Submission #370157

#	Time	Username	Problem	Language	Result	Execution time	Memory
370157		KoD	Aliens (IOI16_aliens)	C++17	100 / 100	178 ms	5464 KiB

aliens

#include <bits/stdc++.h>
#include "aliens.h"

template <class T>
using Vec = std::vector<T>;
using ll = long long;
using bigll = __int128_t;

constexpr ll square(const ll x) {
    return x * x;
}

struct Line {
    ll a, b;
    ll get(const ll x) const {
        return a * x + b;
    }
};

struct CHT {
    std::deque<Line> line;
    CHT(): line() { }

    void add(const Line &l) {
        while (line.size() >= 2) {
            const auto &m = line[line.size() - 1];
            const auto &n = line[line.size() - 2];
            if (bigll(m.b - n.b) * bigll(m.a - l.a) < bigll(l.b - m.b) * bigll(n.a - m.a)) {
                break;
            }
            line.pop_back();
        }
        line.push_back(l);
    } 

    ll get(const ll x) {
        while (line.size() >= 2) {
            const auto &m = line[0];
            const auto &n = line[1];
            if (m.get(x) < n.get(x)) {
                break;
            }
            line.pop_front();
        }
        return line[0].get(x);
    }
};

ll take_photos(int n, int m, int k, Vec<int> r, Vec<int> c) {
    Vec<std::pair<int, int>> star;
    {
        for (int i = 0; i < n; ++i) {
            if (r[i] > c[i]) {
                std::swap(r[i], c[i]);
            }
            c[i] += 1;
        }
        Vec<int> order(n);
        std::iota(order.begin(), order.end(), (int) 0);
        std::sort(order.begin(), order.end(), [&](const int i, const int j) {
            if (r[i] == r[j]) return c[i] > c[j];
            return r[i] < r[j];
        });
        int last_c = -1;
        for (const int i: order) {
            if (last_c < c[i]) {
                star.emplace_back(r[i], c[i]);
                last_c = c[i];
            }
        }
    }
    n = (int) star.size();
    k = std::min(k, n);
    const ll fix_coeff = n + 1;
    const auto compute = [&](const ll penalty) {
        Vec<ll> dp(n + 1);
        CHT cht;
        for (int i = 0; i < n; ++i) {
            const ll a = fix_coeff * (-2 * star[i].first); 
            const ll dup = (i == 0 ? 0 : std::max(star[i - 1].second - star[i].first, 0));
            const ll b = dp[i] + fix_coeff * (square(star[i].first) - square(dup));
            cht.add(Line { a, b });
            dp[i + 1] = cht.get(star[i].second) + fix_coeff * (square(star[i].second) + penalty) + 1;
        }
        return std::make_pair(dp[n] / fix_coeff, dp[n] % fix_coeff);
    };
    ll ng = -1, ok = (ll) m * m + 1;
    while (ok - ng > 1) {
        const ll md = (ok + ng) / 2;
        (compute(md).second <= k ? ok : ng) = md;
    }   
    const auto p1 = compute(ok);
    const auto p2 = compute(ng);
    const auto a = p1.first - ok * p1.second;
    const auto b = p2.first - ng * p2.second;
    const auto s = k - p1.second;
    const auto t = p2.second - k;
    return s == 0 ? a : (a * t + b * s) / (s + t);
}   

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