POJ 1442 平衡树Treap模板
2017-03-01 16:28
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题意：输入m个数，询问n个数，第一个数如果是3，就输出在m的第三个数输入完成后第1大的数，第二个就输出第二大的数，但前提都是在输入完U[i]个数后
思路：用平衡树Treap进行插入和查询第K大的数，模版题
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#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
const int inf=0x3f3f3f3f;
const int maxn=100010;
class Treap{
public:
struct Treap_Node{
Treap_Node *left,*right;
int value,fix,weight,size;//fix为修正值，是随机产生的，保证二叉树不会退化的重要环节，wweight为权值，size为子树大小
}*root,*null;
Treap(){
null=new struct Treap_Node;
null->size=0;
null->weight=0;
null->value=inf;
null->left=null;
null->right=null;
null->fix=inf;
root=null;
}
void Treap_Print(Treap_Node *P){//从小到大输出
if(P!=null){
Treap_Print(P->left);
printf("%d\n",P->value);
Treap_Print(P->right);
}
}
void Treap_Left_Rotate(Treap_Node *&a){//左旋之后仍不改变二叉树性质
Treap_Node *b=a->right;
a->right=b->left;
b->left=a;
b->size=a->size;
a->size=a->left->size+a->right->size+a->weight;
a=b;
}
void Treap_Right_Rotate(Treap_Node *&a){//右旋之后仍不改变二叉树性质
Treap_Node *b=a->left;
a->left=b->right;
b->right=a;
b->size=a->size;
a->size=a->left->size+a->right->size+a->weight;
a=b;
}
int Treap_Find(Treap_Node *P,int value){//查找有没有value这个数
if(P==null) return 0;
if(P->value==value) return 1;
else if(value<P->value) return Treap_Find(P->left,value);
else return Treap_Find(P->right,value);
}
void Treap_Insert(Treap_Node *&P,int value){//插入一个数
if(P==null){
P=new Treap_Node;
P->left=P->right=null;//左右儿子均为空
P->value=value;
P->fix=rand();
P->weight=1;
P->size=1;
}else if(value==P->value){
P->weight++;
}
else if(value<P->value){
Treap_Insert(P->left,value);
if(P->left->fix<P->fix)
Treap_Right_Rotate(P);
}else{
Treap_Insert(P->right,value);
if(P->right->fix<P->fix)
Treap_Left_Rotate(P);
}
P->size=P->left->size+P->right->size+P->weight;
}
void Treap_Delete(Treap_Node *&P,int value){//删除一个数
if(P==null) return ;
if(value<P->value) Treap_Delete(P->left,value);
else if(value>P->value) Treap_Delete(P->right,value);
else if(P->weight>1) P->weight--;
else if((P->left==NULL)&&(P->right==NULL)){
delete P;
P=NULL;
}else{
if(P->left->fix<P->right->fix) Treap_Left_Rotate(P);
else Treap_Right_Rotate(P);
Treap_Delete(P,value);
}
P->size=P->left->size+P->right->size+P->weight;
}
int Treap_pred(Treap_Node *P,int value,Treap_Node *optimal){//前驱
if(P==null||value==P->value) return optimal->value;
if(P->value<value) return Treap_pred(P->right,value,P);
else return Treap_pred(P->left,value,optimal);
}
int Treap_succ(Treap_Node *P,int value,Treap_Node *optimal){//后继
if(P==null||value==P->value) return optimal->value;
if(P->value>value) return Treap_succ(P->left,value,P);
else return Treap_succ(P->right,value,optimal);
}
int Treap_Findkth(Treap_Node *P,int k){//求第K大的数
if(P==null) return 0;
int t=P->left->size;
if(k<t+1) return Treap_Findkth(P->left,k);
else if(k>t+P->weight) return Treap_Findkth(P->right,k-(t+P->weight));
else return P->value;
}
int Treap_Rank(Treap_Node *P,int value,int cur){//求这个数的排名
int t=P->left->size;
if(value==P->value) return t+cur+1;
else if(value<P->value) return Treap_Rank(P->left,value,cur);
else return Treap_Rank(P->right,value,t+cur+P->weight);
}
void Treap_erase(Treap_Node *&P) {//将树清空
if(P->left!=null)
Treap_erase(P->left);
if(P->right!=null)
Treap_erase(P->right);
delete P;
}
};
int num[30010],num1[50010];
int main(){
int n,a,b,m;
while(scanf("%d%d",&n,&m)!=-1){
Treap tree;
for(int i=1;i<=n;i++) scanf("%d",&num[i]);
int t=1,k=1;
for(int i=1;i<=m;i++) scanf("%d",&num1[i]);
while(t<=m){
while(k<=num1[t]){
tree.Treap_Insert(tree.root,num[k]);
k++;
}
int ans=tree.Treap_Findkth(tree.root,t++);
printf("%d\n",ans);
}
}
return 0;
}
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#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int inf=0x3f3f3f3f;
const ll INF=0x3f3f3f3f3f3f3f3fll;
const int maxn=15010;
struct Node{
Node *ch[2];
int r,v,s;
Node(int v):v(v){ch[0]=ch[1]=NULL;r=rand();s=1;}
int cmp(int x){
if(x==v) return -1;
return x<v? 0:1;
}
void maintain(){
s=1;
if(ch[0]!=NULL) s+=ch[0]->s;
if(ch[1]!=NULL) s+=ch[1]->s;
}
};
void Rotate(Node* &o,int d){
Node* k=o->ch[d^1];o->ch[d^1]=k->ch[d];k->ch[d]=o;
o->maintain();k->maintain();o=k;
}
void Insert(Node* &o,int x){
if(o==NULL) o=new Node(x);
else{
int d=x<(o->v)? 0:1;
Insert(o->ch[d],x);
if(o->ch[d]->r>o->r) Rotate(o,d^1);
}
o->maintain();
}
void Remove(Node* &o,int x){
int d=o->cmp(x);
if(d
14c77
==-1){
Node* u=o;
if(o->ch[0]!=NULL&&o->ch[1]!=NULL){
int d2=(o->ch[0]->r>o->ch[1]->r?1:0);
Rotate(o,d2);Remove(o->ch[d2],x);
}else{
if(o->ch[0]==NULL) o=o->ch[1];
else o=o->ch[0];
delete u;
}
}else Remove(o->ch[d],x);
if(o!=NULL) o->maintain();
}
int Kth(Node* &o,int k){//第K大的值
if(o==NULL||k<=0||k>o->s) return 0;
int s=(o->ch[0]==NULL?0:o->ch[0]->s);
if(k==s+1) return o->v;
else if(k<=s) return Kth(o->ch[0],k);
else return Kth(o->ch[1],k-s-1);
}
int Rank(Node* &o,int x){//x的排名
if(o==NULL) return -1;//未找到
int num=o->ch[0]==NULL?0:o->ch[0]->s;
if(x==o->v) return num+1;
else if(x<o->v) return Rank(o->ch[0],x);
else return Rank(o->ch[1],x)+num+1;
}
void deletetree(Node* &o){
if(o->ch[0]!=NULL) deletetree(o->ch[0]);
if(o->ch[1]!=NULL) deletetree(o->ch[1]);
delete o;o=NULL;
}
int num[30010],num1[50010];
int main(){
int n,m,a,b;
while(scanf("%d%d",&n,&m)!=-1){
Node* root=NULL;
for(int i=1;i<=n;i++) scanf("%d",&num[i]);
for(int i=1;i<=m;i++) scanf("%d",&num1[i]);
int t=1,k=1;
while(t<=m){
while(k<=num1[t]){
Insert(root,num[k]);
k++;
}
int ans=Kth(root,t++);
printf("%d\n",ans);
}
deletetree(root);
}
return 0;
}
题意：输入m个数，询问n个数，第一个数如果是3，就输出在m的第三个数输入完成后第1大的数，第二个就输出第二大的数，但前提都是在输入完U[i]个数后
思路：用平衡树Treap进行插入和查询第K大的数，模版题
[html] view
plain copy
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
const int inf=0x3f3f3f3f;
const int maxn=100010;
class Treap{
public:
struct Treap_Node{
Treap_Node *left,*right;
int value,fix,weight,size;//fix为修正值，是随机产生的，保证二叉树不会退化的重要环节，wweight为权值，size为子树大小
}*root,*null;
Treap(){
null=new struct Treap_Node;
null->size=0;
null->weight=0;
null->value=inf;
null->left=null;
null->right=null;
null->fix=inf;
root=null;
}
void Treap_Print(Treap_Node *P){//从小到大输出
if(P!=null){
Treap_Print(P->left);
printf("%d\n",P->value);
Treap_Print(P->right);
}
}
void Treap_Left_Rotate(Treap_Node *&a){//左旋之后仍不改变二叉树性质
Treap_Node *b=a->right;
a->right=b->left;
b->left=a;
b->size=a->size;
a->size=a->left->size+a->right->size+a->weight;
a=b;
}
void Treap_Right_Rotate(Treap_Node *&a){//右旋之后仍不改变二叉树性质
Treap_Node *b=a->left;
a->left=b->right;
b->right=a;
b->size=a->size;
a->size=a->left->size+a->right->size+a->weight;
a=b;
}
int Treap_Find(Treap_Node *P,int value){//查找有没有value这个数
if(P==null) return 0;
if(P->value==value) return 1;
else if(value<P->value) return Treap_Find(P->left,value);
else return Treap_Find(P->right,value);
}
void Treap_Insert(Treap_Node *&P,int value){//插入一个数
if(P==null){
P=new Treap_Node;
P->left=P->right=null;//左右儿子均为空
P->value=value;
P->fix=rand();
P->weight=1;
P->size=1;
}else if(value==P->value){
P->weight++;
}
else if(value<P->value){
Treap_Insert(P->left,value);
if(P->left->fix<P->fix)
Treap_Right_Rotate(P);
}else{
Treap_Insert(P->right,value);
if(P->right->fix<P->fix)
Treap_Left_Rotate(P);
}
P->size=P->left->size+P->right->size+P->weight;
}
void Treap_Delete(Treap_Node *&P,int value){//删除一个数
if(P==null) return ;
if(value<P->value) Treap_Delete(P->left,value);
else if(value>P->value) Treap_Delete(P->right,value);
else if(P->weight>1) P->weight--;
else if((P->left==NULL)&&(P->right==NULL)){
delete P;
P=NULL;
}else{
if(P->left->fix<P->right->fix) Treap_Left_Rotate(P);
else Treap_Right_Rotate(P);
Treap_Delete(P,value);
}
P->size=P->left->size+P->right->size+P->weight;
}
int Treap_pred(Treap_Node *P,int value,Treap_Node *optimal){//前驱
if(P==null||value==P->value) return optimal->value;
if(P->value<value) return Treap_pred(P->right,value,P);
else return Treap_pred(P->left,value,optimal);
}
int Treap_succ(Treap_Node *P,int value,Treap_Node *optimal){//后继
if(P==null||value==P->value) return optimal->value;
if(P->value>value) return Treap_succ(P->left,value,P);
else return Treap_succ(P->right,value,optimal);
}
int Treap_Findkth(Treap_Node *P,int k){//求第K大的数
if(P==null) return 0;
int t=P->left->size;
if(k<t+1) return Treap_Findkth(P->left,k);
else if(k>t+P->weight) return Treap_Findkth(P->right,k-(t+P->weight));
else return P->value;
}
int Treap_Rank(Treap_Node *P,int value,int cur){//求这个数的排名
int t=P->left->size;
if(value==P->value) return t+cur+1;
else if(value<P->value) return Treap_Rank(P->left,value,cur);
else return Treap_Rank(P->right,value,t+cur+P->weight);
}
void Treap_erase(Treap_Node *&P) {//将树清空
if(P->left!=null)
Treap_erase(P->left);
if(P->right!=null)
Treap_erase(P->right);
delete P;
}
};
int num[30010],num1[50010];
int main(){
int n,a,b,m;
while(scanf("%d%d",&n,&m)!=-1){
Treap tree;
for(int i=1;i<=n;i++) scanf("%d",&num[i]);
int t=1,k=1;
for(int i=1;i<=m;i++) scanf("%d",&num1[i]);
while(t<=m){
while(k<=num1[t]){
tree.Treap_Insert(tree.root,num[k]);
k++;
}
int ans=tree.Treap_Findkth(tree.root,t++);
printf("%d\n",ans);
}
}
return 0;
}
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#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int inf=0x3f3f3f3f;
const ll INF=0x3f3f3f3f3f3f3f3fll;
const int maxn=15010;
struct Node{
Node *ch[2];
int r,v,s;
Node(int v):v(v){ch[0]=ch[1]=NULL;r=rand();s=1;}
int cmp(int x){
if(x==v) return -1;
return x<v? 0:1;
}
void maintain(){
s=1;
if(ch[0]!=NULL) s+=ch[0]->s;
if(ch[1]!=NULL) s+=ch[1]->s;
}
};
void Rotate(Node* &o,int d){
Node* k=o->ch[d^1];o->ch[d^1]=k->ch[d];k->ch[d]=o;
o->maintain();k->maintain();o=k;
}
void Insert(Node* &o,int x){
if(o==NULL) o=new Node(x);
else{
int d=x<(o->v)? 0:1;
Insert(o->ch[d],x);
if(o->ch[d]->r>o->r) Rotate(o,d^1);
}
o->maintain();
}
void Remove(Node* &o,int x){
int d=o->cmp(x);
if(d
14c77
==-1){
Node* u=o;
if(o->ch[0]!=NULL&&o->ch[1]!=NULL){
int d2=(o->ch[0]->r>o->ch[1]->r?1:0);
Rotate(o,d2);Remove(o->ch[d2],x);
}else{
if(o->ch[0]==NULL) o=o->ch[1];
else o=o->ch[0];
delete u;
}
}else Remove(o->ch[d],x);
if(o!=NULL) o->maintain();
}
int Kth(Node* &o,int k){//第K大的值
if(o==NULL||k<=0||k>o->s) return 0;
int s=(o->ch[0]==NULL?0:o->ch[0]->s);
if(k==s+1) return o->v;
else if(k<=s) return Kth(o->ch[0],k);
else return Kth(o->ch[1],k-s-1);
}
int Rank(Node* &o,int x){//x的排名
if(o==NULL) return -1;//未找到
int num=o->ch[0]==NULL?0:o->ch[0]->s;
if(x==o->v) return num+1;
else if(x<o->v) return Rank(o->ch[0],x);
else return Rank(o->ch[1],x)+num+1;
}
void deletetree(Node* &o){
if(o->ch[0]!=NULL) deletetree(o->ch[0]);
if(o->ch[1]!=NULL) deletetree(o->ch[1]);
delete o;o=NULL;
}
int num[30010],num1[50010];
int main(){
int n,m,a,b;
while(scanf("%d%d",&n,&m)!=-1){
Node* root=NULL;
for(int i=1;i<=n;i++) scanf("%d",&num[i]);
for(int i=1;i<=m;i++) scanf("%d",&num1[i]);
int t=1,k=1;
while(t<=m){
while(k<=num1[t]){
Insert(root,num[k]);
k++;
}
int ans=Kth(root,t++);
printf("%d\n",ans);
}
deletetree(root);
}
return 0;
}
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