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 isBST();
}
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 RuntimeException("Symbol table underflow");
root = deleteMin(root);
assert isBST();
}
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 RuntimeException("Symbol table underflow");
root = deleteMax(root);
assert isBST();
}
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 isBST();
}
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;
}
public Key ceiling(Key key) {
Node x = ceiling(root, key);
if (x == null) return null;
else return x.key;
}
private Node ceiling(Node x, Key key) {
if (x == null) return null;
int cmp = key.compareTo(x.key);
if (cmp == 0) return x;
if (cmp < 0) {
Node t = ceiling(x.left, key);
if (t != null) return t;
else return x;
}
return ceiling(x.right, key);
}
/***********************************************************************
* 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 x.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);
}
/*************************************************************************
* Check integrity of BST
*************************************************************************/
// is this tree a BST?
private boolean isBST() {
if (isEmpty()) return true;
if (!isBinaryTree()) StdOut.println("Subtree counts not consistent");
if (!isOrdered()) StdOut.println("Not in symmetric order");
if (!hasNoDuplicates()) StdOut.println("Has duplicate keys");
if (!isRankConsistent()) StdOut.println("Rank not consistent");
return isBinaryTree() && isOrdered() && hasNoDuplicates() && isRankConsistent();
}
// are the size fields correct (and consequently is it a binary tree)
private boolean isBinaryTree() { return isBinaryTree(root); }
private boolean isBinaryTree(Node x) {
if (x == null) return true;
if (x.N != size(x.left) + size(x.right) + 1) return false;
return isBinaryTree(x.left) && isBinaryTree(x.right);
}
// does this binary tree satisfy symmetric order?
private boolean isOrdered() {
assert isBinaryTree();
return isOrdered(root, min(), max());
}
// are all the values in the BST rooted at x between min and max, and recursively?
private boolean isOrdered(Node x, Key min, Key max) {
if (x == null) return true;
if (less(x.key, min) || less(max, x.key)) return false;
return isOrdered(x.left, min, x.key) && isOrdered(x.right, x.key, max);
}
// check that there are no duplicate keys
// precondition: inorder traversal gives keys in order
private boolean hasNoDuplicates() {
assert isOrdered();
for (int i = 1; i < size(); i++) {
if (select(i).compareTo(select(i-1)) == 0) return false;
}
return true;
}
// 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;
}
private boolean less(Key x, Key y) {
return x.compareTo(y) < 0;
}
/*****************************************************************************
* Test client
*****************************************************************************/
public static void main(String[] args) {
BST<String, Integer> st = new BST<String, Integer>();
for (int i = 0; !StdIn.isEmpty(); i++) {
String key = StdIn.readString();
st.put(key, i);
}
for (String s : st.keys())
StdOut.println(s + " " + st.get(s));
}
}
/*************************************************************************
* Execution: java BST
*
* A symbol table implemented with a binary search tree.
*
* % more tiny.txt
* S E A R C H E X A M P L E
*
* % java BST < tiny.txt
* A 8
* C 4
* E 12
* H 5
* L 11
* M 9
* P 10
* R 3
* S 0
* X 7
*
*************************************************************************/
Not Satisfied ? Just search & get the result
Related posts:
