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// Exercise 3.2.6 3.2.32 3.2.33 (Solution published at http://algs4.cs.princeton.edu/)
package algs32;
import stdlib.*;
import algs13.Queue;
/* ***********************************************************************
 *  Compilation:  javac BST.java
 *  Execution:    java BST
 *  Dependencies: StdIn.java StdOut.java
 *  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
 *
 *************************************************************************/
public class BST<K extends Comparable<? super K>, V> {
  private Node<K,V> root;             // root of BST

  private static class Node<K extends Comparable<? super K>,V> {
    public final K key;       // sorted by key
    public V val;             // associated data
    public Node<K,V> left, right;  // left and right subtrees
    public int N;             // number of nodes in subtree

    public Node(K key, V 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<K,V> 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(K key) {
    return get(key) != null;
  }

  // return value associated with the given key, or null if no such key exists
  public V get(K key) { return get(root, key); }
  private V get(Node<K,V> x, K 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(K key, V val) {
    if (val == null) { delete(key); return; }
    root = put(root, key, val);
    //assert check();
  }

  private Node<K,V> put(Node<K,V> x, K key, V 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 Error("Symbol table underflow");
    root = deleteMin(root);
    //assert check();
  }

  private Node<K,V> deleteMin(Node<K,V> 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 Error("Symbol table underflow");
    root = deleteMax(root);
    //assert check();
  }

  private Node<K,V> deleteMax(Node<K,V> 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(K key) {
    root = delete(root, key);
    //assert check();
  }

  private Node<K,V> delete(Node<K,V> x, K 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<K,V> 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 K min() {
    if (isEmpty()) return null;
    return min(root).key;
  }

  private Node<K,V> min(Node<K,V> x) {
    if (x.left == null) return x;
    else                return min(x.left);
  }

  public K max() {
    if (isEmpty()) return null;
    return max(root).key;
  }

  private Node<K,V> max(Node<K,V> x) {
    if (x.right == null) return x;
    else                 return max(x.right);
  }

  public K floor(K key) {
    Node<K,V> x = floor(root, key);
    if (x == null) return null;
    else return x.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;
  }

  public K ceiling(K key) {
    Node<K,V> x = ceiling(root, key);
    if (x == null) return null;
    else return x.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) {
      Node<K,V> t = ceiling(x.left, key);
      if (t != null) return t;
      else return x;
    }
    return ceiling(x.right, key);
  }

  /* *********************************************************************
   *  Rank and selection
   ***********************************************************************/
  public K select(int k) {
    if (k < 0 || k >= size())  return null;
    Node<K,V> x = select(root, k);
    return x.key;
  }

  // Return key of rank k.
  private Node<K,V> select(Node<K,V> 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(K key) {
    return rank(key, root);
  }

  // Number of keys in the subtree less than x.key.
  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.
   ***********************************************************************/
  public Iterable<K> keys() {
    Queue<K> q = new Queue<>();
    inOrder(root, q);
    return q;
  }

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

  public Iterable<K> keys(K lo, K hi) {
    Queue<K> queue = new Queue<>();
    inOrder(root, queue, lo, hi);
    return queue;
  }

  private void inOrder(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) inOrder(x.left, queue, lo, hi);
    if (cmplo <= 0 && cmphi >= 0) queue.enqueue(x.key);
    if (cmphi > 0) inOrder(x.right, queue, lo, 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);
  }


  // height of this BST (one-node tree has height 0)
  public int height() { return height(root); }
  private int height(Node<K,V> x) {
    if (x == null) return -1;
    return 1 + Math.max(height(x.left), height(x.right));
  }

  // level order traversal
  public Iterable<K> levelOrder() {
    Queue<K> 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.key);
      queue.enqueue(x.left);
      queue.enqueue(x.right);
    }
    return keys;
  }

  /* ***********************************************************************
   *  Check integrity of 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");
    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<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;
  }

  /* ***************************************************************************
   *  Visualization
   *****************************************************************************/
  public String toString() {
    StringBuilder sb = new StringBuilder();
    for (K key: levelOrder())
      sb.append (key + " ");
    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; }
    gb.addLabeledNode (n, n.key.toString ());
    if (parent != null) gb.addEdge (parent, n);
    toGraphviz (gb, n, n.left);
    toGraphviz (gb, n, n.right);
  }

  // You may modify "drawTree" if you wish
  public void drawTree() {
    if (root != null) {
      StdDraw.setPenColor (StdDraw.BLACK);
      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 = 10;
    StdDraw.text (x, y, n.key.toString ());
    StdDraw.setPenRadius (.007);
    if (n.left != null && depth != CUTOFF) {
      StdDraw.line (x-range, y-.08, x-.01, y-.01);
      drawTree (n.left, x-range, y-.1, range*.5, depth+1);
    }
    if (n.right != null && depth != CUTOFF) {
      StdDraw.line (x+range, y-.08, x+.01, y-.01);
      drawTree (n.right, x+range, y-.1, 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");

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