红黑树
性质
- 节点是红色或黑色
- 根节点是黑色
- 所有叶子都是黑色。（叶子是NUIL节点）
- 每个红色节点的两个子节点都是黑色。（从每个叶子到根的所有路径上不能有两个连续的红色节点）
- 从任一节点到其每个叶子的所有路径都包含相同数目的黑色节点
- 如果一个节点的一个子节点是黑色，那么这个节点一定有2个节点。
插入情景
删除情景
Code
enum Color{red,black};
template<typename T>
struct BiTNode{
BiTNode *left;
BiTNode *right;
BiTNode *parent;
Color color;
T val;
int son;
BiTNode():son(0){}
BiTNode(T val):val(val),son(1){
color=red;
parent=NULL;
left=NULL;
right=NULL;
}
BiTNode *grandpa(){
if(parent==NULL)return NULL;
return parent->parent;
}
BiTNode* sibling(){
if(parent->left==this)return parent->right;
return parent->left;
}
BiTNode* uncle(){
if(grandpa()==NULL)return NULL;
if(grandpa()->left==parent)return grandpa()->right;
return grandpa()->left;
}
};
template<typename T,typename node=BiTNode<T>>
class rb_tree{
public:
rb_tree():n(0),root(NULL){
NIL=new node();
NIL->color=black;
}
~rb_tree(){clear(root);delete NIL;}
rb_tree(T* bg,T* ed):n(0),root(NULL){
NIL=new node();
NIL->color=black;
while(bg!=ed)insert(*bg++);
}
bool empty()const{return n==0;}
int size()const{return n;}
void insert(const T& key){insert(root,key);++n;}
void erase(const T& key){remove(root,key);--n;}
bool find(const T& key)const{return search(root,key)!=NULL;}
void clear(){clear(root);n=0;}
T& MIN(){return MIN(root)->val;}
T& MAX(){return MAX(root)->val;}
T kth(int k){
if(k>n)return -1;
node *p=root;
while(p!=NIL){
if(p->left!=NIL){
if(k<=p->left->son)p=p->left;
else{
k-=p->left->son;
if(k==1)return p->val;
k--;
p=p->right;
}
}else{
if(k==1)return p->val;
k--;
p=p->right;
}
}
}
private:
#define is_red(p) ((p)->color==red)
#define is_black(p) ((p)->color==black)
#define set_red(p) ((p)->color=red)
#define set_black(p) ((p)->color=black)
void clear(node* &rt)
{
if(rt==NIL)return;
clear(rt->left);
clear(rt->right);
delete rt;
}
node* search(node* rt,const T& key)
{
if(rt==NULL)return NULL;
node* p=rt;
while(p!=NIL)
{
if(key==p->val)return p;
if(key<p->val)p=p->left;
else p=p->right;
}
return NULL;
}
node* MIN(node* rt)
{
node* p=rt;
while(p->left!=NIL)p=p->left;
return p;
}
node* MAX(node* rt)
{
node* p=rt;
while(p->right!=NIL)p=p->right;
return p;
}
node* suf(node* rt)
{
if(rt->right!=NIL)return MIN(rt->right);
node* p=rt->parent;
while(p&&rt==p->right)rt=p,p=p->parent;
return p;
}
node* pre(node* rt)
{
if(rt->left!=NIL)return MAX(rt->left);
node* p=rt->parent;
while(p&&rt==p->left)rt=p,p=p->parent;
return p;
}
void insert(node* &rt,const T& key){
if(rt==NULL){
rt=new node(key);
rt->left=rt->right=NIL;
set_black(rt);
return;
}
push(rt,key);
}
int num(node* &p){return p==NIL?0:p->son;}
void up_son(node* &p){p->son=num(p->left)+num(p->right)+1;}
bool lson(node* &p){return p->parent->left==p;}
bool rson(node* &p){return p->parent->right==p;}
void push(node* rt,const T& key){
if(key<=rt->val){
if(rt->left!=NIL)push(rt->left,key);
else{
node* p=new node(key);
rt->left=p;
p->parent=rt;
p->left=p->right=NIL;
up_insert(p);
}
}else if(key>rt->val){
if(rt->right!=NIL)push(rt->right,key);
else{
node* p=new node(key);
rt->right=p;
p->parent=rt;
p->left=p->right=NIL;
up_insert(p);
}
}
up_son(rt);
}
void up_insert(node *p){
if(p->parent==NULL){
root=p;
set_black(p);
return;
}
if(is_black(p->parent))return;
if(is_red(p->uncle())){
set_black(p->parent);
set_black(p->uncle());
set_red(p->grandpa());
up_insert(p->grandpa());return;
}
if(lson(p)&&rson(p->parent)){
rotate_right(p);
p=p->right;
}
else if(rson(p)&&lson(p->parent)){
rotate_left(p);
p=p->left;
}
if(lson(p)&&lson(p->parent)){
set_black(p->parent);
set_red(p->grandpa());
rotate_right(p->parent);
}
else if(rson(p)&&rson(p->parent)){
set_black(p->parent);
set_red(p->grandpa());
rotate_left(p->parent);
}
}
void rotate_left(node *p){
node *grandpa=p->grandpa();
node *parent=p->parent;
node *left=p->left;
parent->right=left;
if(left!=NIL)left->parent=parent;
p->left=parent;
parent->parent=p;
p->parent=grandpa;
if(grandpa==NULL)root=p;
else{
if(grandpa->left==parent)
grandpa->left=p;
else grandpa->right=p;
}
up_son(parent);up_son(p);
}
void rotate_right(node *p){
node *grandpa=p->grandpa();
node *parent=p->parent;
node *right=p->right;
parent->left=right;
if(right!=NIL)right->parent=parent;
p->right=parent;
parent->parent=p;
p->parent=grandpa;
if(grandpa==NULL)root=p;
else{
if(grandpa->left==parent)
grandpa->left=p;
else grandpa->right=p;
}
up_son(parent);up_son(p);
}
void remove(node* p,int key){
if(key<p->val)remove(p->left,key);
else if(key>p->val)remove(p->right,key);
else {
if(p->right==NIL){
remove_one(p);
return;
}
node *replace=suf(p);
std::swap(p->val,replace->val);
remove_one(replace);
}
up_son(p);
}
void remove_one(node *p){
node *child=p->left==NIL?p->right:p->left;
if(p->parent==NULL&&p->left==NIL&&p->right==NIL){
p=NULL;
root=p;return;
}
if(p->parent==NULL){
delete p;
child->parent=NULL;
root=child;
set_black(root);return;
}
if(lson(p))p->parent->left=child;
else p->parent->right=child;
child->parent=p->parent;
if(is_black(p)){
if(is_red(child))set_black(child);
else up_remove(child);
}
delete p;
}
void up_remove(node *p){
if(p->parent==NULL){
set_black(p);
return;
}
if(is_red(p->sibling())){
set_red(p->parent);
set_black(p->sibling());
if(lson(p))rotate_left(p->parent);
else rotate_right(p->parent);
}
if(is_black(p->parent)&&is_black(p->sibling()) \
&&is_black(p->sibling()->left)&&is_black(p->sibling()->right)){
set_red(p->sibling());
up_remove(p->parent);
}else if(is_red(p->parent)&&is_black(p->sibling()) \
&&is_black(p->sibling()->left)&&is_black(p->sibling()->right)){
set_red(p->sibling());
set_black(p->parent);
}
else{
if(is_black(p->sibling())){
if(lson(p)&&is_red(p->sibling()->left) \
&&is_black(p->sibling()->right)){
set_red(p->sibling());
set_black(p->sibling()->left);
rotate_right(p->sibling()->left);
}else if(rson(p)&&is_black(p->sibling()->left) \
&&is_red(p->sibling()->right)){
set_red(p->sibling());
set_black(p->sibling()->right);
rotate_left(p->sibling()->right);
}
}
p->sibling()->color=p->parent->color;
set_black(p->parent);
if(lson(p)){
set_black(p->sibling()->right);
rotate_left(p->sibling());
}else{
set_black(p->sibling()->left);
rotate_right(p->sibling());
}
}
}
public:
vector<T> DLR(){vector<T>v;DLR(root,v);return v;}
vector<T> LDR(){vector<T>v;LDR(root,v);return v;}
vector<T> LRD(){vector<T>v;LRD(root,v);return v;}
vector<T> bfs(){vector<T>v;bfs(root,v);return v;}
private:
void bfs(node *Tree,vector<T>&v)
{
if(Tree==NULL)return;
queue<node*>q;
q.push(Tree);
while(!q.empty())
{
node *p=q.front();
v.push_back(p->val);
q.pop();
if(p->left!=NIL)q.push(p->left);
if(p->right!=NIL)q.push(p->right);
}
}
void DLR(node *Tree,vector<T>&v)
{
if(Tree==NULL||Tree==NIL){return ;}
v.push_back(Tree->val);
DLR(Tree->left,v);
DLR(Tree->right,v);
}
void LDR(node *Tree,vector<T>&v)
{
if(Tree==NULL||Tree==NIL){return ;}
LDR(Tree->left,v);
v.push_back(Tree->val);
LDR(Tree->right,v);
}
void LRD(node *Tree,vector<T>&v)
{
if(Tree==NULL||Tree==NIL){return ;}
LRD(Tree->left,v);
LRD(Tree->right,v);
v.push_back(Tree->val);
}
private:
node *root,*NIL;
int n;
};Hello Code 文章被收录于专栏
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