001
002
003
004
005
006
007
008
009
010
011
012
013
014
015
016
017
018
019
020
021
022
023
024
025
026
027
028
029
030
031
032
033
034
035
036
037
038
039
040
041
042
043
044
045
046
047
048
049
050
051
052
053
054
055
056
057
058
059
060
061
062
063
064
065
066
067
068
069
070
071
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
090
091
092
093
094
095
096
097
098
099
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
package algs32;

import java.util.Scanner;
import stdlib.*;

// A Playground for binary trees

public class XBTree {
  static class BNode {
    public BNode (double item, BNode left, BNode right) {
      this.item = item;
      this.left = left;
      this.right = right;
    }
    public double item;
    public BNode left;
    public BNode right;
  }
  BNode root;

  // height/depth of empty tree is -1
  // height/depth of singleton tree is 0
  public int height () {
    //TODO
    return StdRandom.uniform (100);
  }
  public int depth () {
    //TODO
    return StdRandom.uniform (100);
  } 
  public int depthOfShallowestFive () {
    //TODO
    return StdRandom.uniform (100);
  }
  public int heightOfShortestFive () {
    //TODO
    return StdRandom.uniform (100);
  }

  // prefix with parenthesis
  public String toString () {
    StringBuilder sb = new StringBuilder ();
    toString (sb, root);
    return sb.toString ();
  }
  private static void toString (StringBuilder sb, BNode n) {
    if (n == null) {
      sb.append ("X ");     
    } else if (n.left == null && n.right == null) {
      sb.append (n.item);
      sb.append (" ");
    } else {
      sb.append ("( ");
      sb.append (n.item);
      sb.append (" ");
      toString (sb, n.left);      
      toString (sb, n.right);     
      sb.append (") ");
    }
  }
  public void toGraphviz (String filename) {
    GraphvizBuilder gb = new GraphvizBuilder ();
    toGraphviz (gb, null, root);
    gb.toFileUndirected (filename, "ordering=\"out\"");
  }
  private void toGraphviz (GraphvizBuilder gb, BNode parent, BNode n) {
    if (n == null) {
      gb.addNullEdge (parent);
      return;
    }
    gb.addLabeledNode (n, Double.toString (n.item));
    if (parent != null) gb.addEdge (parent, n);
    toGraphviz (gb, n, n.left);
    toGraphviz (gb, n, n.right);
  }

  public static XBTree randomTree (double chanceOfNull, int maxDepth) {
    XBTree result = new XBTree ();
    result.root = randomTreeHelper (chanceOfNull, maxDepth, 0);
    return result;
  }
  private static BNode randomTreeHelper (double chanceOfNull, int maxDepth, int depth) {
    if (depth > maxDepth || StdRandom.uniform () < chanceOfNull * depth) 
      return null;
    BNode left = randomTreeHelper (chanceOfNull, maxDepth, depth+1);
    BNode right = randomTreeHelper (chanceOfNull, maxDepth, depth+1);
    double val = StdRandom.uniform (10);
    return new BNode (val, left, right);
  }
  
  // Parses the following kinds of tree "T"
  // T ::= "X" -- empty
  // T ::= num -- a node with no children
  // T ::= ( num T T ) -- a node with children
  // For example: ( 0 ( 01 12 X ) 02 )
  public static XBTree from (String in) {
    Scanner sc = new Scanner (in);
    XBTree result = new XBTree ();
    result.root = ofHelper (sc);
    return result;
  }
  private static BNode ofHelper (Scanner sc) {
    BNode result = null;
    if (sc.hasNext ("X")) {     
      sc.next (); // gobble "X"
    }
    if (sc.hasNextDouble ()) {
      double val = sc.nextDouble ();
      result = new BNode (val, null, null);
    } else if (sc.hasNext ("\\(")) {
      sc.next (); // gobble "("
      double val = sc.nextDouble ();
      result = new BNode (val, null, null);
      result.left = ofHelper (sc);
      result.right = ofHelper (sc);
      sc.next ("\\)"); //gobble ")"
    } 
    return result;
  }
  private static int count = 0;
  private static void testHeightOfShortestFive (XBTree tree, int expected) {
    int actual = tree.heightOfShortestFive ();
    if (!DEBUG && expected != actual) {
      //if (!DEBUG && ((expected >= 0 && expected != actual) || (expected < 0 && actual > 0))) {
      count++;
      tree.toGraphviz ("error" + count + ".png");
      StdOut.format ("error%d.heightOfShortestFive: expected=%d, actual=%d\n", count, expected, actual);
    }
  }
  private static void testDepthOfShallowestFive (XBTree tree, int expected) {
    int actual = tree.depthOfShallowestFive ();
    if (!DEBUG && expected != actual) {
      count++;
      tree.toGraphviz ("error" + count + ".png");
      StdOut.format ("error%d.depthOfShallowestFive: expected=%d, actual=%d\n", count, expected, actual);
    }
  }
  
  public static boolean DEBUG = false;
  public static XBTree demoTree () {
    String sl = "( 0 ( 0 X ( 0 ( 0 X ( 0 X X ) ) X ) ) ( 0 X ( 0 X X ) ) )";
    String sr = "( 0 ( 0 ( 0 ( 0 X X ) ( 0 X X ) ) ( 0 X ( 0 ( 0 X X ) X ) ) ) ( 0 ( 0 X X ) X ) )";
    String s = "( 0 " + sl + " " + sr + " )";
    return XBTree.from (s);
  }
  public static void main (String[] args) {
    if (DEBUG) Trace.run (); 
    
    XBTree t0 = demoTree();     
    testDepthOfShallowestFive(t0, -1);
    t0.root.right.left.right.left.left.item = 5.0;
    testDepthOfShallowestFive(t0, 5);
    t0.root.left.left.left.left.left.item = 5.0;
    testDepthOfShallowestFive(t0, 5);
    t0.root.left.left.left.left.item = 5.0;
    testDepthOfShallowestFive(t0, 4);
    t0.root.right.left.right.item = 5.0;
    testDepthOfShallowestFive(t0, 3);
    t0.root.right.right.item = 5.0;
    testDepthOfShallowestFive(t0, 2);
    t0.root.left.item = 5.0;
    testDepthOfShallowestFive(t0, 1);
    t0.root.item = 5.0;
    testDepthOfShallowestFive(t0, 0);

    XBTree t1 = demoTree();     
    testHeightOfShortestFive(t1, -7);
    t1.root.item = 5.0;
    testHeightOfShortestFive(t1, 5);
    t1.root.left.item = 5.0;
    testHeightOfShortestFive(t1, 4);
    t1.root.right.item = 5.0;
    testHeightOfShortestFive(t1, 4);    
    t1.root.right.left.item = 5.0;
    testHeightOfShortestFive(t1, 3);
    t1.root.left.left.left.item = 5.0;
    testHeightOfShortestFive(t1, 2);
    t1.root.left.left.left.left.item = 5.0;
    testHeightOfShortestFive(t1, 1);
    t1.root.right.left.right.left.left.item = 5.0;
    testHeightOfShortestFive(t1, 0);
    StdOut.println ("Finished tests");
    
//    YBTree t2 = demoTree();     
//    t2.toGraphviz ("t2.png");   
//    StdOut.format ("t2: %s\n", t2);
//    StdOut.format ("%d = t2.depth()\n", t2.depth ());
//    StdOut.format ("%d = t2.height()\n", t2.height ());
//    StdOut.format ("%d = t2.depthOfShallowestFive()\n", t2.depthOfShallowestFive ());
//    StdOut.format ("%d = t2.heightOfShortestFive()\n", t2.heightOfShortestFive ());
//    
//    YBTree t3 = randomTree (0.10, 6);
//    t3.toGraphviz ("t3.png");
//    StdOut.format ("t3: %s\n", tree0);      
//    StdOut.format ("%d = t3.depth()\n", t3.depth ());
//    StdOut.format ("%d = t3.height()\n", t3.height ());
//    StdOut.format ("%d = t3.depthOfShallowestFive()\n", t3.depthOfShallowestFive ());
//    StdOut.format ("%d = t3.heightOfShortestFive()\n", t3.heightOfShortestFive ());
  }
}