// This class represents a binary search tree of integers
// A binary search tree is one that every value to the left of a value is less
// than it, and every value to the right is greater than it. Duplicates are not allowed.
public class IntSearchTree {
   private IntTreeNode overallRoot;

   // Constructs a tree with no numbers
   public IntSearchTree() {
      overallRoot = null;
   }

   // Returns true if the value is in this tree, false otherwise
   public boolean contains(int value) {
       return contains(overallRoot, value);
   }

   // Returns true if the given value is contained in the tree
   // rooted at the given root, false otherwise
   private boolean contains(IntTreeNode root, int value) {
       if (root == null) {
           return false;
       } else if (root.data == value) {
           return true;
       } else if (value < root.data) {
           return contains(root.left, value);
       } else { // value > root.data
           return contains(root.right, value);
       }
   }

   // pre: This is a binary search tree
   // post: Adds the value to the tree such that
   //       it maintains the binary search tree property
   public void add(int value) {
       overallRoot = add(overallRoot, value);
   }

   // pre: the subtree rooted at `root` is a binary search tree
   // post: adds the given value to the subtree rooted at
   //       `root` such that it preserves the binary search tree
   //       property
   private IntTreeNode add(IntTreeNode root, int value) {
       if (root == null) {
           root = new IntTreeNode(value);
       } else if (value < root.data) {
           root.left = add(root.left, value);
       } else if (value > root.data) {
           root.right = add(root.right, value);
       }
       return root;
   }

   /****   Don't do this or I'll cry  :'( ****/
   private void addNoXEqualsChangeX(IntTreeNode root, int value) {
       // this doesn't even work if overallRoot is null,
       // need to add a special case in the public method too :'(
       if (root.left == null && root.right == null) {
           if (value < root.data) {
               root.left = new IntTreeNode(value);
           } else if (value > root.data) {
               root.right = new IntTreeNode(value);
           }
       } else if (value < root.data) {
           if (root.left == null) {
               root.left = new IntTreeNode(value);
           } else {
               add(root.left, value);
           }
       } else if (value > root.data) {
           if (root.right == null) {
               root.right = new IntTreeNode(value);
           } else {
               add(root.right, value);
           }
       }
   }

   // prints the numbers in this tree in a in-order fashion.
   public void print() {
      print(overallRoot);
   }

   // prints the numbers of the subtree rooted at root
   // using a in-order traversal.
   private void print(IntTreeNode root) {
      if (root != null) {
         print(root.left);                  // print the left
         System.out.print(root.data + " "); // print yourself
         print(root.right);                 // print the right
      }
   }

   // Returns the number of numbers in this tree.
   public int size() {
      return size(overallRoot);
   }

   // Returns the number of nodes in the tree starting at root.
   private int size(IntTreeNode root) {
      if (root == null) {
         return 0;
      } else {
         int leftSize = size(root.left);
         int rightSize = size(root.right);
         return 1 + leftSize + rightSize;
      }
   }
}