content: /*************************************************************************
   *  Compilation:  javac RedBlackBST.java
   *  Execution:    java RedBlackBST < input.txt
   *  Dependencies: StdIn.java StdOut.java  
   *  Data files:   http://algs4.cs.princeton.edu/33balanced/tinyST.txt  
   *    
   *  A symbol table implemented using a left-leaning red-black BST.
   *  This is the 2-3 version.
   *
   *  % more tinyST.txt
   *  S E A R C H E X A M P L E
   *  
   *  % java RedBlackBST < tinyST.txt
   *  A 8
   *  C 4
   *  E 12
   *  H 5
   *  L 11
   *  M 9
   *  P 10
   *  R 3
   *  S 0
   *  X 7
   *
   *************************************************************************/
  
  public class RedBlackBST<Key extends Comparable<Key>, Value> {
  
      private static final boolean RED   = true;
      private static final boolean BLACK = false;
  
      private Node root;     // root of the BST
  
      // BST helper node data type
      private class Node {
          private Key key;           // key
          private Value val;         // associated data
          private Node left, right;  // links to left and right subtrees
          private boolean color;     // color of parent link
          private int N;             // subtree count
  
          public Node(Key key, Value val, boolean color, int N) {
              this.key = key;
              this.val = val;
              this.color = color;
              this.N = N;
          }
      }
  
     /*************************************************************************
      *  Node helper methods
      *************************************************************************/
      // is node x red; false if x is null ?
      private boolean isRed(Node x) {
          if (x == null) return false;
          return (x.color == RED);
      }
  
      // number of node in subtree rooted at x; 0 if x is null
      private int size(Node x) {
          if (x == null) return 0;
          return x.N;
      } 
  
  
     /*************************************************************************
      *  Size methods
      *************************************************************************/
  
      // return number of key-value pairs in this symbol table
      public int size() { return size(root); }
  
      // is this symbol table empty?
      public boolean isEmpty() {
          return root == null;
      }
  
     /*************************************************************************
      *  Standard BST search
      *************************************************************************/
  
      // value associated with the given key; null if no such key
      public Value get(Key key) { return get(root, key); }
  
      // value associated with the given key in subtree rooted at x; null if no such key
      private Value get(Node x, Key key) {
          while (x != null) {
              int cmp = key.compareTo(x.key);
              if      (cmp < 0) x = x.left;
              else if (cmp > 0) x = x.right;
              else              return x.val;
          }
          return null;
      }
  
      // is there a key-value pair with the given key?
      public boolean contains(Key key) {
          return (get(key) != null);
      }
  
      // is there a key-value pair with the given key in the subtree rooted at x?
      private boolean contains(Node x, Key key) {
          return (get(x, key) != null);
      }
  
     /*************************************************************************
      *  Red-black insertion
      *************************************************************************/
  
      // insert the key-value pair; overwrite the old value with the new value
      // if the key is already present
      public void put(Key key, Value val) {
          root = put(root, key, val);
          root.color = BLACK;
          assert check();
      }
  
      // insert the key-value pair in the subtree rooted at h
      private Node put(Node h, Key key, Value val) { 
          if (h == null) return new Node(key, val, RED, 1);
  
          int cmp = key.compareTo(h.key);
          if      (cmp < 0) h.left  = put(h.left,  key, val); 
          else if (cmp > 0) h.right = put(h.right, key, val); 
          else              h.val   = val;
  
          // fix-up any right-leaning links
          if (isRed(h.right) && !isRed(h.left))      h = rotateLeft(h);
          if (isRed(h.left)  &&  isRed(h.left.left)) h = rotateRight(h);
          if (isRed(h.left)  &&  isRed(h.right))     flipColors(h);
          h.N = size(h.left) + size(h.right) + 1;
  
          return h;
      }
  
     /*************************************************************************
      *  Red-black deletion
      *************************************************************************/
  
      // delete the key-value pair with the minimum key
      public void deleteMin() {
          if (isEmpty()) throw new RuntimeException("BST underflow");
  
          // if both children of root are black, set root to red
          if (!isRed(root.left) && !isRed(root.right))
              root.color = RED;
  
          root = deleteMin(root);
          if (!isEmpty()) root.color = BLACK;
          assert check();
      }
  
      // delete the key-value pair with the minimum key rooted at h
      private Node deleteMin(Node h) { 
          if (h.left == null)
              return null;
  
          if (!isRed(h.left) && !isRed(h.left.left))
              h = moveRedLeft(h);
  
          h.left = deleteMin(h.left);
          return balance(h);
      }
  
  
      // delete the key-value pair with the maximum key
      public void deleteMax() {
          if (isEmpty()) throw new RuntimeException("BST underflow");
  
          // if both children of root are black, set root to red
          if (!isRed(root.left) && !isRed(root.right))
              root.color = RED;
  
          root = deleteMax(root);
          if (!isEmpty()) root.color = BLACK;
          assert check();
      }
  
      // delete the key-value pair with the maximum key rooted at h
      private Node deleteMax(Node h) { 
          if (isRed(h.left))
              h = rotateRight(h);
  
          if (h.right == null)
              return null;
  
          if (!isRed(h.right) && !isRed(h.right.left))
              h = moveRedRight(h);
  
          h.right = deleteMax(h.right);
  
          return balance(h);
      }
  
      // delete the key-value pair with the given key
      public void delete(Key key) { 
          if (!contains(key)) {
              System.err.println("symbol table does not contain " + key);
              return;
          }
  
          // if both children of root are black, set root to red
          if (!isRed(root.left) && !isRed(root.right))
              root.color = RED;
  
          root = delete(root, key);
          if (!isEmpty()) root.color = BLACK;
          assert check();
      }
  
      // delete the key-value pair with the given key rooted at h
      private Node delete(Node h, Key key) { 
          assert contains(h, key);
  
          if (key.compareTo(h.key) < 0)  {
              if (!isRed(h.left) && !isRed(h.left.left))
                  h = moveRedLeft(h);
              h.left = delete(h.left, key);
          }
          else {
              if (isRed(h.left))
                  h = rotateRight(h);
              if (key.compareTo(h.key) == 0 && (h.right == null))
                  return null;
              if (!isRed(h.right) && !isRed(h.right.left))
                  h = moveRedRight(h);
              if (key.compareTo(h.key) == 0) {
                  h.val = get(h.right, min(h.right).key);
                  h.key = min(h.right).key;
                  h.right = deleteMin(h.right);
              }
              else h.right = delete(h.right, key);
          }
          return balance(h);
      }
  
     /*************************************************************************
      *  red-black tree helper functions
      *************************************************************************/
  
      // make a left-leaning link lean to the right
      private Node rotateRight(Node h) {
          assert (h != null) && isRed(h.left);
          Node x = h.left;
          h.left = x.right;
          x.right = h;
          x.color = x.right.color;
          x.right.color = RED;
          x.N = h.N;
          h.N = size(h.left) + size(h.right) + 1;
          return x;
      }
  
      // make a right-leaning link lean to the left
      private Node rotateLeft(Node h) {
          assert (h != null) && isRed(h.right);
          Node x = h.right;
          h.right = x.left;
          x.left = h;
          x.color = x.left.color;
          x.left.color = RED;
          x.N = h.N;
          h.N = size(h.left) + size(h.right) + 1;
          return x;
      }
  
      // flip the colors of a node and its two children
      private void flipColors(Node h) {
          // h must have opposite color of its two children
          assert (h != null) && (h.left != null) && (h.right != null);
          assert (!isRed(h) &&  isRed(h.left) &&  isRed(h.right))
              || (isRed(h)  && !isRed(h.left) && !isRed(h.right));
          h.color = !h.color;
          h.left.color = !h.left.color;
          h.right.color = !h.right.color;
      }
  
      // Assuming that h is red and both h.left and h.left.left
      // are black, make h.left or one of its children red.
      private Node moveRedLeft(Node h) {
          assert (h != null);
          assert isRed(h) && !isRed(h.left) && !isRed(h.left.left);
  
          flipColors(h);
          if (isRed(h.right.left)) { 
              h.right = rotateRight(h.right);
              h = rotateLeft(h);
              // flipColors(h);
          }
          return h;
      }
  
      // Assuming that h is red and both h.right and h.right.left
      // are black, make h.right or one of its children red.
      private Node moveRedRight(Node h) {
          assert (h != null);
          assert isRed(h) && !isRed(h.right) && !isRed(h.right.left);
          flipColors(h);
          if (isRed(h.left.left)) { 
              h = rotateRight(h);
              // flipColors(h);
          }
          return h;
      }
  
      // restore red-black tree invariant
      private Node balance(Node h) {
          assert (h != null);
  
          if (isRed(h.right))                      h = rotateLeft(h);
          if (isRed(h.left) && isRed(h.left.left)) h = rotateRight(h);
          if (isRed(h.left) && isRed(h.right))     flipColors(h);
  
          h.N = size(h.left) + size(h.right) + 1;
          return h;
      }
  
  
     /*************************************************************************
      *  Utility functions
      *************************************************************************/
  
      // height of tree; 0 if empty
      public int height() { return height(root); }
      private int height(Node x) {
          if (x == null) return 0;
          return 1 + Math.max(height(x.left), height(x.right));
      }
  
     /*************************************************************************
      *  Ordered symbol table methods.
      *************************************************************************/
  
      // the smallest key; null if no such key
      public Key min() {
          if (isEmpty()) return null;
          return min(root).key;
      } 
  
      // the smallest key in subtree rooted at x; null if no such key
      private Node min(Node x) { 
          assert x != null;
          if (x.left == null) return x; 
          else                return min(x.left); 
      } 
  
      // the largest key; null if no such key
      public Key max() {
          if (isEmpty()) return null;
          return max(root).key;
      } 
  
      // the largest key in the subtree rooted at x; null if no such key
      private Node max(Node x) { 
          assert x != null;
          if (x.right == null) return x; 
          else                 return max(x.right); 
      } 
  
      // the largest key less than or equal to the given key
      public Key floor(Key key) {
          Node x = floor(root, key);
          if (x == null) return null;
          else           return x.key;
      }    
  
      // the largest key in the subtree rooted at x 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 t = floor(x.right, key);
          if (t != null) return t; 
          else           return x;
      }
  
      // the smallest key greater than or equal to the given key
      public Key ceiling(Key key) {  
          Node x = ceiling(root, key);
          if (x == null) return null;
          else           return x.key;  
      }
  
      // the smallest key in the subtree rooted at x 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 t = ceiling(x.left, key);
          if (t != null) return t; 
          else           return x;
      }
  
  
      // the key of rank k
      public Key select(int k) {
          if (k < 0 || k >= size())  return null;
          Node x = select(root, k);
          return x.key;
      }
  
      // the key of rank k in the subtree rooted at x
      private Node select(Node x, int k) {
          assert x != null;
          assert k >= 0 && k < size(x);
          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; 
      } 
  
      // number of keys less than key
      public int rank(Key key) {
          return rank(key, root);
      } 
  
      // number of keys less than key in the subtree rooted at x
      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.
      ***********************************************************************/
  
      // all of the keys, as an Iterable
      public Iterable<Key> keys() {
          return keys(min(), max());
      }
  
      // the keys between lo and hi, as an Iterable
      public Iterable<Key> keys(Key lo, Key hi) {
          Queue<Key> queue = new Queue<Key>();
          // if (isEmpty() || lo.compareTo(hi) > 0) return queue;
          keys(root, queue, lo, hi);
          return queue;
      } 
  
      // add the keys between lo and hi in the subtree rooted at x
      // to the 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); 
      } 
  
      // number keys between lo and 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 red-black BST data structure
      *************************************************************************/
      private boolean check() {
          if (!isBST())            StdOut.println("Not in symmetric order");
          if (!isSizeConsistent()) StdOut.println("Subtree counts not consistent");
          if (!isRankConsistent()) StdOut.println("Ranks not consistent");
          if (!is23())             StdOut.println("Not a 2-3 tree");
          if (!isBalanced())       StdOut.println("Not balanced");
          return isBST() && isSizeConsistent() && isRankConsistent() && is23() && isBalanced();
      }
  
      // 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;
      }
  
      // Does the tree have no red right links, and at most one (left)
      // red links in a row on any path?
      private boolean is23() { return is23(root); }
      private boolean is23(Node x) {
          if (x == null) return true;
          if (isRed(x.right)) return false;
          if (x != root && isRed(x) && isRed(x.left))
              return false;
          return is23(x.left) && is23(x.right);
      } 
  
      // do all paths from root to leaf have same number of black edges?
      private boolean isBalanced() { 
          int black = 0;     // number of black links on path from root to min
          Node x = root;
          while (x != null) {
              if (!isRed(x)) black++;
              x = x.left;
          }
          return isBalanced(root, black);
      }
  
      // does every path from the root to a leaf have the given number of black links?
      private boolean isBalanced(Node x, int black) {
          if (x == null) return black == 0;
          if (!isRed(x)) black--;
          return isBalanced(x.left, black) && isBalanced(x.right, black);
      } 
  
  
     /*****************************************************************************
      *  Test client
      *****************************************************************************/
      public static void main(String[] args) { 
          RedBlackBST<String, Integer> st = new RedBlackBST<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));
      }
  }
  