紅黑樹

public class RedBlackBST<Key extends Comparable<Key>,value>
{
    private Node root;
    private static final boolean RED = true;
    private static final boolean BLACK = false;
    private class Node
    {
        Key key;  
        Vlaue val;  //value是個啥？  彷佛不須要。 我再看看 - -
        Node left,right,parent;
        boolean color;

        public Node(Key key, Vlaue val, Node parent,boolean color)
        {
            this.key = key;
            this.val = val;
            this.color = color;
        }
    }
        public Vlaue get(Key key)
        {
            Node x = root;
            while(x != null)
            {
                int cmp = key.compareTo(x.key);
                if(cmp < 0) x = x.left;
                else if(cmp > 0) x = x.right;
                else return x.val;
            }
            return null;
        }

        //插入節點
        public void put(Key key, Value value)
        {
            if(root == null) root = new Node(key, value, null, BLACK);

            //從根節點往下尋找合適的插入位置
            Node parent = null;   //查找位置，而後插入節點
            Node cur = root;
            //保持二叉樹的特性，while循環尋找插入位置。插入位置確定是null處
            while(cur != null)
            {
                parent = cur;
                if(key.compareTo(cur.key) > 0) cur = cur.right;
                else cur = cur.left;
            }

            Node n = new Node(key, value, parent, RED);//普通的新建節點爲紅色
            //將新節點插入parent下
            if(key.compareTo(parent.key) > 0)parent.right = n;
            else parent.left = n;

            //插入新節點後要調整樹中部分節點的顏色和屬性來紅黑樹的特徵不被破壞
            fixAfterInsertion(n);

        }

        private Node parentOf(Node x) {return x == null? null:x.parent;}

        private boolean colorOf(Node x){return x == null? null:x.color;}
    
        private Node leftOf(Node x){return x == null? null : x.left;}

        private Node rightOf(Node x){return x == null? null: x.right;}

        private void setColor(Node x, boolean color){if(x!=null) x.color = color;}

        //變色
        //不知道下面的case是怎麼出來，應該是總結出來的
        private void fixAfterInsertion(Node x)
        {
            //父節點的顏色爲紅色
            while(x!=null && colorOf(parentOf(x)) == RED)
            {
                //父節點的父節點
                Node grandPa = parentOf(parentOf(x));
                Node parent = parentOf(x);

                //父節點是祖父節點的左孩子
                if(parent == leftOf(grandPa)){
                    Node uncle = rightOf(grandPa);
                    //case1: 叔叔節點是紅色
                    if(colorOf(uncle) == RED)
                    {
                        setColor(parent, BLACK);
                        setColor(uncle, BLACK);
                        setColor(grandPa, RED);
                        x = grandPa;  //這一步是爲了以後的旋轉
                    }else
                    {
                        //case2: 叔叔是黑色，且當前是右孩子
                        if(x == rightOf(parent))
                        {
                            x = parent;
                            rotateLeft(x);
                        }

                        //case3: 叔叔是黑色，且當前是左孩子
                        setColor(parent, BLACK);
                        setColor(grandPa, RED);
                        rotateRight(grandPa);
                    }
                }
                //父節點時祖父節點的右孩子
                else
                {
                    //case4: 叔叔節點時紅色
                    Node uncle = leftOf(grandPa);
                    if(colorOf(uncle) ==  RED)
                    {
                        setColor(parent, BLACK);
                        setColor(uncle, BLACK);
                        setColor(grandPa, RED);
                        x= grandPa;
                                            }
                    //case5: 叔叔黑色，且當前是左孩子
                    else
                    {
                        if(x == leftOf(parent))
                        {
                            x = parent;
                            rotateRight(x)
                        }
                        //case6: 叔叔是黑色，且當前節點時右孩子
                        setColor(parent, BLACK);
                        setColor(grandPa,RED);
                        rotateLeft(grandPa);
                    }
                    
                }
            }
            setColor(this.root, BLACK);
        }
        //左旋轉， 右孩子升爲根節點， 右孩子的左孩子左移
        //知道指針和鏈表這裏就很好理解了
        public viod rotateLeft(Node x)
        {
            if(x == null) return;
            Node y = x.right;  //右孩子
            //創建旋轉後的父子關係
            x.right = y.left;  //右孩子的左孩子變爲變化後的x的右孩子
            if(y.left != null) y.left.parent = x;
            y.parent = x.parent;   //將x的parent賦值給y的parent .  

            if(x.parent == null) root = y;
            else if(x.parent.left == x) x.parent.left = y;
            else x.parent.right = y;

            y.left = x;  //將x設爲y的左孩子
            x.parent = y; //將y設爲x的parent
        }

        //右旋轉  左孩子上升爲根節點。左孩子的右孩子變爲x的左孩子
        public void rotateRight(Node x)
        {
            if(x == null) rturn;
            Node y = x.left;
            x.left = y.right;
            if(y.right == null) y.right.parent = x;
            y.parent = x.parent;

            if(x.parent == null) root = y;
            else if(x.parent.left == x) x.parent.left = y;
            else x.parent.right = y;

            y.left = x;
            x.parent = y;
        }
    }
}