/******************************************************************************
* Compilation: javac BTree.java
* Execution: java BTree
* Dependencies: StdOut.java
*
* B-tree.
*
* Limitations
* -----------
* - Assumes M is even and M >= 4
* - should b be an array of children or list (it would help with
* casting to make it a list)
*
******************************************************************************/
/**
* The {@code BTree} class represents an ordered symbol table of generic
* key-value pairs.
* It supports the put, get, contains,
* size, and is-empty methods.
* A symbol table implements the associative array abstraction:
* when associating a value with a key that is already in the symbol table,
* the convention is to replace the old value with the new value.
* Unlike {@link java.util.Map}, this class uses the convention that
* values cannot be {@code null}—setting the
* value associated with a key to {@code null} is equivalent to deleting the key
* from the symbol table.
*
* This implementation uses a B-tree. It requires that
* the key type implements the {@code Comparable} interface and calls the
* {@code compareTo()} and method to compare two keys. It does not call either
* {@code equals()} or {@code hashCode()}.
* The get, put, and contains operations
* each make logm(n) probes in the worst case,
* where n is the number of key-value pairs
* and m is the branching factor.
* The size, and is-empty operations take constant time.
* Construction takes constant time.
*
* For additional documentation, see
* Section 6.2 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*/
public class BTree, Value> {
// max children per B-tree node = M-1
// (must be even and greater than 2)
private static final int M = 4;
private Node root; // root of the B-tree
private int height; // height of the B-tree
private int n; // number of key-value pairs in the B-tree
// helper B-tree node data type
private static final class Node {
private int m; // number of children
private Entry[] children = new Entry[M]; // the array of children
// create a node with k children
private Node(int k) {
m = k;
}
}
// internal nodes: only use key and next
// external nodes: only use key and value
private static class Entry {
private Comparable key;
private Object val;
private Node next; // helper field to iterate over array entries
public Entry(Comparable key, Object val, Node next) {
this.key = key;
this.val = val;
this.next = next;
}
}
/**
* Initializes an empty B-tree.
*/
public BTree() {
root = new Node(0);
}
/**
* Returns true if this symbol table is empty.
* @return {@code true} if this symbol table is empty; {@code false} otherwise
*/
public boolean isEmpty() {
return size() == 0;
}
/**
* Returns the number of key-value pairs in this symbol table.
* @return the number of key-value pairs in this symbol table
*/
public int size() {
return n;
}
/**
* Returns the height of this B-tree (for debugging).
*
* @return the height of this B-tree
*/
public int height() {
return height;
}
/**
* Returns the value associated with the given key.
*
* @param key the key
* @return the value associated with the given key if the key is in the symbol table
* and {@code null} if the key is not in the symbol table
* @throws IllegalArgumentException if {@code key} is {@code null}
*/
public Value get(Key key) {
if (key == null) throw new IllegalArgumentException("argument to get() is null");
return search(root, key, height);
}
private Value search(Node x, Key key, int ht) {
Entry[] children = x.children;
// external node
if (ht == 0) {
for (int j = 0; j < x.m; j++) {
if (eq(key, children[j].key)) return (Value) children[j].val;
}
}
// internal node
else {
for (int j = 0; j < x.m; j++) {
if (j+1 == x.m || less(key, children[j+1].key))
return search(children[j].next, key, ht-1);
}
}
return null;
}
/**
* Inserts the key-value pair into the symbol table, overwriting the old value
* with the new value if the key is already in the symbol table.
* If the value is {@code null}, this effectively deletes the key from the symbol table.
*
* @param key the key
* @param val the value
* @throws IllegalArgumentException if {@code key} is {@code null}
*/
public void put(Key key, Value val) {
if (key == null) throw new IllegalArgumentException("argument key to put() is null");
Node u = insert(root, key, val, height);
n++;
if (u == null) return;
// need to split root
Node t = new Node(2);
t.children[0] = new Entry(root.children[0].key, null, root);
t.children[1] = new Entry(u.children[0].key, null, u);
root = t;
height++;
}
private Node insert(Node h, Key key, Value val, int ht) {
int j;
Entry t = new Entry(key, val, null);
// external node
if (ht == 0) {
for (j = 0; j < h.m; j++) {
if (less(key, h.children[j].key)) break;
}
}
// internal node
else {
for (j = 0; j < h.m; j++) {
if ((j+1 == h.m) || less(key, h.children[j+1].key)) {
Node u = insert(h.children[j++].next, key, val, ht-1);
if (u == null) return null;
t.key = u.children[0].key;
t.val = null;
t.next = u;
break;
}
}
}
for (int i = h.m; i > j; i--)
h.children[i] = h.children[i-1];
h.children[j] = t;
h.m++;
if (h.m < M) return null;
else return split(h);
}
// split node in half
private Node split(Node h) {
Node t = new Node(M/2);
h.m = M/2;
for (int j = 0; j < M/2; j++)
t.children[j] = h.children[M/2+j];
return t;
}
/**
* Returns a string representation of this B-tree (for debugging).
*
* @return a string representation of this B-tree.
*/
public String toString() {
return toString(root, height, "") + "\n";
}
private String toString(Node h, int ht, String indent) {
StringBuilder s = new StringBuilder();
Entry[] children = h.children;
if (ht == 0) {
for (int j = 0; j < h.m; j++) {
s.append(indent + children[j].key + " " + children[j].val + "\n");
}
}
else {
for (int j = 0; j < h.m; j++) {
if (j > 0) s.append(indent + "(" + children[j].key + ")\n");
s.append(toString(children[j].next, ht-1, indent + " "));
}
}
return s.toString();
}
// comparison functions - make Comparable instead of Key to avoid casts
private boolean less(Comparable k1, Comparable k2) {
return k1.compareTo(k2) < 0;
}
private boolean eq(Comparable k1, Comparable k2) {
return k1.compareTo(k2) == 0;
}
/**
* Unit tests the {@code BTree} data type.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
BTree st = new BTree();
st.put("www.cs.princeton.edu", "128.112.136.12");
st.put("www.cs.princeton.edu", "128.112.136.11");
st.put("www.princeton.edu", "128.112.128.15");
st.put("www.yale.edu", "130.132.143.21");
st.put("www.simpsons.com", "209.052.165.60");
st.put("www.apple.com", "17.112.152.32");
st.put("www.amazon.com", "207.171.182.16");
st.put("www.ebay.com", "66.135.192.87");
st.put("www.cnn.com", "64.236.16.20");
st.put("www.google.com", "216.239.41.99");
st.put("www.nytimes.com", "199.239.136.200");
st.put("www.microsoft.com", "207.126.99.140");
st.put("www.dell.com", "143.166.224.230");
st.put("www.slashdot.org", "66.35.250.151");
st.put("www.espn.com", "199.181.135.201");
st.put("www.weather.com", "63.111.66.11");
st.put("www.yahoo.com", "216.109.118.65");
StdOut.println("cs.princeton.edu: " + st.get("www.cs.princeton.edu"));
StdOut.println("hardvardsucks.com: " + st.get("www.harvardsucks.com"));
StdOut.println("simpsons.com: " + st.get("www.simpsons.com"));
StdOut.println("apple.com: " + st.get("www.apple.com"));
StdOut.println("ebay.com: " + st.get("www.ebay.com"));
StdOut.println("dell.com: " + st.get("www.dell.com"));
StdOut.println();
StdOut.println("size: " + st.size());
StdOut.println("height: " + st.height());
StdOut.println(st);
StdOut.println();
}
}