package algs33;
import stdlib.*;
import algs13.Queue;
/* ***********************************************************************
 *  Compilation:  javac RedBlackLiteBST.java
 *  Execution:    java RedBlackLiteBST < 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.
 *
 *  This implementation implements only put, get, and contains.
 *  See RedBlackBST.java for a full implementation including delete.
 *
 *
 *  % more tinyST.txt
 *  S E A R C H E X A M P L E
 *
 *  % java RedBlackLiteBST < tinyST.txt
 *  A 8
 *  C 4
 *  E 12
 *  H 5
 *  L 11
 *  M 9
 *  P 10
 *  R 3
 *  S 0
 *  X 7
 *
 *************************************************************************/

public class XRedBlackLiteBST<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
  private int N;          // number of key-value pairs in BST

  // BST helper node data type
  private static class Node<K,V> {
    public final 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 Node(K key, V val, boolean color) {
      this.key = key;
      this.val = val;
      this.color = color;
    }
  }

  /* ***********************************************************************
   *  Standard BST search
   *************************************************************************/

  // return value associated with the given key, or null if no such key exists
  public V get(K key) { return get(root, key); }
  public 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 in the symbol table with the given key?
  public boolean contains(K key) {
    return (get(key) != null);
  }


  /* ***********************************************************************
   *  Red-black insertion
   *************************************************************************/

  public void put(K key, V val) {
    root = insert(root, key, val);
    root.color = BLACK;
    assert check();
  }

  private Node<K,V> insert(Node<K,V> h, K key, V val) {
    if (h == null) {
      N++;
      return new Node<>(key, val, RED);
    }

    int cmp = key.compareTo(h.key);
    if      (cmp < 0) h.left  = insert(h.left,  key, val);
    else if (cmp > 0) h.right = insert(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);

    return h;
  }

  /* ***********************************************************************
   *  red-black tree helper functions
   *************************************************************************/

  // is node x red (and non-null) ?
  private boolean isRed(Node<K,V> x) {
    if (x == null) return false;
    return (x.color == RED);
  }

  // rotate 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 = h.color;
    h.color = RED;
    return x;
  }

  // rotate 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 = h.color;
    h.color = RED;
    return x;
  }

  // precondition: two children are red, node is black
  // postcondition: two children are black, node is red
  private void flipColors(Node<K,V> h) {
    assert !isRed(h) && isRed(h.left) && isRed(h.right);
    h.color = RED;
    h.left.color = BLACK;
    h.right.color = BLACK;
  }


  /* ***********************************************************************
   *  Utility functions
   *************************************************************************/
  // return number of key-value pairs in symbol table
  public int size() { return N; }

  // is the symbol table empty?
  public boolean isEmpty() { return N == 0; }

  // height of tree (empty tree height = 0)
  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));
  }

  // return the smallest key; null if no such key
  public K min() { return min(root); }
  private K min(Node<K,V> x) {
    K key = null;
    while (x != null) {
      key = x.key;
      x = x.left;
    }
    return key;
  }

  // return the largest key; null if no such key
  public K max() { return max(root); }
  private K max(Node<K,V> x) {
    K key = null;
    while (x != null) {
      key = x.key;
      x = x.right;
    }
    return key;
  }


  /* *********************************************************************
   *  Iterate using an inorder traversal.
   *  Iterating through N elements takes O(N) time.
   ***********************************************************************/
  public Iterable<K> keys() {
    Queue<K> queue = new Queue<>();
    keys(root, queue);
    return queue;
  }

  private void keys(Node<K,V> x, Queue<K> queue) {
    if (x == null) return;
    keys(x.left, queue);
    queue.enqueue(x.key);
    keys(x.right, queue);
  }


  /* ***********************************************************************
   *  Check integrity of red-black BST data structure
   *************************************************************************/
  private boolean check() {
    if (!isBST())            StdOut.println("Not in symmetric order");
    if (!is23())             StdOut.println("Not a 2-3 tree");
    if (!isBalanced())       StdOut.println("Not balanced");
    return isBST() && 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);
  }

  // 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);
  }


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

    String test = "S E A R C H E X A M P L E";
    String[] keys = test.split(" ");
    XRedBlackLiteBST<String, Integer> st = new XRedBlackLiteBST<>();
    for (int i = 0; i < keys.length; i++)
      st.put(keys[i], i);

    StdOut.println("size = " + st.size());
    StdOut.println("min  = " + st.min());
    StdOut.println("max  = " + st.max());
    StdOut.println();


    // print keys in order using allKeys()
    StdOut.println("Testing keys()");
    StdOut.println("--------------------------------");
    for (String s : st.keys())
      StdOut.println(s + " " + st.get(s));
    StdOut.println();

    // insert N elements in order if one command-line argument supplied
    if (args.length == 0) return;
    int N = Integer.parseInt(args[0]);
    XRedBlackLiteBST<Integer, Integer> st2 = new XRedBlackLiteBST<>();
    for (int i = 0; i < N; i++) {
      st2.put(i, i);
      int h = st2.height();
      StdOut.println("i = " + i + ", height = " + h + ", size = " + st2.size());
    }


    StdOut.println("size = " + st2.size());
  }
}