Bài toán
Cài đặt cây đỏ đen.
Độ phức tạp
chèn : O(logn)
xóa : O(logn)
tìm kiếm : O(logn)
bộ nhớ : O(n)
Code này của Bùi Đức Thiện
#include <bits/stdc++.h>
#define RED 1
#define BLACK 0
typedef bool colour;
using namespace std;
struct node{
node *parent,*left,*right;
int key;
colour color;
};
#define NIL &sentinel /* all leafs are sentinels */
node sentinel = {0,NIL, NIL, 0, BLACK};
node *root;
void rotateLeft(node *x){
if(x->right==NIL) return;
node *y=x->right;
x->right=y->left;
if(y->left!=NIL) y->left->parent=x;
y->parent = x->parent;
if(x!=root){
if(x==x->parent->left)
x->parent->left=y;
else x->parent->right=y;
}
else root=y;
y->left=x;
x->parent=y;
}
void rotateRight(node *x){
if(x->left==NIL) return;
node *y=x->left;
x->left=y->right;
if(y->right!=NIL) y->right->parent=x;
y->parent = x->parent;
if(x!=root){
if(x==x->parent->left)
x->parent->left=y;
else x->parent->right=y;
}
else root=y;
y->right=x;
x->parent=y;
}
void fixinsert(node* x){
while(x!=root&&x->parent->color==RED){
if(x->parent==x->parent->parent->left){
node *y=x->parent->parent->right;
if(y->color==RED){
x->parent->color=BLACK;
y->color=BLACK;
x->parent->parent->color=RED;
x=x->parent->parent;
}
else{
if(x==x->parent->right){
x=x->parent;
rotateLeft(x);
}
x->parent->color=BLACK;
x->parent->parent->color=RED;
rotateRight(x->parent->parent);
}
}
else{
node *y=x->parent->parent->left;
if(y->color==RED){
x->parent->color=BLACK;
y->color=BLACK;
x->parent->parent->color=RED;
x=x->parent->parent;
}
else{
if(x==x->parent->left){
x=x->parent;
rotateRight(x);
}
x->parent->color=BLACK;
x->parent->parent->color=RED;
rotateLeft(x->parent->parent);
}
}
}
root->color=BLACK;
}
void insert(int key){
if(root==NIL){
root=new node;
root->left=NIL;
root->right=NIL;
root->parent=NULL;
root->color=BLACK;
root->key=key;
return;
}
node *parent,*current,*x;
parent=NULL;
current=root;
while(current!=NIL){
if(key==current->key) return;
parent=current;
if(key>current->key) current=current->right;
else current=current->left;
}
x=new node;
x->parent=parent;
x->left=NIL;
x->right=NIL;
x->color=RED;
x->key=key;
if(key>parent->key) parent->right=x;
else parent->left=x;
fixinsert(x);
return;
}
void fixerase(node *x){
while (x != root && x->color == BLACK) {
if (x == x->parent->left) {
node *w = x->parent->right;
if (w->color == RED) {
w->color = BLACK;
x->parent->color = RED;
rotateLeft (x->parent);
w = x->parent->right;
}
if (w->left->color == BLACK && w->right->color == BLACK) {
w->color = RED;
x = x->parent;
} else {
if (w->right->color == BLACK) {
w->left->color = BLACK;
w->color = RED;
rotateRight (w);
w = x->parent->right;
}
w->color = x->parent->color;
x->parent->color = BLACK;
w->right->color = BLACK;
rotateLeft (x->parent);
x = root;
}
} else {
node *w = x->parent->left;
if (w->color == RED) {
w->color = BLACK;
x->parent->color = RED;
rotateRight (x->parent);
w = x->parent->left;
}
if (w->right->color == BLACK && w->left->color == BLACK) {
w->color = RED;
x = x->parent;
} else {
if (w->left->color == BLACK) {
w->right->color = BLACK;
w->color = RED;
rotateLeft (w);
w = x->parent->left;
}
w->color = x->parent->color;
x->parent->color = BLACK;
w->left->color = BLACK;
rotateRight (x->parent);
x = root;
}
}
}
x->color = BLACK;
}
void erase(int key){
node *x,*y,*current;
current=root;
while(current!=NIL){
if(current->key==key) break;
if(key>current->key) current=current->right;
else current=current->left;
}
if(current==NIL) return;
if(current->left==NIL||current->right==NIL){
y=current;
}
else{
y=current->right;
while(y->left!=NIL) y=y->left;
}
if(y->left!=NIL) x=y->left;
else x=y->right;
x->parent=y->parent;
if(y->parent!=NULL){
if(y==y->parent->left)
y->parent->left=x;
else y->parent->right=x;
}
else root=x;
current->key=y->key;
if(y->color==BLACK)
fixerase(x);
free(y);
return;
}
int Min(){
node *current=root;
while(current->left!=NIL) current=current->left;
return current->key;
}
int Max(){
node *current=root;
while(current->right!=NIL) current=current->right;
return current->key;
}
node *succ(int key,bool ch){
node *current=root;
node *ans=NULL;
while(current!=NIL){
if(current->key==key){
if(ch){
ans=current;
return ans;
}
}
else{
if(current->key>key) ans=current;
}
if(current->key>key) current=current->left;
else current=current->right;
}
return ans;
}
node *pred(int key,bool ch){
node *current=root;
node *ans=NULL;
while(current!=NIL){
if(current->key==key){
if(ch){
ans=current;
return ans;
}
}
else{
if(current->key<key) ans=current;
}
if(current->key>=key) current=current->left;
else current=current->right;
}
return ans;
}
#define elif else if
main(){
root=NIL;
ios_base::sync_with_stdio(false);
int x,y;
while(cin>>x&&x){
if(x==1){
cin>>y;
insert(y);
}
elif(x==2){
cin>>y;
erase(y);
}
elif(x==3){
if(root==NIL) printf("empty\n");
else printf("%d\n",Min());
}
elif(x==4){
if(root==NIL) printf("empty\n");
else printf("%d\n",Max());
}
elif(x==5||x==6){
cin>>y;
if(root==NIL) printf("empty\n");
else{
node *r=succ(y,x-5);
if(r==NULL) printf("no\n");
else printf("%d\n",r->key);
}
}
else{
cin>>y;
if(root==NIL) printf("empty\n");
else{
node *r=pred(y,x-7);
if(r==NULL) printf("no\n");
else printf("%d\n",r->key);
}
}
}
}
Nhận xét
Code này đã được dùng để nộp cho một bài tập trên SPOJ.
Cảm ơn bạn Bùi Đức Thiện đã giúp tôi hoàn thành bài viết này