// Represents a set of elements. When accessed, elements
// will be returned in their "natural ordering".

import java.util.NoSuchElementException;

public class TreeIntSet implements IntSet {
	private TreeNode overallRoot;

	// Constructs an empty TreeSet
	public TreeIntSet() {
		overallRoot = null;
	}

	// Adds the given value to this TreeSet. Returns true if the set was modified
	// and false if the value was already contained in this set.
	public boolean add(int value) {
		if (contains(value)) {
			return false;
		}
		overallRoot = add(overallRoot, value);
		return true;
	}

	// Adds the given value to the BST starting at the given root.
	// Post: the tree is still a valid BST
	private TreeNode add(TreeNode root, int value) {
		if (root == null) {
			root = new TreeNode(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;
	}
	// Returns true if the value is in this set, false otherwise.
	public boolean contains(int value) {
		return contains(overallRoot, value);
	}

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

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

	// Returns the number of nodes in the subtree with root as its root node.
	private int size(TreeNode root) {
		if (root == null) {
			return 0;
		} else {
			return 1 + size(root.left) + size(root.right);
		}
	}

	// Returns true if there are no elements in this set, false
	// otherwise.
	public boolean isEmpty() {
		return size() == 0;
	}

	// Removes the given value to this TreeSet. Returns true if the set was modified
	// and false if the value was not contained in this set.
	public boolean remove(int value) {
		if (!contains(value)) {
			return false;
		}
		overallRoot = remove(overallRoot, value);
		return true;
	}

	// Removes the given value from the BST starting at the given root.
    // Post: The tree is still a valid BST
    private IntTreeNode remove(IntTreeNode root, int value) {
       if (root != null) {
          if (value < root.data) {
             root.left = remove(root.left, value);
          } else if (value > root.data) {
             root.right = remove(root.right, value);
          } else { // found it!
             // leaf node case is same as removeLeaves
             if (root.left == null && root.right == null) {
                root = null;
             } else if (root.right == null) { // left child only
                root = root.left;
             } else if (root.left == null) { // right child only;
                root = root.right;
             } else {
                // Need to find the smallest value in the right (larger values) subtree
                int newRootValue = getMin(root.right);
                root.right = remove(root.right, newRootValue);
                root.data = newRootValue; // morphing nodes is generally bad! (don't do this on your homework)
             }
          }
       }
       return root;
    }


	// Returns the minimum value from this set.
	// Throws a NoSuchElementException if the set is empty.
	public int getMin() {
		if (isEmpty()) {
			throw new NoSuchElementException();
		}
		return getMinNode(overallRoot).data;
	}

	// Returns the minimum value from the tree with the given root.
	// Pre: root is not null
	private TreeNode getMinNode(TreeNode root) {
		if (root.left == null) {
			return root;
		} else {
			return getMinNode(root.left);
		}
	}

	// Returns a comma-separated list of the elements in this set
	// in sorted order.
	public String toString() {
		if (overallRoot == null) {
			return "[]";
		} else {
			String contents = toString(overallRoot);
			return "[" + contents.substring(0, contents.length() - 2) + "]";
		}
	}

	// Returns a String of the elements in the tree at the given root.
	private String toString(TreeNode root) {
		if (root == null) {
			return "";
		} else {
			return toString(root.left) + root.data + ", " + toString(root.right);
		}
	}

	private class TreeNode {
		public int data; // data stored at this node
		public TreeNode left; // reference to left subtree
		public TreeNode right; // reference to right subtree

		// Constructs a leaf node with the given data.
		public TreeNode(int data) {
			this(data, null, null);
		}

		// Constructs a leaf or branch node with the given data and links.
		public TreeNode(int data, TreeNode left, TreeNode right) {
			this.data = data;
			this.left = left;
			this.right = right;
		}
	}
}