/*This is a Java Program to implement AA Tree. An AA tree is a form of balanced tree used for storing and retrieving ordered data efficiently. AA trees are named for Arne Andersson, their inventor. AA trees are a variation of the red-black tree, which in turn is an enhancement to the binary search tree.*/

/**
 *  Java Program to Implement AA Tree
 */

import java.util.Scanner;
import java.util.NoSuchElementException;

/** Class AANode **/
class AANode
{
    AANode left, right;
    int element, level;

    /** Constructor **/
    public AANode()
    {
        this.element = 0;
        this.left = this;
        this.right = this;
        this.level = 0;
    }

    /** Constructor **/
    public AANode(int ele)
    {
        this(ele, null, null);
    }

    /** Constructor **/
    public AANode(int ele, AANode left, AANode right)
    {
        this.element = ele;
        this.left = left;
        this.right = right;
        this.level = 1;
    }
}

/** Class AATree **/
class AATree
{
    private AANode root;
    private static AANode nil = new AANode();

    /** Constructor **/
    public AATree()
    {
        root = nil;
    }

    /** Function to check if tree is empty **/
    public boolean isEmpty()
    {
        return root == nil;
    }

    /** Make the tree empty **/
    public void clear()
    {
        root = nil;
    }

    /* Functions to insert data */
    public void insert(int X)
    {
        root = insert(X, root);
    }
    private AANode insert(int X, AANode T)
    {
        if (T == nil)
            T = new AANode(X, nil, nil);
        else if ( X < T.element )
            T.left = insert(X, T.left);
        else if ( X > T.element)
            T.right = insert(X, T.right);
        else
            return T;
        T = skew(T);
        T = split(T);
        return T;
    }

    /** Function Skew **/
    private AANode skew(AANode T)
    {
        if (T == nil)
            return nil;
        else if (T.left == nil)
            return T;
        else if (T.left.level == T.level)
            {
                AANode L = T.left;
                T.left = L.right;
                L.right = T;
                return L;
            }
        else
            return T;
    }

    /** Function split **/
    private AANode split(AANode T)
    {
        if (T == nil)
            return nil;
        else if (T.right == nil || T.right.right == nil)
            return T;
        else if (T.level == T.right.right.level)
            {
                AANode R = T.right;
                T.right = R.left;
                R.left = T;
                R.level = R.level + 1;
                return R;
            }
        else
            return T;
    }

    /** Function decrease key **/
    private AANode decreaseLevel(AANode T)
    {
        int shouldBe = Math.min(T.left.level, T.right.level) + 1;
        if (shouldBe < T.level)
            {
                T.level = shouldBe;
                if (shouldBe < T.right.level)
                    T.right.level = shouldBe;
            }
        return T;
    }

    /** Functions to count number of nodes **/
    public int countNodes()
    {
        return countNodes(root);
    }
    private int countNodes(AANode r)
    {
        if (r == nil)
            return 0;
        else
            {
                int l = 1;
                l += countNodes(r.left);
                l += countNodes(r.right);
                return l;
            }
    }
    /** Functions to search for an element **/
    public boolean search(int val)
    {
        return search(root, val);
    }
    private boolean search(AANode r, int val)
    {
        boolean found = false;
        while ((r != nil) && !found)
            {
                int rval = r.element;
                if (val < rval)
                    r = r.left;
                else if (val > rval)
                    r = r.right;
                else
                    {
                        found = true;
                        break;
                    }
                found = search(r, val);
            }
        return found;
    }
    /** Function for inorder traversal **/
    public void inorder()
    {
        inorder(root);
    }
    private void inorder(AANode r)
    {
        if (r != nil)
            {
                inorder(r.left);
                System.out.print(r.element +" ");
                inorder(r.right);
            }
    }
    /** Function for preorder traversal **/
    public void preorder()
    {
        preorder(root);
    }
    private void preorder(AANode r)
    {
        if (r != nil)
            {
                System.out.print(r.element +" ");
                preorder(r.left);
                preorder(r.right);
            }
    }
    /** Function for postorder traversal **/
    public void postorder()
    {
        postorder(root);
    }
    private void postorder(AANode r)
    {
        if (r != nil)
            {
                postorder(r.left);
                postorder(r.right);
                System.out.print(r.element +" ");
            }
    }
}

/** Class AATree **/
public class AATreeTest
{
    public static void main(String[] args)
    {
        Scanner scan = new Scanner(System.in);
        /** Creating object of AATree **/
        AATree aat = new AATree();
        System.out.println("AATree Tree Test\n");
        char ch;
        /**  Perform tree operations  **/
        do
            {
                System.out.println("\nAATree Operations\n");
                System.out.println("1. insert ");
                System.out.println("2. search");
                System.out.println("3. count nodes");
                System.out.println("4. check empty");
                System.out.println("5. clear");
                int choice = scan.nextInt();
                switch (choice)
                    {
                    case 1 :
                        System.out.println("Enter integer element to insert");
                        aat.insert( scan.nextInt() );
                        break;
                    case 2 :
                        System.out.println("Enter integer element to search");
                        System.out.println("Search result : "+ aat.search( scan.nextInt() ));
                        break;
                    case 3 :
                        System.out.println("Nodes = "+ aat.countNodes());
                        break;
                    case 4 :
                        System.out.println("Empty status = "+ aat.isEmpty());
                        break;
                    case 5 :
                        System.out.println("\nTree Cleared");
                        aat.clear();
                        break;
                    default :
                        System.out.println("Wrong Entry \n ");
                        break;
                    }
                /**  Display tree  **/
                System.out.print("\nPost order : ");
                aat.postorder();
                System.out.print("\nPre order : ");
                aat.preorder();
                System.out.print("\nIn order : ");
                aat.inorder();
                System.out.println("\nDo you want to continue (Type y or n) \n");
                ch = scan.next().charAt(0);
            }
        while (ch == 'Y'|| ch == 'y');
    }
}

/*
AATree Tree Test


AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
4
Empty status = true

Post order :
Pre order :
In order :
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
1
Enter integer element to insert
24

Post order : 24
Pre order : 24
In order : 24
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
1
Enter integer element to insert
5

Post order : 24 5
Pre order : 5 24
In order : 5 24
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
1
Enter integer element to insert
28

Post order : 5 28 24
Pre order : 24 5 28
In order : 5 24 28
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
1
Enter integer element to insert
6

Post order : 6 5 28 24
Pre order : 24 5 6 28
In order : 5 6 24 28
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
1
Enter integer element to insert
94

Post order : 6 5 94 28 24
Pre order : 24 5 6 28 94
In order : 5 6 24 28 94
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
1
Enter integer element to insert
63

Post order : 6 5 28 94 63 24
Pre order : 24 5 6 63 28 94
In order : 5 6 24 28 63 94
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
1
Enter integer element to insert
19

Post order : 5 19 6 28 94 63 24
Pre order : 24 6 5 19 63 28 94
In order : 5 6 19 24 28 63 94
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
2
Enter integer element to search
24
Search result : true

Post order : 5 19 6 28 94 63 24
Pre order : 24 6 5 19 63 28 94
In order : 5 6 19 24 28 63 94
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
2
Enter integer element to search
6
Search result : true

Post order : 5 19 6 28 94 63 24
Pre order : 24 6 5 19 63 28 94
In order : 5 6 19 24 28 63 94
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
2
Enter integer element to search
7
Search result : false

Post order : 5 19 6 28 94 63 24
Pre order : 24 6 5 19 63 28 94
In order : 5 6 19 24 28 63 94
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
3
Nodes = 7

Post order : 5 19 6 28 94 63 24
Pre order : 24 6 5 19 63 28 94
In order : 5 6 19 24 28 63 94
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
5

Tree Cleared

Post order :
Pre order :
In order :
Do you want to continue (Type y or n)

y

AATree Operations

1. insert
2. search
3. count nodes
4. check empty
5. clear
4
Empty status = true

Post order :
Pre order :
In order :
Do you want to continue (Type y or n)

n