
/*************************************************************************
 *  Compilation:  javac BST.java
 *  Execution:    java BST
 *  Dependencies: None
 *  Data files:   http://algs4.cs.princeton.edu/32bst/tinyST.txt  
 *
 *  A symbol table implemented with a binary search tree.
 * 
 *  % more tinyST.txt
 *  S E A R C H E X A M P L E
 *  
 *  % java BST < tinyST.txt
 *  A 8
 *  C 4
 *  E 12
 *  H 5
 *  L 11
 *  M 9
 *  P 10
 *  R 3
 *  S 0
 *  X 7
 *
 *************************************************************************/

import java.util.Scanner;
import java.util.LinkedList;
import java.util.Queue;

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 RuntimeException("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 RuntimeException("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; 
	} 

	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 LinkedList<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.add(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));
	}

	/*************************************************************************
	 *  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 static void main(String[] args) { 

		BST<String, Integer> st = new BST<String, Integer>();

		Scanner scan = new Scanner(System.in);
		int i = 0;

		while (scan.hasNext()) {
			String key = scan.next();
			st.put(key, i);
			i++;
		}

		for (String s : st.keys())
			System.out.println(s + " " + st.get(s));
	}
}

