/******************************************************************************
 *  Compilation:  javac AVLTreeST.java
 *  Execution:    java AVLTreeST < input.txt
 *  Dependencies: StdIn.java StdOut.java  
 *  Data files:   http://algs4.cs.princeton.edu/33balanced/tinyST.txt  
 *    
 *  A symbol table implemented using an AVL tree.
 *
 *  % more tinyST.txt
 *  S E A R C H E X A M P L E
 *  
 *  % java AVLTreeST < tinyST.txt
 *  A 8
 *  C 4
 *  E 12
 *  H 5
 *  L 11
 *  M 9
 *  P 10
 *  R 3
 *  S 0
 *  X 7
 *
 ******************************************************************************/

package edu.princeton.cs.algs4;

import java.util.NoSuchElementException;

/**
 *  The <code>AVLTreeST</code> class represents an ordered symbol table of
 *  generic key-value pairs. It supports the usual <em>put</em>, <em>get</em>,
 *  <em>contains</em>, <em>delete</em>, <em>size</em>, and <em>is-empty</em>
 *  methods. It also provides ordered methods for finding the <em>minimum</em>,
 *  <em>maximum</em>, <em>floor</em>, and <em>ceiling</em>. It also provides a
 *  <em>keys</em> method for iterating over all of the keys. A symbol table
 *  implements the <em>associative array</em> 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</code>
 *  —setting the value associated with a key to <code>null</code> is
 *  equivalent to deleting the key from the symbol table.
 *  <p>
 *  This symbol table implementation uses internally an
 *  <a href="https://en.wikipedia.org/wiki/AVL_tree"> AVL tree </a> (Georgy
 *  Adelson-Velsky and Evgenii Landis' tree) which is a self-balancing BST.
 *  In an AVL tree, the heights of the two child subtrees of any
 *  node differ by at most one; if at any time they differ by more than one,
 *  rebalancing is done to restore this property.
 *  <p>
 *  This implementation requires that the key type implements the
 *  <code>Comparable</code> interface and calls the <code>compareTo()</code> and
 *  method to compare two keys. It does not call either <code>equals()</code> or
 *  <code>hashCode()</code>. The <em>put</em>, <em>get</em>, <em>contains</em>,
 *  <em>delete</em>, <em>minimum</em>, <em>maximum</em>, <em>ceiling</em>, and
 *  <em>floor</em> operations each take logarithmic time in the worst case. The
 *  <em>size</em>, and <em>is-empty</em> operations take constant time.
 *  Construction also takes constant time.
 * 
 *  For other implementations of the same API, see {@link ST}, {@link BinarySearchST},
 *  {@link SequentialSearchST}, {@link BST}, {@link RedBlackBST},
 *  {@link SeparateChainingHashST}, and {@link LinearProbingHashST}.
 * 
 *  @author Marcelo Silva
 */

public class AVLTreeST<Key extends Comparable<Key>, Value> {

    /**
     * The root node.
     */
    private Node root;

    /**
     * This class represents an inner node of the AVL tree.
     */
    private class Node {
        private Key key;    // the key
        private Value val;  // the associated value
        private int h;      // height of the subtree
        private int N;      // number of nodes in subtree
        private Node left;  // left subtree
        private Node right; // right subtree

        public Node(Key key, Value val, int h, int N) {
            this.key = key;
            this.val = val;
            this.N = N;
            this.h = h;
        }
    }

    /**
     * Initializes an empty symbol table.
     */
    public AVLTreeST() {
    }

    /**
     * Checks if the symbol table is empty.
     * 
     * @return <code>true</code> if the symbol table is empty.
     */
    public boolean isEmpty() {
        return root == null;
    }

    /**
     * Returns the number key-value pairs in the symbol table.
     * 
     * @return the number key-value pairs in the symbol table
     */
    public int size() {
        return size(root);
    }

    /**
     * Returns the number of nodes in the subtree.
     * 
     * @param x the subtree
     * 
     * @return the number of nodes in the subtree
     */
    private int size(Node x) {
        if (x == null) return 0;
        return x.N;
    }

    /**
     * Returns the height of the internal AVL tree. It is assumed that the
     * height of an empty tree is -1 and the height of a tree with just one node
     * is 0.
     * 
     * @return the height of the internal AVL tree
     */
    public int height() {
        return height(root);
    }

    /**
     * Returns the height of the subtree.
     * 
     * @param x the subtree
     * 
     * @return the height of the subtree.
     */
    private int height(Node x) {
        if (x == null) return -1;
        return x.h;
    }

    /**
     * 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</code> if the key is not in the
     *         symbol table
     * @throws NullPointerException if <code>key</code> is <code>null</code>
     */
    public Value get(Key key) {
        if (key == null) throw new NullPointerException("argument to get() is null");
        Node x = get(root, key);
        if (x == null) return null;
        return x.val;
    }

    /**
     * Returns value associated with the given key in the subtree or
     * <code>null</code> if no such key.
     * 
     * @param x the subtree
     * @param key the key
     * @return value associated with the given key in the subtree or
     *         <code>null</code> if no such key
     */
    private Node 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;
    }

    /**
     * Checks if the symbol table contains the given key.
     * 
     * @param key the key
     * @return <code>true</code> if the symbol table contains <code>key</code>
     *         and <code>false</code> otherwise
     * @throws NullPointerException if <code>key</code> is <code>null</code>
     */
    public boolean contains(Key key) {
        return get(key) != null;
    }

    /**
     * Inserts the specified key-value pair into the symbol table, overwriting
     * the old value with the new value if the symbol table already contains the
     * specified key. Deletes the specified key (and its associated value) from
     * this symbol table if the specified value is <code>null</code>.
     * 
     * @param key the key
     * @param val the value
     * @throws NullPointerException if <code>key</code> is <code>null</code>
     */
    public void put(Key key, Value val) {
        if (key == null) throw new NullPointerException("first argument to put() is null");
        if (val == null) {
            delete(key);
            return;
        }
        root = put(root, key, val);
        // assert check();
    }

    /**
     * Inserts the key-value pair in the subtree. It overrides the old value
     * with the new value if the symbol table already contains the specified key
     * and deletes the specified key (and its associated value) from this symbol
     * table if the specified value is <code>null</code>.
     * 
     * @param x the subtree
     * @param key the key
     * @param val the value
     * @return the subtree
     */
    private Node put(Node x, Key key, Value val) {
        if (x == null) return new Node(key, val, 0, 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;
            return x;
        }
        x.N = 1 + size(x.left) + size(x.right);
        x.h = 1 + Math.max(height(x.left), height(x.right));
        return balance(x);
    }

    /**
     * Restores the AVL tree property of the subtree.
     * 
     * @param x the subtree
     * @return the subtree with restored AVL property
     */
    private Node balance(Node x) {
        if (balanceFactor(x) < -1) {
            if (balanceFactor(x.right) > 0) {
                x.right = rotateRight(x.right);
            }
            x = rotateLeft(x);
        }
        else if (balanceFactor(x) > 1) {
            if (balanceFactor(x.left) < 0) {
                x.left = rotateLeft(x.left);
            }
            x = rotateRight(x);
        }
        return x;
    }

    /**
     * Returns the balance factor of the subtree. The balance factor is defined
     * as the difference in height of the left subtree and right subtree, in
     * this order. Therefore, a subtree with a balance factor of -1, 0 or 1 has
     * the AVL property since the heights of the two child subtrees differ by at
     * most one.
     * 
     * @param x the subtree
     * @return the balance factor of the subtree
     */
    private int balanceFactor(Node x) {
        return height(x.left) - height(x.right);
    }

    /**
     * Rotates the given subtree to the right.
     * 
     * @param x the subtree
     * @return the right rotated subtree
     */
    private Node rotateRight(Node x) {
        Node y = x.left;
        x.left = y.right;
        y.right = x;
        y.N = x.N;
        x.N = 1 + size(x.left) + size(x.right);
        x.h = 1 + Math.max(height(x.left), height(x.right));
        y.h = 1 + Math.max(height(y.left), height(y.right));
        return y;
    }

    /**
     * Rotates the given subtree to the left.
     * 
     * @param x the subtree
     * @return the left rotated subtree
     */
    private Node rotateLeft(Node x) {
        Node y = x.right;
        x.right = y.left;
        y.left = x;
        y.N = x.N;
        x.N = 1 + size(x.left) + size(x.right);
        x.h = 1 + Math.max(height(x.left), height(x.right));
        y.h = 1 + Math.max(height(y.left), height(y.right));
        return y;
    }

    /**
     * Removes the specified key and its associated value from the symbol table
     * (if the key is in the symbol table).
     * 
     * @param key the key
     * @throws NullPointerException if <code>key</code> is <code>null</code>
     */
    public void delete(Key key) {
        if (key == null) throw new NullPointerException("argument to delete() is null");
        if (!contains(key)) return;
        root = delete(root, key);
        // assert check();
    }

    /**
     * Removes the specified key and its associated value from the given
     * subtree.
     * 
     * @param x the subtree
     * @param key the key
     * @return the updated subtree
     */
    private Node delete(Node x, Key key) {
        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.left == null) {
                return x.right;
            }
            else if (x.right == null) {
                return x.left;
            }
            else {
                Node y = x;
                x = min(y.right);
                x.right = deleteMin(y.right);
                x.left = y.left;
            }
        }
        x.N = 1 + size(x.left) + size(x.right);
        x.h = 1 + Math.max(height(x.left), height(x.right));
        return balance(x);
    }

    /**
     * Removes the smallest key and associated value from the symbol table.
     * 
     * @throws NoSuchElementException if the symbol table is empty
     */
    public void deleteMin() {
        if (isEmpty()) throw new NoSuchElementException("called deleteMin() with empty symbol table");
        root = deleteMin(root);
    }

    /**
     * Removes the smallest key and associated value from the given subtree.
     * 
     * @param x the subtree
     * @return the updated subtree
     */
    private Node deleteMin(Node x) {
        if (x.left == null) return x.right;
        x.left = deleteMin(x.left);
        x.N = 1 + size(x.left) + size(x.right);
        x.h = 1 + Math.max(height(x.left), height(x.right));
        return balance(x);
    }

    /**
     * Removes the largest key and associated value from the symbol table.
     * 
     * @throws NoSuchElementException if the symbol table is empty
     */
    public void deleteMax() {
        if (isEmpty()) throw new NoSuchElementException("called deleteMax() with empty symbol table");
        root = deleteMax(root);
    }

    /**
     * Removes the largest key and associated value from the given subtree.
     * 
     * @param x the subtree
     * @return the updated subtree
     */
    private Node deleteMax(Node x) {
        if (x.right == null) return x.left;
        x.right = deleteMax(x.right);
        x.N = 1 + size(x.left) + size(x.right);
        x.h = 1 + Math.max(height(x.left), height(x.right));
        return balance(x);
    }

    /**
     * Returns the smallest key in the symbol table.
     * 
     * @return the smallest key in the symbol table
     * @throws NoSuchElementException if the symbol table is empty
     */
    public Key min() {
        if (isEmpty()) throw new NoSuchElementException("called min() with empty symbol table");
        return min(root).key;
    }

    /**
     * Returns the node with the smallest key in the subtree.
     * 
     * @param x the subtree
     * @return the node with the smallest key in the subtree
     */
    private Node min(Node x) {
        if (x.left == null) return x;
        return min(x.left);
    }

    /**
     * Returns the largest key in the symbol table.
     * 
     * @return the largest key in the symbol table
     * @throws NoSuchElementException if the symbol table is empty
     */
    public Key max() {
        if (isEmpty()) throw new NoSuchElementException("called max() with empty symbol table");
        return max(root).key;
    }

    /**
     * Returns the node with the largest key in the subtree.
     * 
     * @param x the subtree
     * @return the node with the largest key in the subtree
     */
    private Node max(Node x) {
        if (x.right == null) return x;
        return max(x.right);
    }

    /**
     * Returns the largest key in the symbol table less than or equal to
     * <code>key</code>.
     * 
     * @param key the key
     * @return the largest key in the symbol table less than or equal to
     *         <code>key</code>
     * @throws NoSuchElementException if the symbol table is empty
     * @throws NullPointerException if <code>key</code> is <code>null</code>
     */
    public Key floor(Key key) {
        if (key == null) throw new NullPointerException("argument to floor() is null");
        if (isEmpty()) throw new NoSuchElementException("called floor() with empty symbol table");
        Node x = floor(root, key);
        if (x == null) return null;
        else return x.key;
    }

    /**
     * Returns the node in the subtree with the largest key less than or equal
     * to the given key.
     * 
     * @param x the subtree
     * @param key the key
     * @return the node in the subtree with the largest key less than or equal
     *         to the given 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 y = floor(x.right, key);
        if (y != null) return y;
        else return x;
    }

    /**
     * Returns the smallest key in the symbol table greater than or equal to
     * <code>key</code>.
     * 
     * @param key the key
     * @return the smallest key in the symbol table greater than or equal to
     *         <code>key</code>
     * @throws NoSuchElementException if the symbol table is empty
     * @throws NullPointerException if <code>key</code> is <code>null</code>
     */
    public Key ceiling(Key key) {
        if (key == null) throw new NullPointerException("argument to ceiling() is null");
        if (isEmpty()) throw new NoSuchElementException("called ceiling() with empty symbol table");
        Node x = ceiling(root, key);
        if (x == null) return null;
        else return x.key;
    }

    /**
     * Returns the node in the subtree with the smallest key greater than or
     * equal to the given key.
     * 
     * @param x the subtree
     * @param key the key
     * @return the node in the subtree with the smallest key greater than or
     *         equal to the given 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) return ceiling(x.right, key);
        Node y = ceiling(x.left, key);
        if (y != null) return y;
        else return x;
    }

    /**
     * Returns the kth smallest key in the symbol table.
     * 
     * @param k the order statistic
     * @return the kth smallest key in the symbol table
     * @throws IllegalArgumentException unless <code>k</code> is between 0 and
     *             <code> size() -1 </code>
     */
    public Key select(int k) {
        if (k < 0 || k >= size()) throw new IllegalArgumentException("k is not in range 0-" + (size() - 1));
        Node x = select(root, k);
        return x.key;
    }

    /**
     * Returns the node with key the kth smallest key in the subtree.
     * 
     * @param x the subtree
     * @param k the kth smallest key in the subtree
     * @return the node with key the kth smallest key in the subtree
     */
    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;
    }

    /**
     * Returns the number of keys in the symbol table strictly less than
     * <code>key</code>.
     * 
     * @param key the key
     * @return the number of keys in the symbol table strictly less than
     *         <code>key</code>
     * @throws NullPointerException if <code>key</code> is <code>null</code>
     */
    public int rank(Key key) {
        if (key == null) throw new NullPointerException("argument to rank() is null");
        return rank(key, root);
    }

    /**
     * Returns the number of keys in the subtree less than key.
     * 
     * @param key the key
     * @param x the subtree
     * @return the 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);
    }

    /**
     * Returns all keys in the symbol table.
     * 
     * @return all keys in the symbol table
     */
    public Iterable<Key> keys() {
        return keysInOrder();
    }

    /**
     * Returns all keys in the symbol table following an in-order traversal.
     * 
     * @return all keys in the symbol table following an in-order traversal
     */
    public Iterable<Key> keysInOrder() {
        Queue<Key> queue = new Queue<Key>();
        keysInOrder(root, queue);
        return queue;
    }

    /**
     * Adds the keys in the subtree to queue following an in-order traversal.
     * 
     * @param x the subtree
     * @param queue the queue
     */
    private void keysInOrder(Node x, Queue<Key> queue) {
        if (x == null) return;
        keysInOrder(x.left, queue);
        queue.enqueue(x.key);
        keysInOrder(x.right, queue);
    }

    /**
     * Returns all keys in the symbol table following a level-order traversal.
     * 
     * @return all keys in the symbol table following a level-order traversal.
     */
    public Iterable<Key> keysLevelOrder() {
        Queue<Key> queue = new Queue<Key>();
        if (!isEmpty()) {
            Queue<Node> queue2 = new Queue<Node>();
            queue2.enqueue(root);
            while (!queue2.isEmpty()) {
                Node x = queue2.dequeue();
                queue.enqueue(x.key);
                if (x.left != null) {
                    queue2.enqueue(x.left);
                }
                if (x.right != null) {
                    queue2.enqueue(x.right);
                }
            }
        }
        return queue;
    }

    /**
     * Returns all keys in the symbol table in the given range.
     * 
     * @param lo the lowest key
     * @param hi the highest key
     * @return all keys in the symbol table between <code>lo</code> (inclusive)
     *         and <code>hi</code> (exclusive)
     * @throws NullPointerException if either <code>lo</code> or <code>hi</code>
     *             is <code>null</code>
     */
    public Iterable<Key> keys(Key lo, Key hi) {
        if (lo == null) throw new NullPointerException("first argument to keys() is null");
        if (hi == null) throw new NullPointerException("second argument to keys() is null");
        Queue<Key> queue = new Queue<Key>();
        keys(root, queue, lo, hi);
        return queue;
    }

    /**
     * Adds the keys between <code>lo</code> and <code>hi</code> in the subtree
     * to the <code>queue</code>.
     * 
     * @param x the subtree
     * @param queue the queue
     * @param lo the lowest key
     * @param hi the highest key
     */
    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);
    }

    /**
     * Returns the number of keys in the symbol table in the given range.
     * 
     * @return the number of keys in the symbol table between <code>lo</code>
     *         (inclusive) and <code>hi</code> (exclusive)
     * @throws NullPointerException if either <code>lo</code> or <code>hi</code>
     *             is <code>null</code>
     */
    public int size(Key lo, Key hi) {
        if (lo == null) throw new NullPointerException("first argument to size() is null");
        if (hi == null) throw new NullPointerException("second argument to size() is null");
        if (lo.compareTo(hi) > 0) return 0;
        if (contains(hi)) return rank(hi) - rank(lo) + 1;
        else return rank(hi) - rank(lo);
    }

    /**
     * Checks if the AVL tree invariants are fine.
     * 
     * @return <code>true</code> if the AVL tree invariants are fine
     */
    private boolean check() {
        if (!isBST()) StdOut.println("Symmetric order not consistent");
        if (!isAVL()) StdOut.println("AVL property not consistent");
        if (!isSizeConsistent()) StdOut.println("Subtree counts not consistent");
        if (!isRankConsistent()) StdOut.println("Ranks not consistent");
        return isBST() && isAVL() && isSizeConsistent() && isRankConsistent();
    }

    /**
     * Checks if AVL property is consistent.
     * 
     * @return <code>true</code> if AVL property is consistent.
     */
    private boolean isAVL() {
        return isAVL(root);
    }

    /**
     * Checks if AVL property is consistent in the subtree.
     * 
     * @param x the subtree
     * @return <code>true</code> if AVL property is consistent in the subtree
     */
    private boolean isAVL(Node x) {
        if (x == null) return true;
        int bf = balanceFactor(x);
        if (bf > 1 || bf < -1) return false;
        return isAVL(x.left) && isAVL(x.right);
    }

    /**
     * Checks if the symmetric order is consistent.
     * 
     * @return <code>true</code> if the symmetric order is consistent
     */
    private boolean isBST() {
        return isBST(root, null, null);
    }

    /**
     * Checks if the tree rooted at x is 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
     * 
     * @param x the subtree
     * @param min the minimum key in subtree
     * @param max the maximum key in subtree
     * @return <code>true</code> if if the symmetric order is consistent
     */
    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);
    }

    /**
     * Checks if size is consistent.
     * 
     * @return <code>true</code> if size is consistent
     */
    private boolean isSizeConsistent() {
        return isSizeConsistent(root);
    }

    /**
     * Checks if the size of the subtree is consistent.
     * 
     * @return <code>true</code> if the size of the subtree is consistent
     */
    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);
    }

    /**
     * Checks if rank is consistent.
     * 
     * @return <code>true</code> if rank is 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;
    }

    /**
     * Unit tests the <code>AVLTreeST</code> data type.
     */
    public static void main(String[] args) {
        AVLTreeST<String, Integer> st = new AVLTreeST<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));
        StdOut.println();
    }
}