《算法导论》学习总结 — 15. 第13章 红黑树(4)

建议先看看前言:http://www.wutianqi.com/?p=2298

这一章把前面三篇的代码总结起来,然后推荐一些网上红黑树的优秀讲解资源。

代码:

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/*
* Author: Tanky Woo
* Blog:   www.WuTianQi.com
* Description: 《算法导论》第13章 Red Black Tree
*/
#include <iostream>
//#define NULL 0
using namespace std;
 
const int RED = 0;
const int BLACK = 1;
 
// ①
typedef struct Node{
	int color;
	int key;
	Node *lchild, *rchild, *parent; 
}Node, *RBTree;
 
static Node NIL = {BLACK, 0, 0, 0, 0};
 
#define NULL (&NIL)
 
// ②
Node * RBTreeSearch(RBTree T, int k)
{
	if(T == NULL || k == T->key)
		return T;
	if(k < T->key)
		return RBTreeSearch(T->lchild, k);
	else
		return RBTreeSearch(T->rchild, k);
}
 
/*
 
BSNode * IterativeRBTreeSearch(RBTree T, int k)
{
	while(T != NULL && k != T->key)
	{
		if(k < T->lchild->key);
			x = T->lchild;
		else
			x = T->rchild;
	}
	return x;
}
*/
 
// ③
Node * RBTreeMinimum(RBTree T)
{
	while(T->lchild != NULL)
		T = T->lchild;
	return T;
}
 
Node * RBTreeMaximum(RBTree T)
{
	while(T->rchild != NULL)
		T = T->rchild;
	return T;
}
 
// ④
Node *RBTreeSuccessor(Node *x)
{
	if(x->rchild != NULL)
		return RBTreeMinimum(x->rchild);
	Node *y = x->parent;
	while(y != NULL && x == y->rchild)
	{
		x = y;
		y = y->parent;
	}
	return y;
}
 
void LeftRotate(RBTree &T, Node *x)
{
	Node *y = x->rchild;
	x->rchild = y->lchild;
	if(y->lchild != NULL)
		y->lchild->parent = x;
	y->parent = x->parent;
	if(x->parent == NULL)
		T = y;
	else
	{
		if(x == x->parent->lchild)
			x->parent->lchild = y;
		else
			x->parent->rchild = y;
	}
	y->lchild = x;
	x->parent = y;
}
 
void RightRotate(RBTree &T, Node *x)
{
	Node *y = x->rchild;
	x->rchild = y->lchild;
	if(y->lchild != NULL)
		y->lchild->parent = x;
	y->parent = x->parent;
	if(x->parent == NULL)
		T = y;
	else
	{
		if(x == x->parent->lchild)
			x->parent->lchild = y;
		else
			x->parent->rchild = y;
	}
	y->lchild = x;
	x->parent = y;
}
 
// ⑤
void RBInsertFixup(RBTree &T, Node *z)
{
	while(z->parent->color == RED)
	{
		if(z->parent == z->parent->parent->lchild)
		{
			Node *y = z->parent->parent->rchild;
			//////////// Case1 //////////////
			if(y->color == RED) 
			{
				z->parent->color = BLACK;
				y->color = BLACK;
				z->parent->parent->color = RED;
				z = z->parent->parent;
			}
			else
			{
				////////////// Case 2 //////////////
				if(z == z->parent->rchild)
				{
					z = z->parent;
					LeftRotate(T, z);
				}
				////////////// Case 3 //////////////
				z->parent->color = BLACK;
				z->parent->parent->color = RED;
				RightRotate(T, z->parent->parent);
			}
		}
		else
		{
			Node *y = z->parent->parent->lchild;
			if(y->color == RED)
			{
				z->parent->color = BLACK;
				y->color = BLACK;
				z->parent->parent->color = RED;
				z = z->parent->parent;
			}
			else
			{
				if(z == z->parent->lchild)
				{
					z = z->parent;
					RightRotate(T, z);
				}
				z->parent->color = BLACK;
				z->parent->parent->color = RED;
				LeftRotate(T, z->parent->parent);
			}
		}
	}
	T->color = BLACK;
}
 
void RBTreeInsert(RBTree &T, int k)
{
	//T->parent->color = BLACK;
	Node *y = NULL;
	Node *x = T;
	Node *z = new Node;
	z->key = k;
	z->lchild = z->parent = z->rchild = NULL;
 
	while(x != NULL)
	{
		y = x;
 
		if(k < x->key)
			x = x->lchild;
		else
			x = x->rchild;
	}
 
	z->parent = y;
	if(y == NULL)
	{
		T = z;
		T->parent = NULL;
		T->parent->color = BLACK;
	}
	else
		if(k < y->key)
			y->lchild = z;
		else
			y->rchild = z;
	z->lchild = NULL;
	z->rchild = NULL;
	z->color = RED;
	RBInsertFixup(T, z);
}
 
 
 
// ⑤
void RBDeleteFixup(RBTree &T, Node *x)
{
	while(x != T && x->color == BLACK)
	{
		if(x == x->parent->lchild)
		{
			Node *w = x->parent->rchild;
			///////////// Case 1 /////////////
			if(w->color == RED)
			{
				w->color = BLACK;
				x->parent->color = RED;
				LeftRotate(T, x->parent);
				w = x->parent->rchild;
			}
			///////////// Case 2 /////////////
			if(w->lchild->color == BLACK && w->rchild->color == BLACK)
			{
				w->color = RED;
				x = x->parent;
			}
			else
			{
				///////////// Case 3 /////////////
				if(w->rchild->color == BLACK)
				{
					w->lchild->color = BLACK;
					w->color = RED;
					RightRotate(T, w);
					w = x->parent->rchild;
				}
				///////////// Case 4 /////////////
				w->color = x->parent->color;
				x->parent->color = BLACK;
				w->rchild->color = BLACK;
				LeftRotate(T, x->parent);
				x = T;
			}
		}
		else
		{
			Node *w = x->parent->lchild;
			if(w->color == RED)
			{
				w->color = BLACK;
				x->parent->color = RED;
				RightRotate(T, x->parent);
				w = x->parent->lchild;
			}
			if(w->lchild->color == BLACK && w->rchild->color == BLACK)
			{
				w->color = RED;
				x = x->parent;
			}
			else
			{
				if(w->lchild->color == BLACK)
				{
					w->rchild->color = BLACK;
					w->color = RED;
					LeftRotate(T, w);
					w = x->parent->lchild;
				}
				w->color = x->parent->color;
				x->parent->color = BLACK;
				w->lchild->color = BLACK;
				RightRotate(T, x->parent);
				x = T;
			}
		}
	}
	x->color = BLACK;
}
 
Node* RBTreeDelete(RBTree T, Node *z)
{
	Node *x, *y;
	// z是要删除的节点,而y是要替换z的节点
	if(z->lchild == NULL || z->rchild == NULL)   
		y = z;   // 当要删除的z至多有一个子树,则y=z;
	else
		y = RBTreeSuccessor(z);  // y是z的后继
	if(y->lchild != NULL)
		x = y->lchild;  
	else
		x = y->rchild;
	// 无条件执行p[x] = p[y]
	x->parent = y->parent;  //如果y至多只有一个子树,则使y的子树成为y的父亲节点的子树
	if(y->parent == NULL)   // 如果y没有父亲节点,则表示y是根节点,词典其子树x为根节点
		T = x;
	else if(y == y->parent->lchild)   
		// 如果y是其父亲节点的左子树,则y的子树x成为其父亲节点的左子树,
		// 否则成为右子树
		y->parent->lchild = x;
	else
		y->parent->rchild = x;
	if(y != z)
		z->key = y->key;
	if(y->color == BLACK)
		RBDeleteFixup(T, x);
	return y;
}
 
void InRBTree(RBTree T)
{
	if(T != NULL)
	{
		InRBTree(T->lchild);
		cout << T->key << " ";
		InRBTree(T->rchild);
	}
}
 
void PrintRBTree(RBTree T)
{
	if(T != NULL)
	{
		PrintRBTree(T->lchild);
		cout << T->key << ": ";
		// 自身的颜色
		if(T->color == 0)
			cout << " Color: RED ";
		else
			cout << " Color: BLACK ";
 
		// 父亲结点的颜色
		if(T == NULL)
			cout << " Parent: BLACK ";
		else
		{
			if(T->color == 0)
				cout << " Parent: RED ";
			else
				cout << " Parent: BLACK ";
		}
 
		// 左儿子结点的颜色
		if(T->lchild == NULL)
			cout << " Lchild: BLACK ";
		else
		{
			if(T->lchild->color == 0)
				cout << " Lchild: RED ";
			else
				cout << " Lchild: BLACK ";
		}
 
		// 右儿子结点的颜色
		if(T->rchild == NULL)
			cout << " Rchild: BLACK ";
		else
		{
			if(T->rchild->color == 0)
				cout << " Rchild: RED ";
			else
				cout << " Rchild: BLACK ";
		}
		cout << endl;
		PrintRBTree(T->rchild);
	}
}
 
int main()
{
	int m;
	RBTree T = NULL;
	for(int i=0; i<9; ++i)
	{
		cin >> m;
		RBTreeInsert(T, m);
		cout << "在红黑树中序查找:";
		InRBTree(T);
		cout << endl;
	}
	PrintRBTree(T);
	cout << "删除根节点后:";
	RBTreeDelete(T, T);
	InRBTree(T);
}

截图如图:

rbt4

如图显示,这里用到了书上图13-4.可以看到,结点1, 5, 7, 8, 14是黑结点.和图13-4显示一样.

另外,我在学习红黑树的过程中,在网上发现了几个不错的资料,这里给大家推荐下:

天枰座的唐风朋友的:

http://liyiwen.iteye.com/blog/345800

http://liyiwen.iteye.com/blog/345799

wangdei的红黑树算法,附AVL树的比较:

http://wangdei.iteye.com/blog/236157

July的红黑树算法层层剖析与逐步实现:

1、教你透彻了解红黑树
2、红黑树算法的实现与剖析
3、红黑树的c源码实现与剖析
4、一步一图一代码,R-B Tree
5、红黑树插入和删除结点的全程演示
6、红黑树的c++完整实现源码

感谢上面的朋友写的这么好的分析文章。

发布者

Tanky Woo

Tanky Woo,[个人主页:https://tankywoo.com] / [新博客:https://blog.tankywoo.com]

《《算法导论》学习总结 — 15. 第13章 红黑树(4)》有2个想法

  1. 博主你好,感谢你的博文,很有参考价值。这段红黑树的程序里面是不是有一个不足,就是红黑树的NIL结点不等于BST的NULL结点,它是有颜色属性的。因此程序里涉及到的NULL其实应该是NIL。否则的话,举个例子,当红黑树删除一个节点z时,假设y是z的后续结点,y没有子女,这时y的父节点应该链接到y->rchild即NIL结点,这个NIL结点会具备两重黑色属性。如果这里是NULL的话,RBDeleteFixup程序里的判断条件while(x!=T && x->color==BLACK)里面的x->color对NULL来说是不存在颜色属性的,有可能影响程序。
    不知道我的说法对不对,呵呵。

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