import java.util.*;

// An IntSearchTree object represents an entire binary search tree of ints.
// Class invariant: 
//    - nodes to the left of a root have smaller values
//    - nodes to the right of a root have larger values
//	  - there are no duplicates
public class IntSearchTree {
	private IntTreeNode overallRoot;
	private int size;

	// Constructs an empty binary tree
	public IntSearchTree() {
		overallRoot = null;
		size = 0;
	}

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

	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 {
			return contains(root.right, value);
		}
	}

	// adds a value to the bst
	// post: the tree is still a valid bst
	public void add(int value) {
		overallRoot = add(overallRoot, value);
	}

	private IntTreeNode add(IntTreeNode root, int value) {
		if (root == null) {
			size++;
			root = new IntTreeNode(value);
			// return root; // useful for visualizing with jGRASP debugger
		} 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 the minimum value from this BST.
	// Throws a NoSuchElementException if the tree is empty.
	public int getMin() {
		if (overallRoot == null) {
			throw new NoSuchElementException();
		}
		return getMin(overallRoot);
	}

	private int getMin(IntTreeNode root) {
		if (root.left == null) {
			return root.data;
		} else {
			return getMin(root.left);
		}
	}

	// Removes the node with the given value from this BST.
	public void remove(int value) {
		overallRoot = remove(overallRoot, value);
	}

	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!
				size--;

				if (root.left == null && root.right == null) { // leaf node
					root = null;
				} else if (root.right == null) {
					root = root.left;
				} else if (root.left == null) {
					root = root.right;
				} else {
					int min = getMin(root.right);
					root.data = min;
					size++; // to compensate for the remove below
					root.right = remove(root.right, min);
				}
			}
		}
		return root;
	}

	public int size() {
		return size;
	}

	public boolean isEmpty() {
		return size == 0;
	}
}