Submission #370060

#	Time	Username	Problem	Language	Result	Execution time	Memory
370060		KoD	Aliens (IOI16_aliens)	C++17	25 / 100	5 ms	620 KiB

aliens

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

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

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 ((m.b - n.b) * (m.a - l.a) < (l.b - m.b) * (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;
    {
        std::map<int, int> map;
        for (int i = 0; i < n; ++i) {
            if (r[i] > c[i]) {
                std::swap(r[i], c[i]);
            }
            auto &val = map[r[i]];
            val = std::max(val, c[i] + 1);
        }
        int last = -1;
        for (const auto [x, y]: map) {
            if (last < y) {
                star.emplace_back(x, y);
                last = y;
            }
        }
    }
    const int size = (int) star.size();
    // Vec<Vec<ll>> cost(size, Vec<ll>(size));
    // for (int i = 0; i < size; ++i) {
    //     for (int j = i + 1; j < size; ++j) {
    //         const auto L = star[j].second - star[i + 1].first;
    //         const auto l = std::max(star[i].second - star[i + 1].first, 0);
    //         cost[i][j] = (ll) L * L - (ll) l * l;
    //     }
    // }
    // for (int i = 0; i < size; ++i) {
    //     for (int j = 0; j < size; ++j) {
    //         std::cerr << cost[i][j] << " \n"[j + 1 == size];
    //     }
    // }
    Vec<ll> dp(size);
    for (int i = 0; i < size; ++i) {
        const auto L = star[i].second - star[0].first;
        dp[i] = (ll) L * L;
    }
    for (int step = 1; step < k; ++step) {
        auto next = dp;
        CHT cht;
        for (int i = 1; i < size; ++i) {
            const auto c = star[i].second * star[i].second;
            const auto a = -2 * star[i].first;
            const auto l = std::max(star[i - 1].second - star[i].first, 0);
            const auto b = dp[i - 1] - l * l + star[i].first * star[i].first;
            cht.add(Line { a, b });
            next[i] = std::min(next[i], cht.get(star[i].second) + c);
        }
        dp = std::move(next);
    }
    return dp[size - 1];
}

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