Submission #940784

#	Time	Username	Problem	Language	Result	Execution time	Memory
940784		Pannda	Aliens (IOI16_aliens)	C++17	4 / 100	3 ms	424 KiB

aliens

#include "aliens.h"

#include <bits/stdc++.h>
using namespace std;

template <class T>
struct LiChao {
    const T INF = numeric_limits<T>::max() / 2;

    int C;
    vector<T> dom;
    vector<array<T, 2>> first;
    vector<int> label;

    T f(array<T, 2> p, int x) {
        return p[0] * dom[x] + p[1];
    }

    LiChao(vector<T> _dom) : dom(_dom) {
        sort(dom.begin(), dom.end());
        dom.resize(unique(dom.begin(), dom.end()) - dom.begin());
        C = dom.size();
        first.resize(4 * C, array<T, 2>{0, INF});
        label.resize(4 * C, -1);
    }

    void add(T a, T b, int lab) {
        array<T, 2> p{a, b};
        int idx = 0, l = 0, r = C;
        while (l < r) {
            int m = (l + r) >> 1;
            bool doml = f(p, l) < f(first[idx], l);
            bool domm = f(p, m) < f(first[idx], m);
            if (domm) swap(p, first[idx]), swap(label[idx], lab);
            if (l + 1 == r) break;
            if (doml != domm) idx = 2 * idx + 1, r = m;
            else idx = 2 * idx + 2, l = m;
        }
    }

    pair<T, int> getMin(T x) {
//        x -= 1e-9;
        x = lower_bound(dom.begin(), dom.end(), x) - dom.begin();
        T mn = INF;
        int lab = -1;
        int idx = 0, l = 0, r = C;
        while (l < r) {
            if (f(first[idx], x) < mn) mn = f(first[idx], x), lab = label[idx];
            if (l + 1 == r) break;
            int m = (l + r) >> 1;
            if (x < m) idx = 2 * idx + 1, r = m;
            else idx = 2 * idx + 2, l = m;
        }
        return make_pair(mn, lab);
    }
};

long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
    auto [fl, fr] = [&]() -> array<vector<long long>, 2> {
        vector<array<int, 2>> fetch;
        for (int i = 0; i < n; i++) {
            fetch.push_back({min(r[i], c[i]), max(r[i], c[i]) + 1});
        }
        sort(fetch.begin(), fetch.end(), [&](array<int, 2> lr0, array<int, 2> lr1) {
             if (lr0[0] != lr1[0]) return lr0[0] < lr1[0];
             return lr0[1] > lr1[1];
        });
        vector<long long> fl, fr;
        for (auto [l, r] : fetch) {
            if (!fr.empty() && (r <= fr.back() || fl.back() == l)) continue;
            fl.push_back(l);
            fr.push_back(r);
        }
        return {fl, fr};
    }();
    n = fl.size();

    auto getExtremum = [&](long long lambda) -> pair<long long, int> {
        vector<long long> dp(n + 1);
        vector<int> arg(n + 1);
        dp[0] = arg[0] = 0;
        LiChao<long long> lc(fr);
        for (int i = 0; i < n; i++) {
            if (i == 0 || fl[i] >= fr[i - 1]) {
                lc.add(-2 * fl[i], dp[i] + fl[i] * fl[i], i);
            } else {
                lc.add(-2 * fl[i], dp[i] + 2 * fr[i - 1] * fl[i] - fr[i - 1] * fr[i - 1], i);
            }
            auto [mn, j] = lc.getMin(fr[i]);
            dp[i + 1] = mn + fr[i] * fr[i] + lambda;
            arg[i + 1] = arg[j] + 1;
        }
        return make_pair(dp[n], arg[n]);
    };

    long long lambda = [&]() -> long long {
        long long l = 0, r = 1e18;
        while (l < r) {
            long long m = (l + r) >> 1;
            auto [extre, arg] = getExtremum(m);
            if (arg <= k) {
                r = m;
            } else {
                l = m + 1;
            }
        }
        return l;
    }();

    auto [extre, arg] = getExtremum(lambda);
//    cout << lambda << ' ' << extre << ' ' << arg << '\n';
    return extre - lambda * k;
}

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