/*************************************************************************
*
* Based on BST.java from Algorithms 4 by Sedgewick
*
*************************************************************************/
import java.util.NoSuchElementException;
public class BST<Key extends Comparable<Key>, Value>
{
private Node root; // root of BST
private class Node
{
private Key key; // sorted by key
private Value val; // associated data
private Node left, right; // left and right subtrees
private int N; // number of nodes in subtree
public Node(Key key, Value val, int N)
{
this.key = key;
this.val = val;
this.N = N;
}
}
// is the symbol table empty?
public boolean isEmpty()
{
return size() == 0;
}
// return number of key-value pairs in BST
public int size()
{
return size(root);
}
// return number of key-value pairs in BST rooted at x
private int size(Node x)
{
if (x == null)
return 0;
else
return x.N;
}
/***********************************************************************
* Search BST for given key, and return associated value if found, return
* null if not found
***********************************************************************/
// does there exist a key-value pair with given key?
public boolean contains(Key key)
{
return get(key) != null;
}
// return value associated with the given key, or null if no such key exists
public Value get(Key key)
{
return get(root, key);
}
private Value get(Node x, Key key)
{
if (x == null)
return null;
int cmp = key.compareTo(x.key);
if (cmp < 0)
return get(x.left, key);
else if (cmp > 0)
return get(x.right, key);
else
return x.val;
}
/***********************************************************************
* Insert key-value pair into BST If key already exists, update with new
* value
***********************************************************************/
public void put(Key key, Value val)
{
if (val == null)
{
delete(key);
return;
}
root = put(root, key, val);
assert check();
}
private Node put(Node x, Key key, Value val)
{
if (x == null)
return new Node(key, val, 1);
int cmp = key.compareTo(x.key);
if (cmp < 0)
x.left = put(x.left, key, val);
else if (cmp > 0)
x.right = put(x.right, key, val);
else
x.val = val;
x.N = 1 + size(x.left) + size(x.right);
return x;
}
/***********************************************************************
* Delete
***********************************************************************/
public void deleteMin()
{
if (isEmpty())
throw new NoSuchElementException("Symbol table underflow");
root = deleteMin(root);
assert check();
}
private Node deleteMin(Node x)
{
if (x.left == null)
return x.right;
x.left = deleteMin(x.left);
x.N = size(x.left) + size(x.right) + 1;
return x;
}
public void deleteMax()
{
if (isEmpty())
throw new NoSuchElementException("Symbol table underflow");
root = deleteMax(root);
assert check();
}
private Node deleteMax(Node x)
{
if (x.right == null)
return x.left;
x.right = deleteMax(x.right);
x.N = size(x.left) + size(x.right) + 1;
return x;
}
public void delete(Key key)
{
root = delete(root, key);
assert check();
}
private Node delete(Node x, Key key)
{
if (x == null)
return null;
int cmp = key.compareTo(x.key);
if (cmp < 0)
x.left = delete(x.left, key);
else if (cmp > 0)
x.right = delete(x.right, key);
else
{
if (x.right == null)
return x.left;
if (x.left == null)
return x.right;
Node t = x;
x = min(t.right);
x.right = deleteMin(t.right);
x.left = t.left;
}
x.N = size(x.left) + size(x.right) + 1;
return x;
}
/***********************************************************************
* Min, max, floor, and ceiling
***********************************************************************/
public Key min()
{
if (isEmpty())
return null;
return min(root).key;
}
private Node min(Node x)
{
if (x.left == null)
return x;
else
return min(x.left);
}
public Key max()
{
if (isEmpty())
return null;
return max(root).key;
}
private Node max(Node x)
{
if (x.right == null)
return x;
else
return max(x.right);
}
public Key floor(Key key)
{
Node x = floor(root, key);
if (x == null)
return null;
else
return x.key;
}
private Node floor(Node x, Key key)
{
if (x == null)
return null;
int cmp = key.compareTo(x.key);
if (cmp == 0)
return x;
if (cmp < 0)
return floor(x.left, key);
Node t = floor(x.right, key);
if (t != null)
return t;
else
return x;
}
/***********************************************************************
* Rank and selection
***********************************************************************/
public Key select(int k)
{
if (k < 0 || k >= size())
return null;
Node x = select(root, k);
return x.key;
}
// Return key of rank k.
private Node select(Node x, int k)
{
if (x == null)
return null;
int t = size(x.left);
if (t > k)
return select(x.left, k);
else if (t < k)
return select(x.right, k - t - 1);
else
return x;
}
public int rank(Key key)
{
return rank(key, root);
}
// Number of keys in the subtree less than key.
private int rank(Key key, Node x)
{
if (x == null)
return 0;
int cmp = key.compareTo(x.key);
if (cmp < 0)
return rank(key, x.left);
else if (cmp > 0)
return 1 + size(x.left) + rank(key, x.right);
else
return size(x.left);
}
/***********************************************************************
* Range count and range search.
***********************************************************************/
public Iterable<Key> keys()
{
return keys(min(), max());
}
public Iterable<Key> keys(Key lo, Key hi)
{
Queue<Key> queue = new Queue<Key>();
keys(root, queue, lo, hi);
return queue;
}
private void keys(Node x, Queue<Key> queue, Key lo, Key hi)
{
if (x == null)
return;
int cmplo = lo.compareTo(x.key);
int cmphi = hi.compareTo(x.key);
if (cmplo < 0)
keys(x.left, queue, lo, hi);
if (cmplo <= 0 && cmphi >= 0)
queue.enqueue(x.key);
if (cmphi > 0)
keys(x.right, queue, lo, hi);
}
public int size(Key lo, Key hi)
{
if (lo.compareTo(hi) > 0)
return 0;
if (contains(hi))
return rank(hi) - rank(lo) + 1;
else
return rank(hi) - rank(lo);
}
// height of this BST (one-node tree has height 0)
public int height()
{
return height(root);
}
private int height(Node x)
{
if (x == null)
return -1;
return 1 + Math.max(height(x.left), height(x.right));
}
// level order traversal
public Iterable<Key> levelOrder()
{
Queue<Key> keys = new Queue<Key>();
Queue<Node> queue = new Queue<Node>();
queue.enqueue(root);
while (!queue.isEmpty())
{
Node x = queue.dequeue();
if (x == null)
continue;
keys.enqueue(x.key);
queue.enqueue(x.left);
queue.enqueue(x.right);
}
return keys;
}
/*************************************************************************
* Check integrity of BST data structure
*************************************************************************/
private boolean check()
{
if (!isBST())
System.out.println("Not in symmetric order");
if (!isSizeConsistent())
System.out.println("Subtree counts not consistent");
if (!isRankConsistent())
System.out.println("Ranks not consistent");
return isBST() && isSizeConsistent() && isRankConsistent();
}
// does this binary tree satisfy symmetric order?
// Note: this test also ensures that data structure is a binary tree since
// order is strict
private boolean isBST()
{
return isBST(root, null, null);
}
// is the tree rooted at x a BST with all keys strictly between min and max
// (if min or max is null, treat as empty constraint)
// Credit: Bob Dondero's elegant solution
private boolean isBST(Node x, Key min, Key max)
{
if (x == null)
return true;
if (min != null && x.key.compareTo(min) <= 0)
return false;
if (max != null && x.key.compareTo(max) >= 0)
return false;
return isBST(x.left, min, x.key) && isBST(x.right, x.key, max);
}
// are the size fields correct?
private boolean isSizeConsistent()
{
return isSizeConsistent(root);
}
private boolean isSizeConsistent(Node x)
{
if (x == null)
return true;
if (x.N != size(x.left) + size(x.right) + 1)
return false;
return isSizeConsistent(x.left) && isSizeConsistent(x.right);
}
// check that ranks are consistent
private boolean isRankConsistent()
{
for (int i = 0; i < size(); i++)
if (i != rank(select(i)))
return false;
for (Key key : keys())
if (key.compareTo(select(rank(key))) != 0)
return false;
return true;
}
public Iterable<Key> postOrder()
{
Queue<Key> keys = new Queue<Key>();
postOrder(root, keys);
return keys;
}
public void postOrder(Node root, Queue<Key> keys)
{
if(root == null)
return;
postOrder(root.left,keys);
postOrder(root.right,keys);
keys.enqueue(root.key);
}
public Iterable<Key> inOrder()
{
Queue<Key> keys = new Queue<Key>();
inOrder(root, keys);
return keys;
}
public void inOrder(Node root, Queue<Key> keys)
{
if(root == null)
return;
inOrder(root.left,keys);
keys.enqueue(root.key);
inOrder(root.right,keys);
}
public Iterable<Key> preOrder()
{
Queue<Key> keys = new Queue<Key>();
preOrder(root, keys);
return keys;
}
public void preOrder(Node root, Queue<Key> keys)
{
if(root == null)
return;
keys.enqueue(root.key);
preOrder(root.left,keys);
preOrder(root.right,keys);
}
}