紅黑樹是一種經典的數據結構，在linux內存管理、nginx 等很多地方用到它。主要操作包括插入、刪除，其中插入6種情況，刪除8種情況，詳細的思路就不說了，如果不太明白的請參考算法導論13章，看的時候一定要把每一種插入、刪除的情況在紙上自己畫出來，這樣會節省你很多時間。下面是java實現的代碼：
package com.algorithm.rbtree;
public class RBTree {
private final Node NIL = new Node(null,null,null,Color.BLACK,-1);
private Node root;
public RBTree() {
root = NIL;
}
public RBTree(Node root) {
this.root = root;
}
//插入節點
public void rbInsert(Node node) {
Node previous = NIL;
Node temp = root;
while (temp != NIL) {
previous = temp;
if (temp.getValue() < node.getValue()) {
temp = temp.getRight();
} else {
temp = temp.getLeft();
}
}
node.setParent(previous);
if (previous == NIL) {
root = node;
root.setParent(NIL);
} else if (previous.getValue() > node.getValue()) {
previous.setLeft(node);
} else {
previous.setRight(node);
}
node.setLeft(NIL);
node.setRight(NIL);
node.setColor(Color.RED);
rb_Insert_Fixup(node);
}
//插入節點後的調整
private void rb_Insert_Fixup(Node node) {
while (node.getParent().getColor() == Color.RED) {
if (node.getParent() == node.getParent().getParent().getLeft()) {
Node rightNuncle = node.getParent().getParent().getRight();
if (rightNuncle.getColor() == Color.RED) { //Case 1
rightNuncle.setColor(Color.BLACK);
node.getParent().setColor(Color.BLACK);
node.getParent().getParent().setColor(Color.RED);
node = node.getParent().getParent();
} else if (node == node.getParent().getRight()) { //case 2
node = node.getParent();
leftRotate(node);
} else { //case 3
node.getParent().setColor(Color.BLACK);
node.getParent().getParent().setColor(Color.RED);
rightRotate(node.getParent().getParent());
}
} else {
Node leftNuncle = node.getParent().getParent().getLeft();
if (leftNuncle.getColor() == Color.RED) { //case 4
leftNuncle.setColor(Color.BLACK);
node.getParent().setColor(Color.BLACK);
node.getParent().getParent().setColor(Color.RED);
node = node.getParent().getParent();
} else if (node == node.getParent().getLeft()) { //case 5
node = node.getParent();
rightRotate(node);
} else { // case 6
node.getParent().setColor(Color.BLACK);
node.getParent().getParent().setColor(Color.RED);
leftRotate(node.getParent().getParent());
}
}
}
root.setColor(Color.BLACK);
}
//刪除節點
public Node rbDelete(int data) {
Node node = search(data);
Node temp = NIL;
Node child = NIL;
if (node == null) {
return null;
} else {
if (node.getLeft() == NIL || node.getRight() == NIL) {
temp = node;
} else {
temp = successor(node);
}
if (temp.getLeft() != NIL) {
child = temp.getLeft();
} else {
child = temp.getRight();
}
child.setParent(temp.getParent());
if (temp.getParent() == NIL) {
root = child;
} else if (temp == temp.getParent().getLeft()) {
temp.getParent().setLeft(child);
} else {
temp.getParent().setRight(child);
}
if (temp != node) {
node.setValue(temp.getValue());
}
if (temp.getColor() == Color.BLACK) {
rb_Delete_Fixup(child);
}
return temp;
}
}
//刪除節點後的調整
private void rb_Delete_Fixup(Node node) {
while (node != root && node.getColor() == Color.BLACK) {
if (node == node.getParent().getLeft()) {
Node rightBrother = node.getParent().getRight();
if (rightBrother.getColor() == Color.RED) { //case 1 node節點爲左孩子，node節點的兄弟爲RED
rightBrother.setColor(Color.BLACK);
node.getParent().setColor(Color.RED);
leftRotate(node.getParent());
rightBrother = node.getParent().getRight();
}
if (rightBrother.getLeft().getColor() == Color.BLACK && rightBrother.getRight().getColor() == Color.BLACK) {
rightBrother.setColor(Color.RED);
node = node.getParent();
} else if (rightBrother.getRight().getColor() == Color.BLACK) {
rightBrother.getLeft().setColor(Color.BLACK);
rightBrother.setColor(Color.RED);
rightRotate(rightBrother);
rightBrother = node.getParent().getRight();
} else {
rightBrother.setColor(node.getParent().getColor());
node.getParent().setColor(Color.BLACK);
rightBrother.getRight().setColor(Color.BLACK);
leftRotate(node.getParent());
node = root;
}
} else {
Node leftBrother = node.getParent().getLeft();
if (leftBrother.getColor() == Color.RED) {
leftBrother.setColor(Color.BLACK);
node.getParent().setColor(Color.RED);
rightRotate(node.getParent());
leftBrother = node.getParent().getLeft();
}
if (leftBrother.getLeft().getColor() == Color.BLACK && leftBrother.getRight().getColor() == Color.BLACK) {
leftBrother.setColor(Color.RED);
node = node.getParent();
} else if (leftBrother.getLeft().getColor() == Color.BLACK) {
leftBrother.setColor(Color.RED);
leftBrother.getRight().setColor(Color.BLACK);
leftRotate(leftBrother);
leftBrother = node.getParent().getLeft();
} else {
leftBrother.setColor(node.getParent().getColor());
node.getParent().setColor(Color.BLACK);
leftBrother.getLeft().setColor(Color.BLACK);
rightRotate(node.getParent());
node = root;
}
}
}
node.setColor(Color.BLACK);
}
//查找節點node的後繼節點
public Node successor(Node node) {
Node rightChild = node.getRight();
if (rightChild != NIL) {
Node previous = null;
while (rightChild != NIL) {
previous = rightChild;
rightChild = rightChild.getLeft();
}
return previous;
} else {
Node parent = node.getParent();
while (parent != NIL && node != parent.getLeft()) {
node = parent;
parent = parent.getParent();
}
return parent;
}
}
//查找節點
public Node search(int data) {
Node temp = root;
while (temp != NIL) {
if (temp.getValue() == data) {
return temp;
} else if (data < temp.getValue()) {
temp = temp.getLeft();
} else {
temp = temp.getRight();
}
}
return null;
}
//左轉函數
private void leftRotate(Node node) {
Node rightNode = node.getRight();
node.setRight(rightNode.getLeft());
if (rightNode.getLeft() != NIL) {
rightNode.getLeft().setParent(node);
}
rightNode.setParent(node.getParent());
if (node.getParent() == NIL) {
rightNode = root;
} else if (node == node.getParent().getLeft()) {
node.getParent().setLeft(rightNode);
} else {
node.getParent().setRight(rightNode);
}
rightNode.setLeft(node);
node.setParent(rightNode);
}
//右轉函數
private void rightRotate(Node node) {
Node leftNode = node.getLeft();
node.setLeft(leftNode.getRight());
if (leftNode.getRight() != null) {
leftNode.getRight().setParent(node);
}
leftNode.setParent(node.getParent());
if (node.getParent() == NIL) {
root = leftNode;
} else if (node == node.getParent().getLeft()) {
node.getParent().setLeft(leftNode);
} else {
node.getParent().setRight(leftNode);
}
leftNode.setRight(node);
node.setParent(leftNode);
}
//中序遍歷紅黑樹
public void printTree() {
inOrderTraverse(root);
}
private void inOrderTraverse(Node node) {
if (node != NIL) {
inOrderTraverse(node.getLeft());
System.out.println(" 節點："+node.getValue() + "的顏色爲：" + node.getColor());
inOrderTraverse(node.getRight());
}
}
public Node getNIL() {
return NIL;
}
}
class Node {
private Node left;
private Node right;
private Node parent;
private Color color;
private int value;
public Node(Node left, Node right, Node parent, Color color, int value) {
super();
this.left = left;
this.right = right;
this.parent = parent;
this.color = color;
this.value = value;
}
public Node() {
}
public Node(int value) {
this(null,null,null,null,value);
}
public Node getLeft() {
return left;
}
public void setLeft(Node left) {
this.left = left;
}
public Node getRight() {
return right;
}
public void setRight(Node right) {
this.right = right;
}
public Node getParent() {
return parent;
}
public void setParent(Node parent) {
this.parent = parent;
}
public Color getColor() {
return color;
}
public void setColor(Color color) {
this.color = color;
}
public int getValue() {
return value;
}
public void setValue(int value) {
this.value = value;
}
}
enum Color {
RED,BLACK
}下面是測試代碼：
package com.algorithm.rbtree;
public class RBTreeTest {
/**
* @param args
*/
public static void main(String[] args) {
RBTree rbTree = new RBTree();
rbTree.rbInsert(new Node(41));
rbTree.rbInsert(new Node(38));
rbTree.rbInsert(new Node(31));
rbTree.rbInsert(new Node(12));
rbTree.rbInsert(new Node(19));
rbTree.rbInsert(new Node(8));
//rbTree.printTree();
rbTree.rbDelete(19);
rbTree.printTree();
}
}
