紅黑樹的建立，插入，刪除
這個東西真的是很喜歡，但是學習了很長一段時間都很糊塗，先寫了一個沒有任何考慮特殊情況的紅黑樹，以後再想其他的吧。至於紅黑樹的擴張以後再想吧。
#include <stdio.h>
#include <malloc.h>
#define MAX 99999999
#define MIN -99999999
/*
國慶在家無聊ing，由此學習一些樹的資料結構，深深的為這些資料結構所震撼，牛呀。
描述了紅黑樹的插入刪除操作，這個資料結構真是變態，不過很好用，是可以擴充的樹，喜歡！！！
在隨機的插入下，其搜尋時間複雜度為O(lgn)，這個是普通二叉樹不可以相比的，
之前和好多平衡樹 ，區間樹也是紅黑樹的擴充，當時看的很糊塗，現在終於理清楚了！！！
2007-10-04
*/
struct node
{
long key;
char color;
struct node *p;
struct node *left;
struct node *right;
};
struct node *head;
struct node *nil;
void INORDER_TREE_WALK(struct node* x) //中根遍歷
{
//printf("%ld %c ",x->key,x->color); //debug 先根遍歷
if(x->left!=nil) INORDER_TREE_WALK(x->left);
printf("%ld %c ",x->key,x->color);
if(x->right!=nil) INORDER_TREE_WALK(x->right);
}
struct node *TREE_SEARCH(struct node* x,long k) //查詢關鍵位元組點
{
if(x==nil||x->key==k) return x;
else if(k<x->key) return TREE_SEARCH(x->left,k);
else return TREE_SEARCH(x->right,k);
}
struct node *TREE_MINIMUM(struct node* x) //查詢最小節點
{
while(x->left!=nil)
x=x->left;
return x;
}
struct node *TREE_MAXIMUM(struct node* x) //查詢最大節點
{
while(x->right!=nil)
x=x->right;
return x;
}
struct node *TREE_SUCCESSOR(struct node* x) //查詢後繼
{
if(x->right!=nil) return TREE_MINIMUM(x->right);
struct node* y=x->p;
while(y!=nil&&x==y->right)
{
x=y;
y=y->p;
}
return y;
}
struct node *LEFT_ROTATY(struct node *head,struct node *x) //左旋轉
{
struct node *y=x->right;
x->right=y->left;
if(y->left!=nil) y->left->p=x;
y->p=x->p;
if(x->p==nil) head=y;
else if(x==x->p->left) x->p->left=y;
else x->p->right=y;
y->left=x;
x->p=y;
return head;
}
struct node *RIGHT_ROTATY(struct node *head,struct node *x) //右旋轉
{
struct node *y=x->left;
x->left=y->right;
if(y->right!=nil) y->right->p=x;
y->p=x->p;
if(x->p==nil) head=y;
else if(x==x->p->left) x->p->left=y;
else x->p->right=y;
y->right=x;
x->p=y;
return head;
}
struct node *RB_INSERT_FIXUP(struct node *head,struct node *z)
{
//INORDER_TREE_WALK(head);
// printf(" insert/n");
struct node *y=nil;
while(z->p->color=='R')
{
if(z->p==z->p->p->left)
{
y=z->p->p->right;
if(y->color=='R')
{
z->p->color='B';
y->color='B';
z->p->p->color='R';
z=z->p->p;
}
else if(z==z->p->right)
{
z=z->p;
head=LEFT_ROTATY(head,z);
// INORDER_TREE_WALK(head);
// printf(" left/n");
// getchar();
}
if(z!=head)
{
z->p->color='B';
z->p->p->color='R';
head=RIGHT_ROTATY(head,z->p->p);
}
else
head=RIGHT_ROTATY(head,head);
// INORDER_TREE_WALK(head);
// printf(" right/n");
// getchar();
}
else
{
y=z->p->p->left;
if(y->color=='R')
{
z->p->color='B';
y->color='B';
z->p->p->color='R';
z=z->p->p;
}
else if(z==z->p->left)
{
z=z->p;
head=RIGHT_ROTATY(head,z);
}
z->p->color='B';
z->p->p->color='R';
head=LEFT_ROTATY(head,z->p->p);
}
}
head->color='B';
return head;
}
struct node *RB_INSERT(struct node *head,struct node *z)
{
struct node *y=nil;
struct node *x=head;
while(x!=nil)
{
y=x;
if(z->key<x->key) x=x->left;
else x=x->right;
}
z->p=y;
if(y==nil) head=z;
else if(y->key>z->key) y->left=z;
else y->right=z;
//INORDER_TREE_WALK(head);
//printf(" insert/n");
head=RB_INSERT_FIXUP(head,z);
return head;
}
struct node *RB_DELETE_FIXUP(struct node *head,struct node *x)
{
struct node *w;
while(x!=head&&x->color=='B')
{
if(x==x->p->left) //如果x為左兒子
{
w=x->p->left; //用w表示x的叔叔
if(w->color=='R') //當叔叔節點顏色為紅時，需要處理顏色並左旋轉轉入下述情況
{
w->color='B';
x->p->color='R';
head=LEFT_ROTATY(head,x->p);
w=x->p->right;
}
if(w->left->color=='B'&&w->right->color=='B') //當叔叔的孩子都為黑孩子時
{
w->color='R';
x=x->p;
}
else if(w->right->color=='R') //當叔叔的孩子只有右孩子為黑孩子時，要右旋轉轉入下述情況
{
w->left->color='B'; //交換w和他左孩子的顏色並左旋
w->color='R';
head=RIGHT_ROTATY(head,w);
w=x->p->right;
} //經過以上步驟使得x兄弟w是黑色，而且w的右孩子是紅色的
w->color=x->p->color;
x->p->color='B';
w->right->color='B';
head=LEFT_ROTATY(head,x->p);
}
else
{
w=x->p->right;
if(w->color=='R')
{
w->color='B';
x->p->color='R';
head=RIGHT_ROTATY(head,x->p);
w=x->p->left;
}
if(w->left->color=='B'&&w->right->color=='B')
{
w->color='R';
x=x->p;
}
else if(w->left->color=='R')
{
w->right->color='B';
w->color='R';
head=LEFT_ROTATY(head,w);
w=x->p->left;
}
w->color=x->p->color;
x->p->color='B';
w->left->color='B';
head=RIGHT_ROTATY(head,x->p);
}
x->color='B';
}
return head;
}
struct node *RB_DELETE(struct node *head,struct node *z)
{
struct node *x,*y;
if(z->left==nil||z->right==nil) y=z;
else y=TREE_SUCCESSOR(z);
if(y->left!=nil) x=y->left;
else x=y->right;
if(x!=nil) x->p=y->p;
if(y->p==nil) head=x;
else if(y==y->p->left) y->p->left=x;
else y->p->right=x;
if(y!=z)
{
z->key=y->key;
z->color=y->color;
}
if(y->color=='B')
head=RB_DELETE_FIXUP(head,x);
return head;
}
struct node *NODE_CREAT(long k) //建立節點
{
struct node *tmp;
tmp=(struct node*)malloc(sizeof(struct node));
tmp->left=nil;
tmp->right=nil;
tmp->p=nil;
tmp->color='R';
tmp->key=k;
return tmp;
}
void NIL_CREAT()
{
nil=(struct node*)malloc(sizeof(struct node));
nil->key=MIN;
nil->color='B';
nil->p=nil;
nil->left=nil;
nil->right=nil;
}
int main()
{
long n,t,a[10]={4,1,3,2,16,9,10,14,8,7,};
struct node *ty;
NIL_CREAT();
head=nil;
ty=nil;
for(int i=0;i<10;i++)
head=RB_INSERT(head,NODE_CREAT(a[i]));
INORDER_TREE_WALK(head);
printf(" done/n");
while(scanf("%ld",&n)==1&&n)
{
ty=TREE_SEARCH(head,n);
head=RB_DELETE(head,ty);
INORDER_TREE_WALK(head);
printf("/n");
}
return 0;
}