package algs33;
import stdlib.*;
import algs13.Queue;
/* ***********************************************************************
 *  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<K extends Comparable<? super K>, V> {

  private static final boolean RED   = true;
  private static final boolean BLACK = false;

  private Node<K,V> root;     // root of the BST

  // BST helper node data type
  private static class Node<K,V> {
    public K key;         // key
    public V val;         // associated data
    public Node<K,V> left, right;  // links to left and right subtrees
    public boolean color;     // color of parent link
    public int N;             // subtree count

    public Node(K key, V val, boolean color, int N) {
      this.key = key;
      this.val = val;
      this.color = color;
      this.N = N;
    }
  }

  /* ***********************************************************************
   *  Node<K,V> helper methods
   *************************************************************************/
  // is node x red; false if x is null ?
  private boolean isRed(Node<K,V> 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<K,V> 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 V get(K key) { return get(root, key); }

  // value associated with the given key in subtree rooted at x; null if no such key
  private V get(Node<K,V> x, K 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(K 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<K,V> x, K 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(K key, V val) {
    root = put(root, key, val);
    root.color = BLACK;
    assert check();
  }

  // insert the key-value pair in the subtree rooted at h
  private Node<K,V> put(Node<K,V> h, K key, V 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 Error("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<K,V> deleteMin(Node<K,V> 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 Error("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<K,V> deleteMax(Node<K,V> 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(K 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<K,V> delete(Node<K,V> h, K 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<K,V> rotateRight(Node<K,V> h) {
    assert (h != null) && isRed(h.left);
    Node<K,V> 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<K,V> rotateLeft(Node<K,V> h) {
    assert (h != null) && isRed(h.right);
    Node<K,V> 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<K,V> 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<K,V> moveRedLeft(Node<K,V> 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<K,V> moveRedRight(Node<K,V> 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<K,V> balance(Node<K,V> 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<K,V> 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 K min() {
    if (isEmpty()) return null;
    return min(root).key;
  }

  // the smallest key in subtree rooted at x; null if no such key
  private Node<K,V> min(Node<K,V> x) {
    assert x != null;
    if (x.left == null) return x;
    else                return min(x.left);
  }

  // the largest key; null if no such key
  public K 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<K,V> max(Node<K,V> 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 K floor(K key) {
    Node<K,V> 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<K,V> floor(Node<K,V> x, K 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<K,V> 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 K ceiling(K key) {
    Node<K,V> 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<K,V> ceiling(Node<K,V> x, K 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<K,V> t = ceiling(x.left, key);
    if (t != null) return t;
    else           return x;
  }


  // the key of rank k
  public K select(int k) {
    if (k < 0 || k >= size())  return null;
    Node<K,V> x = select(root, k);
    return x.key;
  }

  // the key of rank k in the subtree rooted at x
  private Node<K,V> select(Node<K,V> 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(K key) {
    return rank(key, root);
  }

  // number of keys less than key in the subtree rooted at x
  private int rank(K key, Node<K,V> 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<K> keys() {
    return keys(min(), max());
  }

  // the keys between lo and hi, as an Iterable
  public Iterable<K> keys(K lo, K hi) {
    Queue<K> queue = new Queue<>();
    // 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<K,V> x, Queue<K> queue, K lo, K 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(K lo, K 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.format("Not in symmetric order: %s\n", this);
    if (!isSizeConsistent()) StdOut.format("Subtree counts not consistent: %s\n", this);
    if (!isRankConsistent()) StdOut.format("Ranks not consistent: %s\n", this);
    if (!is23())             StdOut.format("Not a 2-3 tree: %s\n", this);
    if (!isBalanced())       StdOut.format("Not balanced: %s\n", this);
    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<K,V> x, K min, K 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<K,V> 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 (K 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<K,V> 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<K,V> 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<K,V> x, int black) {
    if (x == null) return black == 0;
    if (!isRed(x)) black--;
    return isBalanced(x.left, black) && isBalanced(x.right, black);
  }

  /* ***************************************************************************
   *  Visualization
   *****************************************************************************/
  private Iterable<Node<K,V>> levelOrderNodes() {
    Queue<Node<K,V>> keys = new Queue<>();
    Queue<Node<K,V>> queue = new Queue<>();
    queue.enqueue(root);
    while (!queue.isEmpty()) {
      Node<K,V> x = queue.dequeue();
      if (x == null) continue;
      keys.enqueue(x);
      queue.enqueue(x.left);
      queue.enqueue(x.right);
    }
    return keys;
  }

  public String toString() {
    StringBuilder sb = new StringBuilder();
    for (Node<K,V> n: levelOrderNodes())
      sb.append (n.key + (n.color ? "* " : " "));
    return sb.toString ();
  }

  public void toGraphviz(String filename) {
    GraphvizBuilder gb = new GraphvizBuilder ();
    toGraphviz (gb, null, root);
    gb.toFileUndirected (filename, "ordering=\"out\"");
  }
  private void toGraphviz (GraphvizBuilder gb, Node<K, V> parent, Node<K, V> n) {
    if (n == null) { gb.addNullEdge (parent); return; }
    String nodeProperties = n.color ? "color=\"red\"" : "";
    String edgeProperties = n.color ? "color=\"red\",style=\"bold\"" : "";
    gb.addLabeledNode (n, n.key.toString (), nodeProperties);
    if (parent != null) gb.addEdge (parent, n, edgeProperties);
    toGraphviz (gb, n, n.left);
    toGraphviz (gb, n, n.right);
  }

  public void drawTree() {
    if (root != null) {
      StdDraw.setCanvasSize(1200,700);
      drawTree(root, .5, 1, .25, 0);
    }
  }
  private void drawTree (Node<K,V> n, double x, double y, double range, int depth) {
    int CUTOFF = 5;
    StdDraw.setPenColor (StdDraw.BLACK);
    StdDraw.text (x, y, n.key.toString ());
    StdDraw.setPenRadius (.005);
    if (n.left != null && depth != CUTOFF) {
      if (n.left.color == RED) {
        StdDraw.setPenRadius (.01);
        StdDraw.setPenColor (StdDraw.RED);
      }
      StdDraw.line (x-range, y-.13, x-.01, y-.01);
      drawTree (n.left, x-range, y-.15, range*.5, depth+1);
    }
    if (n.right != null && depth != CUTOFF) {
      StdDraw.line (x+range, y-.13, x+.01, y-.01);
      drawTree (n.right, x+range, y-.15, range*.5, depth+1);
    }
  }
  /* ***************************************************************************
   *  Test client
   *****************************************************************************/
  public static void main(String[] args) {
    StdIn.fromString ("S E A R C H E X A M P L E");
    //StdIn.fromString ("D F B  G E A C");

    RedBlackBST<String, Integer> st = new RedBlackBST<>();
    for (int i = 0; !StdIn.isEmpty(); i++) {
      String key = StdIn.readString();
      st.put(key, i);
    }
    st.toGraphviz ("g.png");
    for (String s : st.keys())
      StdOut.println(s + " " + st.get(s));
    st.drawTree ();
  }
}