Submission #899481

#	Time	Username	Problem	Language	Result	Execution time	Memory
899481		JakobZorz	Aliens (IOI16_aliens)	C++17	100 / 100	969 ms	202120 KiB

aliens

#include"aliens.h"
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;

struct Line{
    ll a,b;
    int min_pics,max_pics;
};
 
ll eval(Line l,ll x){
    return l.a*x+l.b;
}
 
struct CHT{
    int l,r;
    CHT*ch1,*ch2;
    Line cl;
    
    CHT(int l,int r):l(l),r(r),ch1(nullptr),ch2(nullptr){
        cl.a=0;
        cl.b=1e18;
    }
    
    void add(Line line){
        int mid=(l+r)/2;
        if(eval(line,mid)<eval(cl,mid))
            swap(line,cl);
        
        if(eval(line,mid)==eval(cl,mid)&&eval(line,l)==eval(cl,l)){
            cl.min_pics=min(cl.min_pics,line.min_pics);
            cl.max_pics=max(cl.max_pics,line.max_pics);
            return;
        }
        
        if(l<r-1){
            if(eval(line,l)<eval(cl,l)){
                if(ch1==nullptr)
                    ch1=new CHT(l,mid);
                ch1->add(line);
            }
            
            if(eval(line,r)<eval(cl,r)){
                if(ch2==nullptr)
                    ch2=new CHT(mid,r);
                ch2->add(line);
            }
        }
    }
    
    pair<ll,pair<int,int>>get(ll x){
        int mid=(l+r)/2;
        pair<ll,pair<int,int>>res={eval(cl,x),{cl.min_pics,cl.max_pics}};
        if(x>=mid&&ch2){
            auto res2=ch2->get(x);
            if(res2.first<res.first){
                res=res2;
            }else if(res2.first==res.first){
                res.second.first=min(res.second.first,res2.second.first);
                res.second.second=max(res.second.second,res2.second.second);
            }
        }
        if(x<mid&&ch1){
            auto res2=ch1->get(x);
            if(res2.first<res.first){
                res=res2;
            }else if(res2.first==res.first){
                res.second.first=min(res.second.first,res2.second.first);
                res.second.second=max(res.second.second,res2.second.second);
            }
        }
        return res;
    }
};
 
int n;
vector<ll>l,r;
 
ll sq(ll x){
    return x*x;
}
 
bool cmp(pair<int,int>a,pair<int,int>b){
    if(a.first==b.first)
        return a.second>b.second;
    return a.first<b.first;
}

// (points, num of pictures) if pictures are unlimited but have a specific cost
// num of picures will be minimal and maximal while still having optimal points
pair<ll,pair<int,int>>get(ll cost){
    vector<ll>dp(n+1); // optimum for first i intervals
    vector<pair<int,int>>num_pic(n+1);
    CHT cht(0,1<<20);
    for(int i=1;i<=n;i++){
        Line line;
        line.b=l[i-1]*l[i-1]+dp[i-1]+cost;
        if(i!=1)
            line.b-=sq(max(0LL,r[i-2]-l[i-1]));
        line.a=-2*l[i-1];
        line.min_pics=num_pic[i-1].first+1;
        line.max_pics=num_pic[i-1].second+1;
        cht.add(line);
        
        auto res=cht.get(r[i-1]);
        res.first+=r[i-1]*r[i-1];
        
        dp[i]=res.first;
        num_pic[i]=res.second;
        //cout<<"res1 "<<dp[i]<<" "<<num_pic[i].first<<" "<<num_pic[i].second<<endl;
        
        /*dp[i]=1e18;
        for(int j=0;j<i;j++){
            ll curr=r[i-1]*r[i-1]-2*l[j]*r[i-1]+l[j]*l[j];
            curr+=dp[j];
            curr+=cost;
            if(j)
                curr-=sq(max(0LL,r[j-1]-l[j]));
            
            if(curr<dp[i]){
                dp[i]=curr;
                num_pic[i].first=num_pic[j].first+1;
                num_pic[i].second=num_pic[j].second+1;
            }else if(curr==dp[i]){
                num_pic[i].first=min(num_pic[i].first,num_pic[j].first+1);
                num_pic[i].second=max(num_pic[i].second,num_pic[j].second+1);
            }
        }*/
        
        //cout<<"res2 "<<dp[i]<<" "<<num_pic[i].first<<" "<<num_pic[i].second<<endl;
        //cout<<"\n";
    }
    return{dp[n],num_pic[n]};
}

ll take_photos(int N,int m,int k,vector<int>R,vector<int>C){
    n=N;
    vector<pair<int,int>>intervals_sorted;
    for(int i=0;i<n;i++){
        if(R[i]>C[i])
            swap(R[i],C[i]);
        intervals_sorted.emplace_back(R[i],C[i]);
    }
    sort(intervals_sorted.begin(),intervals_sorted.end(),cmp);
    int right_done=-1;
    for(auto i:intervals_sorted){
        if(i.second>right_done){
            l.push_back(i.first);
            r.push_back(i.second+1);
            right_done=i.second;
        }
    }
    n=(int)l.size();
    
    k=min(n,k);
    
    ll l=0,r=(ll)m*m+1;
    ll opt;
    while(true){
        ll mid=(l+r)/2;
        auto res=get(mid);
        //cout<<mid<<": "<<res.first<<" "<<res.second.first<<" "<<res.second.second<<endl;
        if(res.second.first>k)
            l=mid;
        if(res.second.second<k)
            r=mid;
        if(res.second.first<=k&&k<=res.second.second){
            opt=mid;
            break;
        }
    }
    
    //cout<<"opt "<<opt<<"\n";
    auto res=get(opt);
    ll ret=res.first-opt*k;
    
    return ret;
}

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 40 / 40