public class BTree<Key extends Comparable<Key>, 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 NullPointerException if {@code key} is {@code null}   */  public Value get(Key key)   {    if (key == null)     {      throw new NullPointerException("key must not be null");    }    return search(root, key, height);  }  @SuppressWarnings("unchecked")  private Value search(Node x, Key key, int ht)   {    Entry[] children = x.children;    // external node到最底層葉子結點，遍歷    if (ht == 0)     {      for (int j = 0; j < x.m; j++)             {        if (eq(key, children[j].key))         {          return (Value) children[j].val;        }      }    }    // internal node遞歸查找next地址    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 NullPointerException if {@code key} is {@code null}   */  public void put(Key key, Value val)   {    if (key == null)     {      throw new NullPointerException("key must not be null");    }    Node u = insert(root, key, val, height); //分裂后生成的右結點    n++;    if (u == null)     {      return;    }    // need to split root重組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外部結點，也是葉子結點，在樹的最底層，存的是內容value    if (ht == 0)     {      for (j = 0; j < h.m; j++)       {        if (less(key, h.children[j].key))         {          break;        }      }    }    // internal node內部結點，存的是next地址    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.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         {  //分裂結點      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<String, String> st = new BTree<String, String>();    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");    System.out.println("cs.princeton.edu: " + st.get("www.cs.princeton.edu"));    System.out.println("hardvardsucks.com: " + st.get("www.harvardsucks.com"));    System.out.println("simpsons.com:   " + st.get("www.simpsons.com"));    System.out.println("apple.com:     " + st.get("www.apple.com"));    System.out.println("ebay.com:     " + st.get("www.ebay.com"));    System.out.println("dell.com:     " + st.get("www.dell.com"));    System.out.println();    System.out.println("size:  " + st.size());    System.out.println("height: " + st.height());    System.out.println(st);    System.out.println();  }}