Original link: http://www.cnblogs.com/tanky_woo/archive/2011/05/12/2044548.html

It is suggested to look at the preface first: http://www.cnblogs.com/tanky_woo/archive/2011/04/09/2010263.html

This chapter summarizes the code in the first three chapters, and then recommends some excellent explanation resources of red black tree on the Internet.

Code:

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/*
* Author: Tanky Woo
* Blog:   www.WuTianQi.com
* Description: <Introduction to algorithms Chapter 13 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 is the node to delete, and y is the node to replace z
	if(z->lchild == NULL || z->rchild == NULL)   
		y = z;   // If the z to be deleted has at most one subtree, then y=z;
	else
		y = RBTreeSuccessor(z);  // y is the successor of z
	if(y->lchild != NULL)
		x = y->lchild;  
	else
		x = y->rchild;
	// Unconditional execution p[x] = p[y]
	x->parent = y->parent;  //If y has at most one subtree, then the subtree of Y becomes the subtree of Y's parent node
	if(y->parent == NULL)   // If y does not have a parent node, it means y is the root node, and the dictionary's subtree x is the root node.
		T = x;
	else if(y == y->parent->lchild)   
		// If y is the left subtree of its parent node, then its subtree x becomes the left subtree of its parent node.
		// Otherwise, it becomes a right subtree.
		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 << ": ";
		// Own color
		if(T->color == 0)
			cout << " Color: RED ";
		else
			cout << " Color: BLACK ";
 
		// Color of parent node
		if(T == NULL)
			cout << " Parent: BLACK ";
		else
		{
			if(T->color == 0)
				cout << " Parent: RED ";
			else
				cout << " Parent: BLACK ";
		}
 
		// Color of left son node
		if(T->lchild == NULL)
			cout << " Lchild: BLACK ";
		else
		{
			if(T->lchild->color == 0)
				cout << " Lchild: RED ";
			else
				cout << " Lchild: BLACK ";
		}
 
		// Color of the right son node
		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 << "Search in red black tree order:";
		InRBTree(T);
		cout << endl;
	}
	PrintRBTree(T);
	cout << "After deleting the root node:";
	RBTreeDelete(T, T);
	InRBTree(T);
}

The screenshot is as follows:

As shown in the figure, figure 13-4 is used here. It can be seen that nodes 1, 5, 7, 8 and 14 are black nodes. It is the same as figure 13-4.

In addition, in the process of learning the red black tree, I found several good materials on the Internet. Here is my recommendation:

Tang Feng's friend of Tianzhao:

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

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

Wangdi's red black tree algorithm, with AVL tree comparison:

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

Julie's red black tree algorithm layer by layer analysis and gradual implementation:

1. Teach you a thorough understanding of red and black trees 2. Implementation and analysis of red black tree algorithm 3. Implementation and analysis of c source code of red black tree 4. Step by step, figure by figure, code, R-B Tree 5. Whole process demonstration of inserting and deleting nodes of red black tree 6. Complete source code of c + + for red black tree

 

Thank you for your good analysis.

 

On my own blog: http://www.wutianqi.com/?p=2473

Welcome to learn from each other and make progress!

Reprinted at: https://www.cnblogs.com/tanky'ou woo/archive/2011/05/12/2044548.html