A red-black tree is a binary balanced lookup tree in which each node has a storage bit to represent the color of the node, either RED or BLACK.Red-black trees have the following properties:

(1) Each node is red or black

(2) The root node is black

(3) If a node is red, both of its sons are black

(4) For each node, all paths from that node to its descendants contain the same number of black nodes

By the nature of the red-black tree, all implementations based on it can be guaranteed to run logarithmically (except for range lookup).The extra time it takes is proportional to the number of keys returned.

Java's TreeMap is implemented using red and black trees.

The operation of red and black trees can be confusing without drawing them. The insertion of red and black trees is illustrated below.

After inserting a red node into the red-black tree, there are six situations: N represents the inserted node, P represents the parent node, U represents the uncle node, G represents the grandparent node, X represents the current operation node.

The code is as follows:

  1 public class RedBlackBST<Key extends Comparable<Key>, Value> {
  2     private Node root;
  3     private static final boolean RED = true;
  4     private static final boolean BLACK = false;
  5     private class Node{
  6         private Key key; //key
  7         private Value val; //value
  8         private Node left, right, parent; //Left and right subtrees and parent nodes
  9         private boolean color; //The color of the link pointed to by its parent node
 10         
 11         public Node(Key key, Value val,Node parent, boolean color){
 12             this.key = key;
 13             this.val = val;
 14             this.color = color;
 15         }
 16     }
 17     
 18     public Value get(Key key){
 19         Node x = root;
 20         while(x!=null){
 21             int cmp = key.compareTo(x.key);
 22             if(cmp < 0 ) x = x.left;
 23             else if(cmp > 0) x = x.right;
 24             else return x.val;
 25         }
 26         return null;
 27     }
 28     
 29     public void put(Key key, Value val){
 30         if(root==null) { //If it is the root node, create a new black node
 31             root = new Node(key,val,null,BLACK);
 32             return;
 33         }
 34         //Find a suitable insertion location
 35         Node parent = null;
 36         Node cur = root;
 37         while(cur!=null) {
 38             parent = cur;
 39             if(key.compareTo(cur.key)>0) cur=cur.right;
 40             else cur = cur.left;
 41         }
 42         Node n = new Node(key,val,parent,RED); //Common new node is red
 43         //Insert a new node parent lower
 44         if(key.compareTo(parent.key) > 0) parent.right = n;
 45         else parent.left = n;
 46         //After inserting a new node, adjust the color and attributes of some nodes in the tree to ensure that the characteristics of the red-black tree are not destroyed
 47         fixAfterInsertion(n); 
 48     }
 49     private Node parentOf(Node x) {
 50         return (x==null ? null : x.parent);
 51     }
 52     private boolean colorOf(Node x) {
 53         return (x==null ? BLACK : x.color);
 54     }
 55     private Node leftOf(Node x) {
 56         return (x==null ? null : x.left);
 57     }
 58     private Node rightOf(Node x) {
 59         return(x==null ? null : x.right);
 60     }
 61     private void setColor(Node x, boolean color) {
 62         if(x!=null)
 63             x.color = color;
 64     }
 65     
 66     private void fixAfterInsertion(Node x) {
 67         while(x!=null && colorOf(parentOf(x)) == RED) {
 68             Node grandPa = parentOf(parentOf(x));
 69             Node parent = parentOf(x);
 70             if(parent == leftOf(grandPa)) {//case 1 || case2 || case3
 71                 Node uncle = rightOf(grandPa);
 72                 if(colorOf(uncle) == RED) {//case1, uncle is red
 73                     setColor(parent,BLACK);    //Black parent node
 74                     setColor(uncle, BLACK);    //Uncle node blackened
 75                     setColor(grandPa,RED);    //Grandfather Node Red
 76                     x = grandPa; //Since the grandparent node goes from black to red, the red and black attributes of the parent node and its ancestors are readjusted
 77                 }else {//case2 || case3,uncle is black
 78                     if(x==rightOf(parent)) { //case2
 79                         x = parent;
 80                         rotateLeft(x);
 81                     }
 82                     //case3
 83                     setColor(parent,BLACK);
 84                     setColor(grandPa, RED);
 85                     rotateRight(grandPa);
 86                 }
 87                 
 88             }else {//case4 || case 5 || case6
 89                 Node uncle = leftOf(grandPa);
 90                 if(colorOf(uncle) == RED) { //case4 || case5 || case6
 91                     setColor(parent,BLACK);
 92                     setColor(uncle, BLACK);
 93                     setColor(grandPa,RED);
 94                     x = grandPa;
 95                 }else{ //case5 || case6, uncle is black
 96                     if(x==leftOf(parent)) { //case5
 97                         x = parent;
 98                         rotateRight(x);
 99                     }
100                     //case6
101                     setColor(parent,BLACK);
102                     setColor(grandPa, RED);
103                     rotateLeft(grandPa);
104                 }
105             }
106         }
107     }
108     private void rotateLeft(Node x) {
109         if(x==null) return;
110         Node y = x.right;
111         x.right = y.left;
112         if(y.left!=null)
113             y.left.parent = x;
114         y.left = x;
115         y.parent = x.parent;
116         if(x.parent == null) {
117             root = y;
118         }
119         else if(x.parent.left == x) {
120             x.parent.left = y;
121         }else {
122             x.parent.right = y;
123         }
124         x.parent = y;
125     }
126     private void rotateRight(Node x) {
127         if(x==null) return;
128         Node y = x.left;
129         x.left = y.right;
130         if(y.right != null)
131             y.right.parent = x;
132         y.right = x;
133         y.parent = x.parent;
134         if(x.parent == null) {
135             root = y;
136         }else if(x.parent.left==x) {
137             x.parent.left = y;
138         }else {
139             x.parent.right=y;
140         }
141         x.parent = y;
142     }
143     
144 }

The rotateLeft and rotateRight above need to be illustrated: