Submission #328876

#	Time	Username	Problem	Language	Result	Execution time	Memory
328876		tnk2908	Aliens (IOI16_aliens)	C++14	100 / 100	153 ms	12644 KiB

aliens

//
//  main.cpp
//  aliens
//
//  Created by Trần Nam Khánh on 11/18/20.
//

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
struct ed
{
    long long a,b,minsq;
};
struct pt
{
    long long r,c;
};
vector<ed>ch;
vector<pt>a,b;
vector<pair<long long,long long> >g;
long long n,m,k;
long long check(ed a,ed b,ed c)
{
    //(c.b-b.b)/(b.a-c.a)
    //(b.b-a.b)/(a.a-b.a)
    return (b.b-a.b)*(b.a-c.a)>=(c.b-b.b)*(a.a-b.a);
}
void add(long long x,long long y,long long mi)
{
    ed a;
    a.a=x;
    a.b=y;
    a.minsq=mi;
    while(ch.size()>=2&&check(ch[ch.size()-2],ch[ch.size()-1],a))
    {
        ch.pop_back();
    }
    ch.push_back(a);
}
long long dis(long long x,ed a,ed b)
{
    //(b.b-a.b)/(a.a-b.a)
    return (b.b-a.b)-x*(a.a-b.a);
}
pair<long long,long long> cal(long long c){
    g.clear();
    g.resize(n+1);
    ch.clear();
    g[0]={0,0};
    long long l=0;
    for(long long i=1;i<=n;i++)
    {
        long long tmp=(a[i].c-a[i].r+1)*(a[i].c-a[i].r+1)+g[i-1].first;
        long long tam=max(0ll,a[i-1].c-a[i].r+1);
        tmp-=tam*tam;
        long long A=-2*a[i].r+2,B=tmp+2*a[i].r*a[i].c-a[i].c*a[i].c-2*a[i].c;
        add(A,B,g[i-1].second);
        long long X=a[i].c;
        if(ch.size()&&l>=ch.size())l=ch.size()-1;
        while(l+1<ch.size()&&dis(X,ch[l],ch[l+1])<0)
        {
            l++;
        }
        g[i].first=ch[l].a*a[i].c+ch[l].b+a[i].c*a[i].c+c;
        g[i].second=ch[l].minsq+1;
    }
    return g[n];
}
long long cmp(pt a,pt b)
{
    return (a.c<b.c)||(a.c==b.c&&a.r>b.r);
}
long long cal2()
{
    long long lo=0,hi=m*m,ans=0;
    while(lo<hi)
    {
        long long mid=(lo+hi+1)>>1;
        pair<long long,long long>tmp=cal(mid);
        if(tmp.second>=k)
        {
            lo=mid;
        }else hi=mid-1;
    }
        ans=cal(lo+1).first-k*(lo+1);
        return ans;
}
long long take_photos(int N,int M,int K,vector<int>r,vector<int>c) {
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    n=N;m=M;k=K;
    a.resize(n+1);
    for(long long i=1;i<=n;i++)
    {
        a[i].r=r[i-1];
        a[i].c=c[i-1];
        if(a[i].r>a[i].c)
        {
            swap(a[i].r,a[i].c);
        }
    }
    sort(a.begin()+1,a.end(),cmp);
    for(long long i=1;i<=n;i++)
    {
        while(b.size()!=0&&(a[i].r<=b.back().r))
        {
            b.pop_back();
        }
        b.push_back(a[i]);
    }
    a.resize(b.size()+1);
    for(long long i=0;i<b.size();i++)
    {
        a[i+1]=b[i];
    }
    a[0].r=-1;
    a[0].c=-1;
    n=(long long)b.size();
    k=min(k,n);
    return cal2();
}
/*
int main()
{
    cin>>n>>m>>k;
    vector<int>r(n),c(n);
    for(int i=1;i<=n;i++)
    {
        cin>>r[i-1]>>c[i-1];
    }
    cout<<take_photos(n,m,k,r,c);
    return 0;
}*/
/*
 3 7 2
 0 3
 4 6
 3 4
 */

Compilation message (stderr)

aliens.cpp: In function 'std::pair<long long int, long long int> cal(long long int)':
aliens.cpp:61:24: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<ed>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   61 |         if(ch.size()&&l>=ch.size())l=ch.size()-1;
      |                       ~^~~~~~~~~~~
aliens.cpp:62:18: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<ed>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   62 |         while(l+1<ch.size()&&dis(X,ch[l],ch[l+1])<0)
      |               ~~~^~~~~~~~~~
aliens.cpp: In function 'long long int take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:113:24: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::vector<pt>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  113 |     for(long long i=0;i<b.size();i++)
      |                       ~^~~~~~~~~

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