Submission #1244415

#	Time	Username	Problem	Language	Result	Execution time	Memory
1244415		hugo_pm	Overtaking (IOI23_overtaking)	C++20	100 / 100	3199 ms	93876 KiB

overtaking

#include "overtaking.h"
#include <bits/stdc++.h>
#define int long long
using namespace std;
using i32 = int32_t;
using pii = pair<int, int>;

constexpr int INF = 3e18;
struct Bus {
    int time, inv_speed, id_bus;
    auto operator<=>(const Bus&) const = default;
};
int ceildiv(int x, int y) {
    return (x+y-1) / y;
}

int inv_speed_reserve;
struct Event {
    int time;
    bool is_add;
    int i_dd;
    auto operator<=>(const Event&) const = default;
};
class DemiDroiteMgr {
    vector<Bus> dds;
    int nbDroites;
    vector<pii> flags;

    public:
    DemiDroiteMgr(const vector<Bus> &__dds, bool all_queries) : dds(__dds) {
        nbDroites = dds.size();
        sort(dds.begin(), dds.end());
        if (!all_queries) return;
        vector<Event> events;
        for (int i = 0; i < nbDroites; ++i) {
            auto &cur = dds[i];
            events.push_back({cur.time, true, i});
            int min_tdel = cur.time;
            for (int pw = 1ll << 60; pw; pw /= 2) {
                int tps = min_tdel + pw;
                bool dominated = false;
                for (int j = 0; j < i; ++j) {
                    if (eval(dds[j], tps) < eval(dds[i], tps))
                        dominated = true;
                }
                if (!dominated)
                    min_tdel += pw;
            }
            ++min_tdel;
            assert(cur.time < min_tdel);
            if (min_tdel <= (int)(1e18))
            events.push_back({min_tdel+1, false, i});
        }
        if (!all_queries) return;
        sort(events.begin(), events.end());
        multiset<int> dd_open;
        for (auto &[time, is_add, i_dd] : events) {
            if (is_add) {
                dd_open.insert(i_dd);
            } else {
                dd_open.erase(dd_open.find(i_dd));
            }
            assert(!dd_open.empty());
            flags.push_back({time, *dd_open.rbegin()});
        }
    }
    int eval(const Bus &dd, int temps_reserve) {
        assert(dd.time < temps_reserve);
        return ceildiv(
            temps_reserve - dd.time,
            dd.inv_speed - inv_speed_reserve
        );
    }
    /// returns ceil(dpos of next int)
    int first_intersection(int temps_reserve) {
        if (flags.empty()) {
            int best = INF;
            for (int j = 0; j < nbDroites && dds[j].time < temps_reserve; ++j) {
                if (dds[j].time < temps_reserve) {
                    int n = temps_reserve - dds[j].time;
                    int d = dds[j].inv_speed - inv_speed_reserve;
                    best = min(best, (n+d-1)/d);
                }
            }
            return best; 
        }
        auto it = lower_bound(flags.begin(), flags.end(), pii {temps_reserve, -1});
        if (it == flags.begin()) {
            return INF;
        }
        auto &dd = dds[prev(it)->second];
        return eval(dd, temps_reserve);
    }
};

int nb_bus, nb_stations;
vector<Bus> initial_buses;
vector<int> stations;

void make_table();
void init(i32, i32 N, std::vector<long long> T, std::vector<i32> W, i32 X, i32, std::vector<i32> S)
{
    for (int i = 0; i < N; ++i) {
        if (W[i] > X) {
            Bus bus {T[i], W[i], (int)initial_buses.size()};
            initial_buses.push_back(bus);
        }
    }
    stations = vector<int>(S.begin(), S.end());
    nb_bus = initial_buses.size(), nb_stations = stations.size();
    inv_speed_reserve = X;
    make_table();
}

struct TimeVec {
    int N;
    vector<int> cur_t;
    vector<pii> max_pref_nxt_exclusive;
    TimeVec(const vector<Bus> &cur_a, const vector<Bus> &nxt_a) : N(cur_a.size()) {
        max_pref_nxt_exclusive.push_back({0, 1});
        for (int i = 0; i < N; ++i) {
            cur_t.push_back(cur_a[i].time);
            max_pref_nxt_exclusive.push_back(
                max(max_pref_nxt_exclusive.back(), {nxt_a[i].time, -i})
            );
        }
    }
    /// returns the maximum of nxt(bus), among all buses such that cur(bus) < x
    pii max_strict_below(int x) {
        const int lg = (int)log2(N + 2) + 1;
        int i = 0;
        for (int pw = (1 << lg); pw; pw /= 2) {
            if (i+pw <= N && cur_t[i+pw-1] < x)
                i += pw;
        }
        return max_pref_nxt_exclusive[i];
    }
};
vector<TimeVec> tvecs;
vector<DemiDroiteMgr> help_next_inter;
/// table[i_station][i_bus] = time at which the bus gets to the station
vector<vector<int>> table;

void make_table() {
    auto push_row = [] (const vector<Bus> &cur_buses) {
        table.push_back(vector<int>(nb_bus));
        for (const auto &bus : cur_buses) {
            table.back()[bus.id_bus] = bus.time;
        }
        bool all_queries = help_next_inter.empty();
        help_next_inter.emplace_back(cur_buses, all_queries);
    };
    vector<Bus> cur_buses = initial_buses;
    push_row(cur_buses);
    for (int i_sta = 0; i_sta < nb_stations - 1; ++i_sta) {
        int dis = stations[i_sta+1] - stations[i_sta];
        sort(cur_buses.begin(), cur_buses.end());
        int i_earlier = 0, max_earl = 0;
        vector<Bus> nxt_buses;
        for (int i_time = 0; i_time < nb_bus; ++i_time) {
            const auto& [cur_time, inv_speed, id_bus] = cur_buses[i_time];
            while (i_earlier < i_time && cur_buses[i_earlier].time < cur_time) {
                max_earl = max(nxt_buses[i_earlier++].time, max_earl);
            }
            int nxt_time = max(cur_time + inv_speed * dis, max_earl);
            nxt_buses.push_back({nxt_time, inv_speed, id_bus});
        }
        tvecs.emplace_back(cur_buses, nxt_buses);
        push_row(nxt_buses);
        cur_buses = nxt_buses;
    }
}

struct Position {
    int station, time, rel_time;
    auto operator<=>(const Position&) const = default;
};

int reserve_time_travel(int i_s1, int i_s2) {
    return (stations[i_s2] - stations[i_s1]) * inv_speed_reserve;
}

Position next_pos(Position cur) {
    Position no_inter = {
        nb_stations - 1,
        cur.time + reserve_time_travel(cur.station, nb_stations-1),
        -1
    };
    
    int ceil_delta_pos = help_next_inter[cur.station].first_intersection(cur.time);
    if (ceil_delta_pos == INF)
        return no_inter;
    int ceil_abspos = stations[cur.station] + ceil_delta_pos;
    auto it = lower_bound(stations.begin(), stations.end(), ceil_abspos);
    if (it == stations.end())
        return no_inter;
    Position nxt;
    nxt.station = it - stations.begin(); // after conflict
    int before_conflict = nxt.station - 1;
    int time_at_bef = cur.time + reserve_time_travel(cur.station, before_conflict);
    auto [absnt, relnt] = tvecs[before_conflict].max_strict_below(time_at_bef);
    nxt.time = absnt, nxt.rel_time = -relnt;
    assert(nxt.time >= reserve_time_travel(cur.station, nxt.station));
    return nxt;
}

int dp[1005][1005];
vector<Position> seen;
long long arrival_time(long long dep_time_reserve) {
    Position cur {0, dep_time_reserve, -1};
    seen.clear();
    while (cur.station != nb_stations-1) {
        if (cur.rel_time != -1 && dp[cur.station][cur.rel_time]) {
            cur.time = dp[cur.station][cur.rel_time];
            break;
        }
        seen.push_back(cur);
        cur = next_pos(cur);
    }
    for (Position &pos : seen) if (pos.rel_time != -1)
        dp[pos.station][pos.rel_time] = cur.time;
    return cur.time;
}

• Subtask 0: 0 / 0
• Subtask 1: 9 / 9
• Subtask 2: 10 / 10
• Subtask 3: 20 / 20
• Subtask 4: 26 / 26
• Subtask 5: 35 / 35