Submission #960790

#	Time	Username	Problem	Language	Result	Execution time	Memory
960790		ThegeekKnight16	Aliens (IOI16_aliens)	C++17	100 / 100	156 ms	14216 KiB

aliens

#include <bits/stdc++.h>
#include "aliens.h"
using namespace std;
typedef long long ll;
vector<ll> A, B, ids; int tam = 0, pos = 0;

bool inutil(int novo, int atual, int velho)
{
    return ((B[velho] - B[novo])*(A[atual] - A[velho]) <= (B[velho] - B[atual])*(A[novo] - A[velho]));
}

void update(ll newA, ll newB, ll newId)
{
    A.push_back(newA); B.push_back(newB); ids.push_back(newId);
    ++tam;
    while (tam > 2 && inutil(tam-1, tam-2, tam-3)) {A.erase(A.end()-2); B.erase(B.end()-2); ids.erase(ids.end()-2); --tam;}
}

pair<ll, ll> query(ll x)
{
    if (pos >= tam) pos = tam-1;
    while (pos < tam-1 && (A[pos]*x + B[pos]) >= (A[pos+1]*x + B[pos+1])) ++pos;
    return make_pair(A[pos]*x + B[pos], ids[pos]);
}

void calcDp(ll multa, vector<ll> &dp, vector<ll> &dp2, const vector<pair<ll, ll>> &v, const vector<ll> &sIni, const vector<ll> &inter, int N)
{
    fill(dp.begin(), dp.end(), 0x3f3f3f3f3f3f3f3f); dp[0] = 0;
    fill(dp2.begin(), dp2.end(), 0);
    A.clear(); B.clear(); ids.clear(); tam = pos = 0;
    for (int i = 1; i <= N; i++)
    {
        update(-2*v[i].first, (v[i].first*v[i].first) - 2*v[i].first + sIni[i-1] - inter[i-1] + dp[i-1], i-1);
        dp[i] = multa + ((v[i].second + 1)*(v[i].second + 1)) - sIni[i] + query(v[i].second).first;
        dp2[i] = dp2[query(v[i].second).second] + 1;
    }
}

ll take_photos(int N, int M, int K, std::vector<int> r, std::vector<int> c)
{
    vector<pair<ll, ll>> v(N);
    for (int i = 0; i < N; i++)
    {
        int Y = r[i], X = c[i];
        if (X > Y) swap(X, Y);
        v[i] = make_pair(X, Y);
    }
    sort(v.begin(), v.end(), [&](const pair<int, int> &a, const pair<int, int> &b) {return (a.first == b.first ? a.second < b.second : a.first > b.first);});
    vector<pair<ll, ll>> pareto;
    for (auto [X, Y] : v)
    {
        while (!pareto.empty() && pareto.back().second <= Y) pareto.pop_back();
        pareto.emplace_back(X, Y);
    }
    v = pareto;
    reverse(v.begin(), v.end()); //So pra ficar ordenado por X
    N = v.size(); v.insert(v.begin(), make_pair(-1, -1));
    vector<ll> sIni(N+1), inter(N+1);
    for (int i = 1; i < N; i++) inter[i] = (v[i+1].first > v[i].second ? 0 : (v[i].second - v[i+1].first + 1)*(v[i].second - v[i+1].first + 1));
    for (int i = 1; i <= N; i++) sIni[i] = (v[i].second - v[i].first + 1)*(v[i].second - v[i].first + 1) + sIni[i-1] - inter[i-1];
    //Ate aqui estou so reduzindo o problema

    auto C = [&](int l, int r) {return ((v[r].second - v[l].first + 1LL) * (v[r].second - v[l].first + 1LL)) - (sIni[r] - sIni[l-1] + inter[l-1]);};

    K = min(K, N);

    ll ini = 0LL, fim = (ll)M*(ll)M;
    vector<ll> dp(N+1), dp2(N+1);
    while (ini < fim) //quanto maior a multa, menor o dp2[N]. Quero a maior multa tal que dp2[N] >= K
    {
        ll multa = (ini + fim + 1LL) >> 1LL;
        calcDp(multa, dp, dp2, v, sIni, inter, N);
        if (dp2[N] >= K) ini = multa;
        else fim = multa-1LL;
    }

    calcDp(ini, dp, dp2, v, sIni, inter, N);
    
    dp[N] -= (dp2[N] * ini);
    ll resp = dp[N] + ((dp2[N] - K) * ini);
    return resp + sIni[N];
}

Compilation message (stderr)

aliens.cpp: In function 'll take_photos(int, int, int, std::vector<int>, std::vector<int>)':
aliens.cpp:63:10: warning: variable 'C' set but not used [-Wunused-but-set-variable]
   63 |     auto C = [&](int l, int r) {return ((v[r].second - v[l].first + 1LL) * (v[r].second - v[l].first + 1LL)) - (sIni[r] - sIni[l-1] + inter[l-1]);};
      |          ^

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