---------------------- ------------------------- red-black tree ----
Red-black tree is still a binary search tree, and AVL, are added some restrictions on the basis of the binary search tree: the five specific restrictions are as follows:
1) Each node is either red or black
2) the root is black
3) each leaf node (the last empty node called a leaf node) is black
4) If a node is red, then both its children are black nodes
5) from any node to a leaf node, black node through the same
2-3 tree is an absolute balance of the tree: from the root node to a leaf node through an arbitrary number of nodes is the same, through the integration of newly added nodes and father nodes must be the first fusion (red-black tree is this principle , so the red-black tree newly added node must be red, that default constructor red) - split - a fusion to guarantee balanced.
Red node: on behalf of his father, and it is fused together , on behalf 2-3 tree node 3
Red-black tree "black balance" binary tree: i.e., red-black tree of Article 5 constraints, any node to the leaf node through the black is the same. Strictly speaking meaning, not a balanced binary tree children, the height difference that is about sub-tree is likely to be greater than 1. Red-black tree maximum height 2logn, so the time complexity is O (logn) of
Compared with the red-black tree AVL tree:
Find: red-black tree slightly slower than AVL tree
Add and delete: red-black tree faster than AVL tree
So if the stored data frequently add and delete: select the red-black tree
If the data stored base does not change, only for query: select AVL tree
RBTree code to achieve the following (not implemented deletion method):
package rbTree;
import java.util.ArrayList;
public class RBTree<K extends Comparable<K>, V> {
private static final boolean RED = true;
private static final boolean BLACK = false;
private class Node{
public K key;
public V value;
public Node left, right;
public boolean color;
public Node(K key, V value){
this.key = key;
this.value = value;
left = null;
right = null;
color = RED;
}
}
private Node root;
private int size;
public RBTree(){
root = null;
size = 0;
}
public int getSize(){
return size;
}
public boolean isEmpty(){
return size == 0;
}
// 判断节点node的颜色
private boolean isRed(Node node){
if(node == null)
return BLACK;
return node.color;
}
// node x
// / \ 左旋转 / \
// T1 x ---------> node T3
// / \ / \
// T2 T3 T1 T2
private Node leftRotate(Node node){
Node x = node.right;
// 左旋转
node.right = x.left;
x.left = node;
x.color = node.color;
node.color = RED;
return x;
}
// node x
// / \ 右旋转 / \
// x T2 -------> y node
// / \ / \
// y T1 T1 T2
private Node rightRotate(Node node){
Node x = node.left;
// 右旋转
node.left = x.right;
x.right = node;
x.color = node.color;
node.color = RED;
return x;
}
// 颜色翻转
private void flipColors(Node node){
node.color = RED;
node.left.color = BLACK;
node.right.color = BLACK;
}
// 向红黑树中添加新的元素(key, value)
public void add(K key, V value){
root = add(root, key, value);
root.color = BLACK; // 最终根节点为黑色节点
}
// 向以node为根的红黑树中插入元素(key, value)，递归算法
// 返回插入新节点后红黑树的根
private Node add(Node node, K key, V value){
if(node == null){
size ++;
return new Node(key, value); // 默认插入红色节点
}
if(key.compareTo(node.key) < 0)
node.left = add(node.left, key, value);
else if(key.compareTo(node.key) > 0)
node.right = add(node.right, key, value);
else // key.compareTo(node.key) == 0
node.value = value;
if (isRed(node.right) && !isRed(node.left))
node = leftRotate(node);
if (isRed(node.left) && isRed(node.left.left))
node = rightRotate(node);
if (isRed(node.left) && isRed(node.right))
flipColors(node);
return node;
}
// 返回以node为根节点的二分搜索树中，key所在的节点
private Node getNode(Node node, K key){
if(node == null)
return null;
if(key.equals(node.key))
return node;
else if(key.compareTo(node.key) < 0)
return getNode(node.left, key);
else // if(key.compareTo(node.key) > 0)
return getNode(node.right, key);
}
public boolean contains(K key){
return getNode(root, key) != null;
}
public V get(K key){
Node node = getNode(root, key);
return node == null ? null : node.value;
}
public void set(K key, V newValue){
Node node = getNode(root, key);
if(node == null)
throw new IllegalArgumentException(key + " doesn't exist!");
node.value = newValue;
}
// 返回以node为根的二分搜索树的最小值所在的节点
private Node minimum(Node node){
if(node.left == null)
return node;
return minimum(node.left);
}
}
总结：
1） 二分搜索树适合处理完全随机的数据；不适用于处理近乎有序的数据，这样会退化为链表
2） AVL与红黑树相比，AVL更适合处理查询数据
3） 红黑树牺牲了平衡性，即有可能是不平衡的，但一定是“绝对黑平衡”的，2logn的高度，统计性能更优（即更适合增删改查的综合性操作）