Submission #1308816

#	Time	Username	Problem	Language	Result	Execution time	Memory
1308816		Rares	Aliens (IOI16_aliens)	C++20	25 / 100	2 ms	352 KiB

aliens

///acum n*log (maxval) cu aliens trick+cht trick
#include <bits/stdc++.h>
#include "aliens.h"
using namespace std;
/**ifstream fin ("date.in");
ofstream fout ("date.out");
#define cin fin
#define cout fout**/


const int MAXN=1e5+10;
typedef long long ll;
ll INF=1e15;

ll n,m,k;
__int128 dp[MAXN];
int cnt[MAXN];
pair <__int128,__int128> d[MAXN];
vector <pair <int,int>> aux,v;

bool cmp (pair <ll,ll> a, pair <ll,ll> b){
    if (a.first==b.first) return a.second>b.second;
    return a.first<b.first;
}

__int128 f (pair <__int128,__int128> d, __int128 x){
    return d.first*x+d.second;
}

bool g (ll i, ll j, __int128 x){
    ///daca j <= i atunci scot i
    if (f (d[i],x)>f (d[j],x)) return true;
    if (f (d[i],x)<f (d[j],x)) return false;
    return cnt[i]>=cnt[j];
}


ll solve (__int128 x){
    dp[0]=cnt[0]=0;
    for (int i=1;i<=n;++i){
        dp[i]=INF;
        cnt[i]=1e9;
    }
    deque <int> dq;
    for (int i=0;i<=n;++i){
        if (i){
            dp[i]=v[i].second*v[i].second;
            if (dq.empty ()){
                cnt[i]=1;
            }
            else{
                while (dq.size ()>=2){
                    int i1=dq.front ();
                    dq.pop_front ();
                    int i2=dq.front ();

                    dq.push_front (i1);

                    if (g (i1,i2,v[i].second)){
                        dq.pop_front ();
                    }
                    else
                        break;
                }
                int pcrt=dq.front ();
                dp[i]+=f (d[pcrt],v[i].second);
                cnt[i]=cnt[pcrt]+1;
            }
        }

        if (i<=n-1){
            ll acrt=-2*(v[i+1].first-1);
            __int128 bcrt=dp[i]+1LL*(v[i+1].first-1)*(v[i+1].first-1)+x;

            __int128 aux=max (0,v[i].second-v[i+1].first+1);
            aux*=aux;
            bcrt-=aux;
            bcrt=min (bcrt,__int128(INF));
            d[i]={acrt,bcrt};

            while (dq.size ()>=2){
                int i1=dq.back ();
                dq.pop_back ();
                int i2=dq.back ();
                /**
                x1=(d[i2].second-d[i1].second)/(d[i1].first-d[i2].first)
                x2=(d[i2].second-d[i].second)/(d[i].first-d[i2].first)
                **/
                __int128 a=__int128(d[i2].second-d[i1].second)*__int128 (d[i].first-d[i2].first);
                __int128 b=__int128(d[i1].first-d[i2].first)*__int128 (d[i2].second-d[i].second);
                if (a>b or (a==b and cnt[i]>=cnt[i1])){
                    continue;
                }
                dq.push_back (i1);
                break;
            }
            dq.push_back (i);
        }

    }

    return cnt[n];
}

ll take_photos (int N, int M, int K, vector <int> r, vector <int> c){
    n=N;
    m=M;
    k=K;
    for (int i=0;i<n;++i){
        r[i]++;
        c[i]++;
        if (r[i]>c[i]){
            swap (r[i],c[i]);
        }
        aux.push_back ({r[i],c[i]});
    }

    sort (aux.begin (),aux.end (),cmp);
    v.push_back ({0,0});
    int cmax=0;
    for (auto x:aux){
        if (x.second>cmax){
            cmax=x.second;
            v.push_back (x);
        }
    }

    n=v.size ()-1;


    ll st=0,dr=1e12,rez;
    while (st<=dr){
        ll mij=(st+dr)/2;
        if (solve (mij)>k){
            st=mij+1;
        }
        else{
            dr=mij-1;
            rez=mij;
        }
    }

    solve (rez);

    return dp[n]-__int128 (k)*rez;
}

Compilation message (stderr)

aliens.h:1:9: warning: #pragma once in main file
    1 | #pragma once
      |         ^~~~
aliens_c.h:1:9: warning: #pragma once in main file
    1 | #pragma once
      |         ^~~~

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 0 / 16
• Subtask 5: 0 / 19
• Subtask 6: 0 / 40