因为看内核的时候感觉红黑树挺有意思的，所以利用周末的时间来实现一下玩玩。红黑树的操作主要是插入和删除，而删除的时候需要考虑的情况更多一些。具体的操作就不在这里罗嗦了，百度文库里面有一个比较有好的文章，已经说的很明白了。
在看具体的操作的时候有的人可能感觉有些情况是没有考虑到的（如果没有这种感觉的人很有可能根本没有仔细地想）。但是那些“遗漏”的情况如果存在的话，操作之前的红黑树将违反那几个规则。
写代码的时候很多次因为少考虑情况而导致错误，细节比较多，刚开始rb_node中没有指向父节点的指针，写的快吐血，然后还是加上了。代码具体的含义可以结合文章和注释来看（还是很好理解的）。下面的代码中可能还有没有考虑到的细节，欢迎拍砖。
#include <stdio.h>
#include <stdlib.h>
const int RED = 0;
const int BLACK = 1;
struct rb_node{
rb_node* lchild, *rchild, *parent;
int key, colour;
};
rb_node* root;
rb_node* get_node(rb_node* parent, int key);
void rb_insert(int key);
rb_node* rb_search(int key);
void rb_delete(int key);
rb_node* clock_wise(rb_node* node);
rb_node* counter_clock_wise(rb_node* node);
void show_rb_tree(rb_node* node);
rb_node* get_node(rb_node* parent, int key){
rb_node *tmp = (rb_node*)malloc(sizeof(rb_node));
tmp->key = key;
tmp->colour = RED;
tmp->parent = parent;
tmp->lchild = tmp->rchild = NULL;
return tmp;
}
rb_node* clock_wise(rb_node* node){
if(node == NULL || node->lchild == NULL)
return NULL;
rb_node *rb_1=node, *rb_2=node->lchild, *rb_3=node->lchild->rchild;
if(rb_1->parent != NULL){
if(rb_1->parent->lchild == rb_1)
rb_1->parent->lchild = rb_2;
else
rb_1->parent->rchild = rb_2;
}else if(rb_1 == root){
root = rb_2;
}
rb_2->parent = rb_1->parent;
rb_1->parent = rb_2;
rb_2->rchild = rb_1;
rb_1->lchild = rb_3;
if(rb_3 != NULL)rb_3->parent = rb_1;
return rb_2;
}
rb_node* counter_clock_wise(rb_node* node){
if(node == NULL || node->rchild == NULL)
return NULL;
rb_node *rb_1=node, *rb_2=node->rchild, *rb_3=node->rchild->lchild;
if(rb_1->parent != NULL){
if(rb_1->parent->lchild == rb_1)
rb_1->parent->lchild = rb_2;
else
rb_1->parent->rchild = rb_2;
}
else if(rb_1 == root){
root = rb_2;
}
rb_2->parent = rb_1->parent;
rb_1->parent = rb_2;
rb_2->lchild = rb_1;
rb_1->rchild = rb_3;
if(rb_3 != NULL)rb_3->parent = rb_1;
return rb_2;
}
rb_node* rb_search(int key){
rb_node *p = root;
while(p != NULL){
if(key < p->key)
p = p->lchild;
else if(key > p->key)
p = p->rchild;
else
break;
}
return p;
}
void rb_insert(int key){
rb_node *p=root, *q=NULL;
if(root == NULL){
root = get_node(NULL, key);
root->colour = BLACK;
return;
}
while(p != NULL){
q = p;
if(key < p->key)
p = p->lchild;
else if(key > p->key)
p = p->rchild;
else return;
}
if(key < q->key)
q->lchild = get_node(q, key);
else
q->rchild = get_node(q, key);
while(q != NULL && q->colour == RED){
p = q->parent;//p won't null, or BUG.
if(p->lchild == q){
if(q->rchild != NULL && q->rchild->colour == RED)
counter_clock_wise(q);
q = clock_wise(p);
q->lchild->colour = BLACK;
}
else{
if(q->lchild != NULL && q->lchild->colour == RED)
clock_wise(q);
q = counter_clock_wise(p);
q->rchild->colour = BLACK;
}
q = q->parent;
}
root->colour = BLACK;
}
void show_rb_tree(rb_node* node){
if(node == NULL)
return;
printf("(%d,%d)\n", node->key, node->colour);
if(node->lchild != NULL){
printf("[-1]\n");
show_rb_tree(node->lchild);
}
if(node->rchild != NULL){
printf("[1]\n");
show_rb_tree(node->rchild);
}
printf("[0]\n");
}
void rb_delete(int key){
rb_node *v = rb_search(key), *u, *p, *c, *b;
int tmp;
if(v == NULL) return;
u = v;
if(v->lchild != NULL && v->rchild != NULL){
u = v->rchild;
while(u->lchild != NULL){
u = u->lchild;
}
tmp = u->key;
u->key = v->key;
v->key = tmp;
}
//u is the node to free.
if(u->lchild != NULL)
c = u->lchild;
else
c = u->rchild;
p = u->parent;
if(p != NULL){
//remove u from rb_tree.
if(p->lchild == u)
p->lchild = c;
else
p->rchild = c;
}
else{
//u is root.
root = c;
free((void*)u);
return;
}
//u is not root and u is RED, this will not unbalance.
if(u->colour == RED){
free((void*)u);
return;
}
free((void*)u);
u = c;
//u is the first node to balance.
while(u != root){
if(u != NULL && u->colour == RED){
//if u is RED, change it to BLACK can finsh.
u->colour = BLACK;
return;
}
if(u == p->lchild)
b = p->rchild;
else
b = p->lchild;
printf("%d\n", b->key);
//b is borther of u. b can't be null, or the rb_tree is must not balance.
if(b->colour == BLACK){
//If b's son is RED, rotate the node.
if(b->lchild != NULL && b->lchild->colour == RED){
if(u == p->lchild){
b = clock_wise(b);
b->colour = BLACK;
b->rchild->colour = RED;
p = counter_clock_wise(p);
p->colour = p->lchild->colour;
p->lchild->colour = BLACK;
p->rchild->colour = BLACK;
}
else{
p = clock_wise(p);
p->colour = p->rchild->colour;
p->rchild->colour = BLACK;
p->lchild->colour = BLACK;
}
return;
}
else if(b->rchild != NULL && b->rchild->colour == RED){
if(u == p->rchild){
b = counter_clock_wise(b);
b->colour = BLACK;
b->lchild->colour = RED;
p = clock_wise(p);
p->colour = p->rchild->colour;
p->rchild->colour = BLACK;
p->lchild->colour = BLACK;
}
else{
p = counter_clock_wise(p);
p->colour = p->lchild->colour;
p->lchild->colour = BLACK;
p->rchild->colour = BLACK;
}
return;
}
else{//if b's sons are BLACK, make b RED and move up u.
b->colour = RED;
u = p;
p = u->parent;
continue;
}
}
else{
if(u == p->lchild){
p = counter_clock_wise(p);
p->colour = BLACK;
p->lchild->colour = RED;
p = p->lchild;
}
else{
p = clock_wise(p);
p->colour = BLACK;
p->rchild->colour = RED;
p = p->rchild;
}
}
}
root->colour = BLACK;
}
int main(){
int i;
root = NULL;
for(i = 1; i <= 10; i++){
rb_insert(i);
}
rb_delete(9);
rb_delete(3);
rb_delete(7);
show_rb_tree(root);
printf("\n");
return 0;
}
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