红黑树插入算法的实现

思想：将插入的节点着色为红色插入红黑树中，然后再调用一个辅助程序对节点重新着色并旋转以保证红黑树的性质得以继续保持。调整程序主要处理为三种情况

CASE1：当前调整节点的叔叔是红色的。

CASE2：当前调整节点的叔叔是黑色的，而且当前调整节点是右孩子。

CASE3：当前调整节点的叔叔是黑色的，而且当前调整节点是左孩子。

结果：随机产生1000个数据，输出红黑树的高度

源码：

head.h：

#include<stdio.h>
#include<stdlib.h>
#include<time.h>

enum rb_color {RED,BLACK};

typedef struct node{
int key;
struct node * left;
struct node * right;
struct node * parent;
enum rb_color  color;
}RBNode, *RBTree;

RBTree NIL;
void Init();
RBTree  Creat_Node(RBTree*,int);
void Left_Rotate(RBTree*,RBTree);
void Right_Rotate(RBTree*,RBTree);
void RB_Insert(RBTree*,RBTree);
void RB_Insert_Fixup(RBTree*,RBTree);
void Inorder(RBTree );
void Preorder(RBTree );
int  height(RBTree );

rbtree.c

#include "head.h"

void Init(){
NIL = (RBTree)malloc(sizeof(RBNode));
NIL->key = 0;
NIL->left= NULL;
NIL->parent = NULL;
NIL->right = NULL;
NIL->color = BLACK;
}

RBTree Creat_Node(RBTree *pnode,int key){
if(((*pnode) = (RBTree)malloc(sizeof(RBNode)))!=NULL){
(*pnode)->key = key;
(*pnode)->left = NIL;
(*pnode)->right = NIL;
(*pnode)->parent = NIL;
(*pnode)->color = RED;
return *pnode;
}
else return NULL;
}

void Left_Rotate(RBTree * T,RBTree pnode){

RBTree temp = pnode->right;
pnode->right = temp->left;
if(temp->left!=NIL)
temp->left->parent = pnode;
temp->parent = pnode->parent;
if(pnode->parent==NIL)
*T = temp;
else if(pnode->parent->left==pnode)
pnode->parent->left = temp;
else
pnode->parent->right = temp;
temp->left = pnode;
pnode->parent = temp;
}

void Right_Rotate(RBTree * T,RBTree pnode){

RBTree temp = pnode->left;
pnode->left = temp->right;
if(temp->right!=NIL)
temp->right->parent = pnode;
temp->parent = pnode->parent;
if(pnode->parent==NIL)
*T = temp;
else if(pnode->parent->left==pnode)
pnode->parent->left = temp;
else
pnode->parent->right = temp;
temp->right = pnode;
pnode->parent = temp;

}

void RB_Insert(RBTree *T,RBTree pnode){

RBTree ptemp = *T,qtemp = NIL;
//if(pnode==NULL) {printf("pnode is null\n");return;}
while(ptemp!=NIL){
qtemp = ptemp;
if(pnode->key < ptemp->key)
ptemp = ptemp->left;
else
ptemp = ptemp->right;
}
pnode->parent = qtemp;
if(qtemp == NIL)
*T = pnode;
else if (pnode->key > qtemp->key)
qtemp->right = pnode;
else
qtemp->left = pnode;
pnode->left = NIL;
pnode->right = NIL;
pnode->color = RED;
RB_Insert_Fixup(T,pnode);
}

void RB_Insert_Fixup(RBTree* T,RBTree pnode){

RBTree ptemp = NULL;
while(pnode->parent->color==RED){

if(pnode->parent==pnode->parent->parent->left){
ptemp = pnode->parent->parent->right;
if(ptemp->color==RED){
pnode->parent->color = BLACK;
pnode->parent->parent->color = RED;
ptemp->color = BLACK;
pnode = pnode->parent ->parent ;
}
else{
if(pnode->parent->right==pnode){  //case2:
pnode = pnode->parent ;
Left_Rotate(T,pnode);
}
pnode->parent->color = BLACK;
pnode->parent->parent->color = RED;
Right_Rotate(T,pnode->parent->parent);
}
}//if
else{
ptemp = pnode->parent->parent->left;
if(ptemp->color==RED){
pnode->parent->color = BLACK;
pnode->parent->parent->color = RED;
ptemp->color = BLACK;
pnode = pnode->parent ->parent ;
}
else{
if(pnode->parent->left==pnode){  //case2:
pnode = pnode->parent ;
Right_Rotate(T,pnode);
}
pnode->parent->color = BLACK;
pnode->parent->parent->color = RED;
Left_Rotate(T,pnode->parent->parent);
}
}//else
}//while
(*T)->color = BLACK;
}

void Inorder(RBTree T){
if(T!=NIL){
Inorder(T->left);
printf("key:%d \tcolor:%s\n",T->key,T->color?"BLACK":"RED");
Inorder(T->right);
}
}

void Preorder(RBTree T){
if(T!=NIL){
printf("key:%d \tcolor:%s\n",T->key,T->color?"BLACK":"RED");
Preorder(T->left);
Preorder(T->right);
}
}

int  height(RBTree T){

int left,right;
if(T==NIL) return 0;
left = height(T->left);
right = height(T->right);
return left>right?left+1:right+1;
}

main.c:

#include"head.h"

int main(){
RBTree T ,pnode;
int i,k;
Init();
T = NIL;
pnode = NULL;
srand((unsigned)time(NULL));
for(i = 0;i<1000;i++){
k=rand() % 5000;
if(Creat_Node(&pnode,k)==NULL){
printf("fail to creat node...\n");
exit(1);
}
RB_Insert(&T,pnode);
}
printf("InOrder:\n");
Inorder(T);
printf("\nPreOrder:\n");
Preorder(T);
printf("\nheight:%d",height(T));
}