极角排序+凸包性质——cf1254C

#include<bits/stdc++.h>
using namespace std;
typedef double db;
const db eps=1e-6;
const db pi=acos(-1);

int n;
struct Node{
    int id;db h;
    Node(){}
    Node(int id,db h):id(id),h(h){}
};
int cmp1(Node a,Node b){return a.h<b.h;}
int cmp2(Node a,Node b){return a.h>b.h;} 
vector<Node>v1,v2,v3,v4,v5;
db ask2(int i,int j,int k){//aiaj 和 aiak的叉积 
    cout<<2<<" "<<i<<" "<<j<<" "<<k<<endl;
    db res;
    cin>>res;
    return res;
}
db ask1(int i,int j,int k){//aiaj 和 aiak的叉积 
    cout<<1<<" "<<i<<" "<<j<<" "<<k<<endl;
    db res;
    cin>>res;
    return res;
}
vector<int>ans;
int main(){
    cin>>n;
    for(int i=3;i<=n;i++){
        db res=ask2(1,2,i);db ress=ask1(1,2,i);
        if(res>0)v1.push_back(Node(i,ress));//在a1a2左侧 
        else v2.push_back(Node(i,ress));//在a1a2右侧 
        if(fabs(ress)-fabs(res)>eps)return 0;
    }
    ans.push_back(1);
    int mid=0;
    double Max=-1e16;
    for(auto x:v2){if(x.h>Max)mid=x.id,Max=x.h;}
    for(auto x:v2){
        if(x.id==mid)continue;
        db res=ask2(1,mid,x.id);
        if(res>0)v4.push_back(x);//在1-mid段 
        else v3.push_back(x);//在mid-2段 
    }
    sort(v3.begin(),v3.end(),cmp1);//按h升序 
    sort(v4.begin(),v4.end(),cmp2);//按h降序
    for(auto x:v3)ans.push_back(x.id);
    if(mid)ans.push_back(mid);
    for(auto x:v4)ans.push_back(x.id);
    v5=v4;
    
    ans.push_back(2);
    v3.clear();v4.clear();
    Max=-1e16;
    mid=0;
    for(auto x:v1){if(x.h>Max)mid=x.id,Max=x.h;}
    for(auto x:v1){
        if(x.id==mid)continue;
        db res=ask2(1,mid,x.id);
        if(res>0)v4.push_back(x);//在mid-1段 
        else v3.push_back(x); //在2-mid段 
    }
    sort(v3.begin(),v3.end(),cmp1);//按h升序 
    sort(v4.begin(),v4.end(),cmp2);//按h降序
    for(auto x:v3)ans.push_back(x.id);
    if(mid)ans.push_back(mid);
    for(auto x:v4)ans.push_back(x.id);
    
    cout<<0<<" ";
    for(auto x:ans)cout<<x<<" "; 
    
}