算法导论红黑树学习旋转(二)图文

时间 2019-11-30

标签算法导论学习旋转图文栏目应用数学繁體版

原文原文链接

学习算法仍是建议看看算法导论node

算法导论第三版若是不看数学推导仅看伪代码难度仍是适中ios

本系列只是记录个人学习心得和伪代码转化代码的过程算法

深刻学习仍是建议你们看看算法书籍教程更加系统。函数

本文参考算法导论第13章节红黑树性能

代码由本人写成学习

转载请标明出处测试

红黑树是一个带颜色的二叉树spa

有如下5点性能3d

1 每一个节点或者红色或者黑色指针

2 根节点黑色

3 每一个叶子节点(nil)为黑色

4 若是一个节点是红色的则它的两个子节点都是黑色

5 每一个节点该节点到子孙节点的路径上黑色节点数目相同

如图

nil节点共享版本

隐藏nil节点

红黑树的结构与二叉树相似

可是增长了指向节点父节点的指针和颜色记录

enum Color {
    red = 1,
    black
};

struct node {
    Color color_;
    std::shared_ptr<node> left_;
    std::shared_ptr<node> right_;
    std::shared_ptr<node> parent_;
    int value_;
    node() {
        left_ = right_ = parent_ = nullptr;
        value_ = -1;
        color_ = black;
    }
};

还建立以叶节点nil

std::shared_ptr<node> nil(new node);

打印函数与二叉树变化不大

void PrinTree(std::shared_ptr<node> root) {
    if (root == nil) {
        return;
    }
    std::cout << root->value_ << " ";
    if(root->left_!=nil)
        PrinTree(root->left_);
    if(root->right_ != nil)
        PrinTree(root->right_);
}

旋转操做

旋转是保持平衡的最基本的操做咱们先从这里开始学习

在实际的操做旋转如图

伪代码如图

实际上就是

将Y的左子树更改成X的右子树

X更改成Y的左子树

实际代码为

void RightRotate(std::shared_ptr<node>& root, std::shared_ptr<node> x) {
    std::shared_ptr<node> y = x->left_;
    x->left_ = y->right_;
    if (y->right_ != nil)
        y->right_->parent_ = x;
    y->parent_ = x->parent_;
    if (x->parent_ == nil){
        root = y;
    }
    else if (x->parent_->left_ == x) {
        x->parent_->left_ = y;
    }
    else {
        x->parent_->right_ = y;
    }

    y->right_ = x;
    x->parent_ = y;
}

　咱们来建立一个红黑树测试下旋转操做(先不关注颜色只关注旋转操做)

所有代码以下

// rbShow.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"
#include <memory>
#include <iostream>

using namespace std;

enum Color {
	red = 1,
	black
};

struct node {
	Color color_;
	std::shared_ptr<node> left_;
	std::shared_ptr<node> right_;
	std::shared_ptr<node> parent_;
	int value_;
	node() {
		left_ = right_ = parent_ = nullptr;
		value_ = -1;
		color_ = black;
	}
};

std::shared_ptr<node> nil(new node);


std::shared_ptr<node> CreateNode(Color color, int i) {
	std::shared_ptr<node> p(new node);
	p->color_ = color;
	p->left_ = nil;
	p->right_ = nil;
	p->parent_ = nil;
	p->value_ = i;
	return p;
}

void RightRotate(std::shared_ptr<node>& root, std::shared_ptr<node> x) {
	std::shared_ptr<node> y = x->left_;
	x->left_ = y->right_;
	if (y->right_ != nil)
		y->right_->parent_ = x;
	y->parent_ = x->parent_;
	if (x->parent_ == nil) {
		root = y;
	}
	else if (x->parent_->left_ == x) {
		x->parent_->left_ = y;
	}
	else {
		x->parent_->right_ = y;
	}

	y->right_ = x;
	x->parent_ = y;
}

void LeftRotate(std::shared_ptr<node>& root, std::shared_ptr<node> x) {
	std::shared_ptr<node> y = x->right_;
	x->right_ = y->left_;
	if (y->left_ != nil)
		y->left_->parent_ = x;

	y->parent_ = x->parent_;
	if (x->parent_ == nil) {
		root = y;
	}
	else if (x->parent_->left_ == x) {
		x->parent_->left_ = y;
	}
	else {
		x->parent_->right_ = y;
	}
	y->left_ = x;
	x->parent_ = y;
}

void PrinTree(std::shared_ptr<node> root) {
	if (root == nil) {
		return;
	}
	std::cout << root->value_ << " ";
	if (root->left_ != nil)
		PrinTree(root->left_);
	if (root->right_ != nil)
		PrinTree(root->right_);
}

void TestLeftRotate1() {
	std::shared_ptr<node> root = CreateNode(black, 1);
	root->parent_ = nil;
	std::shared_ptr<node> x = root;
	root->right_ = CreateNode(red, 2);
	root->right_->parent_ = root;


	PrinTree(root);
	std::cout << std::endl;
	LeftRotate(root, x);
	PrinTree(root);
	std::cout << std::endl;
}

void TestRightRotate1() {
	std::shared_ptr<node> root = CreateNode(black, 2);
	root->parent_ = nil;
	std::shared_ptr<node> x = root;
	std::shared_ptr<node> y = CreateNode(red, 1);
	root->left_ = y;
	y->parent_ = x;

	PrinTree(root);
	std::cout << std::endl;
	RightRotate(root, x);
	PrinTree(root);
	std::cout << std::endl;
}


int main()
{
	TestLeftRotate1();
	TestRightRotate1();
    return 0;
}

代码运行效果如图

因为左旋转与右旋转是镜像映射的这里仅仅介绍左旋转

左旋转后

再来一个多节点的旋转

// rbShow.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"
#include <memory>
#include <iostream>

using namespace std;

enum Color {
	red = 1,
	black
};

struct node {
	Color color_;
	std::shared_ptr<node> left_;
	std::shared_ptr<node> right_;
	std::shared_ptr<node> parent_;
	int value_;
	node() {
		left_ = right_ = parent_ = nullptr;
		value_ = -1;
		color_ = black;
	}
};

std::shared_ptr<node> nil(new node);


std::shared_ptr<node> CreateNode(Color color, int i) {
	std::shared_ptr<node> p(new node);
	p->color_ = color;
	p->left_ = nil;
	p->right_ = nil;
	p->parent_ = nil;
	p->value_ = i;
	return p;
}

void RightRotate(std::shared_ptr<node>& root, std::shared_ptr<node> x) {
	std::shared_ptr<node> y = x->left_;
	x->left_ = y->right_;
	if (y->right_ != nil)
		y->right_->parent_ = x;
	y->parent_ = x->parent_;
	if (x->parent_ == nil) {
		root = y;
	}
	else if (x->parent_->left_ == x) {
		x->parent_->left_ = y;
	}
	else {
		x->parent_->right_ = y;
	}

	y->right_ = x;
	x->parent_ = y;
}

void LeftRotate(std::shared_ptr<node>& root, std::shared_ptr<node> x) {
	std::shared_ptr<node> y = x->right_;
	x->right_ = y->left_;
	if (y->left_ != nil)
		y->left_->parent_ = x;

	y->parent_ = x->parent_;
	if (x->parent_ == nil) {
		root = y;
	}
	else if (x->parent_->left_ == x) {
		x->parent_->left_ = y;
	}
	else {
		x->parent_->right_ = y;
	}
	y->left_ = x;
	x->parent_ = y;
}

void PrinTree(std::shared_ptr<node> root) {
	if (root == nil) {
		return;
	}
	std::cout << root->value_ << " ";
	if (root->left_ != nil)
		PrinTree(root->left_);
	if (root->right_ != nil)
		PrinTree(root->right_);
}

void TestLeftRotate2() {
	//测试 1 3 2 4
	std::shared_ptr<node> root = CreateNode(black, 1);
	root->parent_ = nil;

	root->right_ = CreateNode(red, 3);
	root->right_->parent_ = root;

	std::shared_ptr<node> x = root->right_;

	std::shared_ptr<node> y = CreateNode(red, 2);
	x->left_ = y;
	y->parent_ = x;

	std::shared_ptr<node> z = CreateNode(red, 4);
	x->right_ = z;
	z->parent_ = x;

	PrinTree(root);
	std::cout << std::endl;

	LeftRotate(root, x);
	PrinTree(root);
	std::cout << std::endl;
}

void TestRightRotate1() {
	//测试 9 10 6 8 4 2 5
	std::shared_ptr<node> root = CreateNode(black, 9);
	root->parent_ = nil;
	std::shared_ptr<node> a = root;

	std::shared_ptr<node> b = CreateNode(black, 10);
	a->right_ = b;
	b->parent_ = a;

	std::shared_ptr<node> c = CreateNode(black, 6);
	a->left_ = c;
	c->parent_ = a;

	std::shared_ptr<node> d = CreateNode(black, 8);
	c->right_ = d;
	d->parent_ = c;

	std::shared_ptr<node> e = CreateNode(black, 4);
	c->left_ = e;
	e->parent_ = c;

	std::shared_ptr<node> f = CreateNode(black, 2);
	e->left_ = f;
	f->parent_ = e;

	std::shared_ptr<node> g = CreateNode(black, 5);
	e->right_ = g;
	g->parent_ = e;

	PrinTree(root);
	std::cout << std::endl;

	RightRotate(root, c);

	PrinTree(root);
	std::cout << std::endl;
}


int main()
{
	TestLeftRotate1();
	std::cout << std::endl;
	TestRightRotate1();
    return 0;
}

　这里介绍右旋转图示如图

节点6进行右旋转后

算法导论 红黑树 学习 旋转(二)图文

算法导论红黑树学习旋转(二)图文