红黑树描述

<pre name="code" class="java">/* * 红黑树 */public class RedBlackTree {public static final RbTreeNode NIL = new RbTreeNode(RbColor.BLACK);private RbTreeNode root = null;public static void main(String[] args) {RedBlackTree rbt = new RedBlackTree();//测试插入 page 179  红黑树不唯一rbt.insertRbTreeNode(new RbTreeNode(11,RbColor.BLACK));rbt.insertRbTreeNode(new RbTreeNode(2,RbColor.RED));rbt.insertRbTreeNode(new RbTreeNode(1,RbColor.BLACK));rbt.insertRbTreeNode(new RbTreeNode(7,RbColor.BLACK));rbt.insertRbTreeNode(new RbTreeNode(5,RbColor.RED));rbt.insertRbTreeNode(new RbTreeNode(8,RbColor.RED));rbt.insertRbTreeNode(new RbTreeNode(14,RbColor.BLACK));rbt.insertRbTreeNode(new RbTreeNode(15,RbColor.RED));rbt.printTree();rbt.deleteRbTreeNode(rbt.searchRbTreeNode(rbt.root, 7));rbt.printTree();System.out.println("最大节点的键为："+rbt.searchMaximum(rbt.root).key);}public RedBlackTree() {this.root = NIL;}//中序遍历二叉树private void traverseTree(RbTreeNode x) {if(x != NIL) {traverseTree(x.left);System.out.print(x.key + " " + x.color + " ");traverseTree(x.right);}}private void printTree() {System.out.println("root:"+root.key+" "+root.color);traverseTree(root);System.out.println();}//查找某一子节点private RbTreeNode searchRbTreeNode(RbTreeNode x,int key) {while(x != NIL && key != x.key) {if(key < x.key) {x = x.left;} else {x = x.right;}}return x;}//插入某一子节点private void insertRbTreeNode(RbTreeNode z) {RbTreeNode y = NIL;RbTreeNode x = root;while(x != NIL) {y = x;if(z.key < x.key) {x = x.left;} else {x = x.right;}}z.parent = y;if(y == NIL) {root = z;} else if(z.key < y.key) {y.left = z;} else {y.right = z;}z.left = NIL;z.right = NIL;z.color = RbColor.RED;rbInsertFixUp(z);//插入修正}//插入修正  private void rbInsertFixUp(RbTreeNode z) {RbTreeNode y = null;while(z.parent.color == RbColor.RED) {//当z的父节点是黑色时，不需要矫正if(z.parent == z.parent.parent.left) {//左分支情况y = z.parent.parent.right;//根据叔节点分情况if(y.color == RbColor.RED) {z.parent.color = RbColor.BLACK;y.color = RbColor.BLACK;z.parent.parent.color = RbColor.RED;z = z.parent.parent;} else {if(z == z.parent.right) {z = z.parent;leftRotate(z);}z.parent.color = RbColor.BLACK;z.parent.parent.color = RbColor.RED;rightRotate(z.parent.parent);}} else {y = z.parent.parent.left;//根据叔节点分情况if(y.color == RbColor.RED) {z.parent.color = RbColor.BLACK;y.color = RbColor.BLACK;z.parent.parent.color = RbColor.RED;z = z.parent.parent;} else {if(z == z.parent.left) { z = z.parent;rightRotate(z);}z.parent.color = RbColor.BLACK;z.parent.parent.color = RbColor.RED;leftRotate(z.parent.parent);}}}root.color = RbColor.BLACK;}//删除某一子节点private void deleteRbTreeNode(RbTreeNode z) {RbTreeNode y = z;RbTreeNode x = NIL;RbColor yOriginalColor = y.color;if(z.left == NIL) {x = z.right;rbTransplant(z,z.right);} else if(z.right == NIL) {x = z.left;rbTransplant(z,z.left);} else {y = searchMinimum(z.right);yOriginalColor = y.color;x = y.right;if(y.parent == z) {x.parent = y;} else {rbTransplant(y,y.right);y.right = z.right;z.right.parent = y;}rbTransplant(z,y);y.left = z.left;z.left.parent = y;y.color = z.color;}if(yOriginalColor == RbColor.BLACK) {rbDeleteFixUp(x);}}private void rbDeleteFixUp(RbTreeNode x) {//x总是指向一个具有双重黑色的非根节点RbTreeNode w = NIL;while(x != root && x.color == RbColor.BLACK) {if(x == x.parent.left) {w = x.parent.right;//w指向兄节点if(w.color == RbColor.RED) {w.color = RbColor.BLACK;//case 1x.parent.color = RbColor.RED;//case 1leftRotate(x.parent);//case 1w = x.parent.right;//case 1}if(w.left.color == RbColor.BLACK && w.right.color == RbColor.BLACK) {w.color = RbColor.BLACK;//case 2x = x.parent;//case 2}else {if(w.right.color == RbColor.BLACK) {w.left.color = RbColor.BLACK;//case 3w.color = RbColor.RED;//case 3rightRotate(w);//case 3w = x.parent.right;//case 3}w.color = x.parent.color;//case 4x.parent.color = RbColor.BLACK;//case 4w.right.color = RbColor.BLACK;//case 4leftRotate(x.parent);//case 4x = root;//case 4}} else {w = x.parent.left;//w指向兄节点if(w.color == RbColor.RED) {w.color = RbColor.BLACK;//case 1x.parent.color = RbColor.RED;//case 1rightRotate(x.parent);//case 1w = x.parent.left;//case 1}if(w.right.color == RbColor.BLACK && w.left.color == RbColor.BLACK) {w.color = RbColor.BLACK;//case 2x = x.parent;//case 2}else {if(w.left.color == RbColor.BLACK) {w.right.color = RbColor.BLACK;//case 3w.color = RbColor.RED;//case 3leftRotate(w);//case 3w = x.parent.left;//case 3}w.color = x.parent.color;x.parent.color = RbColor.BLACK;w.left.color = RbColor.BLACK;rightRotate(x.parent);x = root;}}}}private void rbTransplant(RbTreeNode u,RbTreeNode v) {if(u.parent == NIL) {root = v;} else if(u == u.parent.left) {u.parent.left = v;}  else {u.parent.right = v;}v.parent = u.parent;}//获取最小键值节点private RbTreeNode searchMinimum(RbTreeNode x) {while(x.left != NIL) {x = x.left;}return x;}//获取最大键值节点private RbTreeNode searchMaximum(RbTreeNode x) {while(x.right != NIL) {x = x.right;}return x;}//左旋private void leftRotate(RbTreeNode x) {RbTreeNode y = x.right;x.right = y.left;if(x.right != NIL) {y.left.parent = x;}y.parent = x.parent;if(x.parent == NIL) {//如果是根节点root = y;} else if(x == x.parent.left) {x.parent.left = y;} else {x.parent.right = y;}y.left = x;x.parent = y;}//右旋private void rightRotate(RbTreeNode y) {RbTreeNode x = y.left;y.left = x.right;if(x.right != NIL) {x.right.parent = y;}x.parent = y.parent;if(y.parent == NIL) {root = x;} else if(y == y.parent.left) {y.parent.left = x;} else {y.parent.right = x;}x.right = y;y.parent = x;}//红黑树节点类private static class RbTreeNode {RbTreeNode left = null;RbTreeNode right = null;RbTreeNode parent = null;RbColor color = RbColor.RED;int key = 0;public RbTreeNode(int key,RbColor color) {this.key = key;this.color = color;}public RbTreeNode(RbColor color) {this.color = color;}}private enum RbColor {RED,BLACK}}

运行结果为：

root:7 BLACK1 BLACK 2 RED 5 BLACK 7 BLACK 8 BLACK 11 RED 14 BLACK 15 RED root:7 BLACK2 RED 5 BLACK 7 BLACK 8 BLACK 11 RED 14 BLACK 15 RED 最大节点的键为：15