
List<V> result = new LinkedList<>();
LeafNode node = this;

while (node != null) {
Iterator<K> kIt = node.keys.iterator();
Iterator<V> vIt = node.values.iterator();

while (kIt.hasNext()) {
K key = kIt.next();
V value = vIt.next();

int cmp1 = key.compareTo(key1);
int cmp2 = key.compareTo(key2);

// (key2 >= key && EXCLUSIVE) || (key2 > key && INCLUSIVE)
boolean condition1 = (policy2 == RangePolicy.EXCLUSIVE && cmp2 >= 0) || (policy2 == RangePolicy.INCLUSIVE && cmp2 > 0);

// key overstep the right boundary of the given range
if (condition1) {
return result;
}

// (key1 > key && EXCLUSIVE) || (key1 >= key && INCLUSIVE)
boolean condition2 = ((policy1 == RangePolicy.EXCLUSIVE && cmp1 > 0) || (policy1 == RangePolicy.INCLUSIVE && cmp1 >= 0));

// (key2 < key && EXCLUSIVE) || (key2 <= key && INCLUSIVE)
boolean condition3 = ((policy2 == RangePolicy.EXCLUSIVE && cmp2 < 0) || (policy2 == RangePolicy.INCLUSIVE && cmp2 <= 0));

// key locates within the given range
if (condition2 && condition3) {
result.add(value);
}
}

node = node.next;
}

return result;
}

@Override
void merge(Node sibling) {

// leaf nodes always merge leaf nodes, index nodes will never be passed in.

LeafNode node = (LeafNode) sibling;

// Don't be afraid of overflow issue, it will automatically split if necessary.

keys.addAll(node.keys);
values.addAll(node.values);

next = node.next;
}

@Override
Node split() {
// create a new sibling, it would be much easier than transferring to an existing sibling.
LeafNode sibling = new LeafNode();

// move half of the keys to next sibling
int from = (keyNumber() + 1) / 2;
int to = keyNumber();

sibling.keys.addAll(keys.subList(from, to));
sibling.values.addAll(values.subList(from, to));

keys.subList(from, to).clear();
values.subList(from, to).clear();

sibling.next = next;
next = sibling;

return sibling;
}

@Override
boolean isOverflow() {
return values.size() > branchingFactor - 1;
}

@Override
boolean isUnderflow() {
return values.size() < branchingFactor / 2;
}
}

private class IndexNode extends Node {
List<Node> children;

IndexNode() {
this.keys = new ArrayList<>();
this.children = new ArrayList<>();
}

@Override
V getValue(K key) {
return getChild(key).getValue(key);
}

@Override
void deleteValue(K key) {
Node child = getChild(key);
child.deleteValue(key);

if (child.isUnderflow()) {
Node childLeftSibling = getChildLeftSibling(key);
Node childRightSibling = getChildRightSibling(key);

// left merge child or child merge right
Node left = childLeftSibling != null ? childLeftSibling : child;

Node right = childLeftSibling != null ? child : childRightSibling;

left.merge(right);

deleteChild(right.getFirstLeafKey());

if (left.isOverflow()) {
Node sibling = left.split();
insertChild(sibling.getFirstLeafKey(), sibling);
}

if (root.keyNumber() == 0) {
root = left;
}
}
}

@Override
void insertValue(K key, V value) {
Node child = getChild(key);

// recursively descend until reach the left node at the bottom of the tree.
child.insertValue(key, value);

// overflow check is always conducted by the parent node because it enables
// parent update the index easily..
if (child.isOverflow()) {
Node sibling = child.split();
insertChild(sibling.getFirstLeafKey(), sibling);
}

// every time after modification, check out if the root node is too full.
// the reason is that root node has no parent, hence the overflow is conducted
// by itself.
if (this == root && root.isOverflow()) {
Node sibling = split();

IndexNode newRoot = new IndexNode();

newRoot.keys.add(sibling.getFirstLeafKey());

newRoot.children.add(this);
newRoot.children.add(sibling);

root = newRoot;
}
}

@Override
K getFirstLeafKey() {
return children.get(0).getFirstLeafKey();
}

@Override
List<V> getRange(K key1, RangePolicy policy1, K key2, RangePolicy policy2) {
return getChild(key1).getRange(key1, policy1, key2, policy2);
}

@Override
void merge(Node sibling) {

// Index nodes always merge index nodes, leaf nodes will never be passed in.

IndexNode node = (IndexNode) sibling;

keys.add(node.getFirstLeafKey());
keys.addAll(node.keys);

children.addAll(node.children);
}

@Override
Node split() {
int from = keyNumber() / 2 + 1, to = keyNumber();

IndexNode sibling = new IndexNode();

sibling.keys.addAll(keys.subList(from, to));
sibling.children.addAll(children.subList(from, to + 1));

keys.subList(from - 1, to).clear();
children.subList(from, to + 1).clear();

return sibling;
}

@Override
boolean isOverflow() {
return children.size() > branchingFactor;
}

@Override
boolean isUnderflow() {
return children.size() < (branchingFactor + 1) / 2;
}

Node getChild(K key) {
int loc = Collections.binarySearch(keys, key);

int childIndex = loc >= 0 ? loc + 1 : -loc - 1;

return children.get(childIndex);
}

void deleteChild(K key) {
int loc = Collections.binarySearch(keys, key);

// 404, return directly
if (loc < 0) {
return;
}

keys.remove(loc);
children.remove(loc + 1);
}

void insertChild(K key, Node child) {
// child is the newly created node, key is the first node key of the child node
int loc = Collections.binarySearch(keys, key);

int childIndex = loc >= 0 ? loc + 1 : -loc - 1;

// index already exists, update it
if (loc >= 0) {
children.set(childIndex, child);
}
// index not exits, create one as a reference to the child node
else {

// For index node, children node is always 1 more than keys
// But leaf nodes are aways of same size about keys and values.

keys.add(childIndex, key);
children.add(childIndex + 1, child);
}
}

Node getChildLeftSibling(K key) {

// two children related with a single index key, < the key is the left child, >= the key is the right child.

// loc >= 0 means found, the position next to it is the insertion point.
// loc < 0 means not found, -loc-1 is the insertion point
int loc = Collections.binarySearch(keys, key);

// 4 situations

// 1. key in keys, then loc >= 0
// 2. key < keys.get(0), then loc = -1
// 3. key == keys.get(0), then loc = 0
// 4. key in range (keys.get(0), keys.get(size-1)], then 1<=loc<=size when key found, or -size-1<=loc<=-2 if not found

// key exits
if (loc >= 0) {
// children.get(loc)>= key and children.get(loc-1) < key, so it is the left sibling
return children.get(loc - 1);
}

// keyIndex == 0 means key < keys.get(0)
// keyIndex == 1 means keys.get(1) > key >= keys.get(0)

// key not exits, but the insertion point is not the head of the key list
if (loc < -1) {
// -loc-1 is the insertion point which is larger than given key, so return the left sibling of children.get(-loc-1)
return children.get(-loc - 2);
}

return null;
}

Node getChildRightSibling(K key) {

// see also above getChildLeftSibling()

int loc = Collections.binarySearch(keys, key);

int childIndex = loc >= 0 ? loc + 1 : -loc - 1;

// children.size = keys.size + 1

// childrenIndex == key.size() means values binding with given key is in children.get(childrenIndex+1)
// which is the right most node without any right sibling nodes.
if (childIndex < keyNumber()) {
return children.get(childIndex + 1);
}

return null;
}
}
}