oj.uz

Submission #841469

# Submission time Handle Problem Language Result Execution time Memory
841469 2023-09-01T15:41:06 Z model_code Overtaking (IOI23_overtaking) C++17
100 / 100
 535 ms 80308 KB 
// correct/author-full.cpp

// This is the full solution.
//
// O(N * P * log(N) + Q * log(N * P))
//
// Can be optimised to O(N * (P + log (N)) + Q * log(N * P)) if the sorting is done carefully,
// by noticing that every pair of cars can only swap positions at most once.
// But this seems kind of difficult to implement,
// and it is likely that the time taken will be hard to distinguish the slower solution from the faster solution.

#include "overtaking.h"

#include <algorithm>
#include <utility>
#include <vector>

// Linked list node for the singly linked list.
template <typename T>
struct singly_node
{
    T val;
    singly_node *next;
};

// Singly linked list that has polong longers to both the front and back.
template <typename T>
struct singly_list
{
private:
    singly_node<T> *first;
    singly_node<T> *last;

public:
    singly_list() : first(nullptr), last(nullptr) {}
    singly_list(singly_list &&other) : first(std::exchange(other.first, nullptr)), last(std::exchange(other.last, nullptr)) {}
    singly_list &operator=(singly_list &&other)
    {
        first = std::exchange(other.first, nullptr);
        last = std::exchange(other.last, nullptr);
        return *this;
    }
    bool empty() const { return first == nullptr; }
    void push_back(singly_node<T> *node)
    {
        node->next = nullptr;
        if (empty())
        {
            first = last = node;
        }
        else
        {
            last->next = node;
            last = node;
        }
    }
    void append(singly_list &&other)
    {
        if (!other.empty())
        {
            if (!empty())
            {
                last->next = std::exchange(other.first, nullptr);
                last = std::exchange(other.last, nullptr);
            }
            else
            {
                first = std::exchange(other.first, nullptr);
                last = std::exchange(other.last, nullptr);
            }
        }
    }
    singly_node<T> *pop_front()
    {
        singly_node<T> *res = std::exchange(first, first->next);
        if (first == nullptr)
            last = nullptr;
        return res;
    }
    singly_node<T> *front() const
    {
        return first;
    }
};

// Represents a car (not my car) that is travelling on the road.
struct car
{
    // The time that this car reaches the current passing place.
    long long curr;
    // The pace that this car drives at.
    long long pace;
};

// Represents what will happen if my car starts at the starting line between orig_first and orig_last.
struct sketch
{
    // The range of times at the starting line that this sketch represents.
    long long orig_first;
    long long orig_last;

    // The range of times at the current passing place that this sketch represents.  This is stored as the time at the starting line in order to get to the current passing place at the correct time.
    // If curr_first != curr_last, then curr_last - curr_first == orig_last - orig_first, meaning that this range of cars have not been forced to slow down due to a car in front yet.
    // Otherwise, curr_first == curr_last, meaning that the range of original times are now compressed long longo a single polong long in time.
    long long curr_first;
    long long curr_last;
};

struct packet
{
    car mCar;
    singly_list<sketch> sketches;
};

constexpr long long MAX_START_TIME = 1'000'000'000'000'000'000;

std::vector<sketch> query_sketches;

void init(int L, int N, std::vector<long long> t, std::vector<int> w, int X, int P, std::vector<int> p2)
{
    // Ignore the number of queries; we don't care about it
    //(void) Q;

    P -= 2;
    std::vector<int> p(P);
    for (int i = 0; i < P; i++)
        p[i] = p2[i + 1];

    std::vector<singly_node<sketch>> list_buf;
    list_buf.reserve((N + 1) * (P + 2));

    // This is the state that we update as we travel down the road
    std::vector<packet> packets;

    std::vector<long long> indices;
    indices.reserve(N);
    for (long long i = 0; i < N; ++i)
    {
        indices.push_back(i);
    }
    std::sort(indices.begin(), indices.end(), [&](long long a, long long b)
              {
        if (t[a] != t[b]) return t[a] < t[b];
        return w[a] < w[b]; });
    packets.push_back({car{-1, X}, {}});
    for (long long i : indices)
    {
        // Ignore any cars at least as fast as my car, because they will never block me
        if (w[i] <= X)
            continue;
        if (packets.back().mCar.curr != t[i])
        {
            singly_node<sketch> &node = list_buf.emplace_back();
            node.val = sketch{static_cast<long long>(packets.back().mCar.curr), t[i], packets.back().mCar.curr, t[i]};
            packets.back().sketches.push_back(&node);
        }
        packets.push_back({car{t[i], w[i]}, {}});
    }
    if (packets.back().mCar.curr != MAX_START_TIME)
    {
        singly_node<sketch> &node = list_buf.emplace_back();
        node.val = sketch{static_cast<long long>(packets.back().mCar.curr), MAX_START_TIME, packets.back().mCar.curr, MAX_START_TIME};
        packets.back().sketches.push_back(&node);
    }
    p.push_back(L);
    for (long long j = 0; j <= P; ++j)
    {
        const long long len = p[j] - (j == 0 ? 0 : p[j - 1]);
        auto it = packets.begin();
        while (it != packets.end())
        {
            singly_list<sketch> collect = std::move(it->sketches);
            const long long curr_time = it->mCar.curr += it->mCar.pace * len;
            auto it2 = it;
            for (++it2; it2 != packets.end() && curr_time >= it2->mCar.curr + it2->mCar.pace * len; ++it2)
            {
                it2->mCar.curr = curr_time;
                collect.append(std::move(it2->sketches));
            }
            // To get the better time complexity (see comment at the top of this file),
            // you need to notice that every pair of cars cannot change relative order more than once,
            // and then change this sorting algorithm to something that is faster when there are subranges that are already sorted.
            // This is probably not going to be distinguishable from the current solution by time limit allowances.
            std::sort(it, it2, [](const packet &a, const packet &b)
                      { return a.mCar.pace < b.mCar.pace; });
            const long long delta = static_cast<long long>(X) * p[j];
            if (!collect.empty() && (collect.front()->val.curr_first + delta < curr_time || collect.front()->val.curr_last + delta <= curr_time))
            {
                const long long orig_first = collect.front()->val.orig_first;
                long long orig_last = orig_first;
                while (!collect.empty() && collect.front()->val.curr_last + delta <= curr_time)
                {
                    orig_last = collect.pop_front()->val.orig_last;
                }
                if (!collect.empty() && collect.front()->val.curr_first + delta < curr_time)
                {
                    orig_last = collect.front()->val.orig_first += (curr_time - delta) - collect.front()->val.curr_first;
                    collect.front()->val.curr_first = curr_time - delta;
                }
                singly_node<sketch> &node = list_buf.emplace_back();
                node.val = sketch{orig_first, orig_last, curr_time - delta, curr_time - delta};
                (it - 1)->sketches.push_back(&node);
            }
            (it2 - 1)->sketches.append(std::move(collect));
            it = it2;
        }
    }
    const long long delta = static_cast<long long>(X) * L;
    for (packet &packet : packets)
    {
        singly_list<sketch> &sketches = packet.sketches;
        while (!sketches.empty())
        {
            query_sketches.push_back(sketches.pop_front()->val);
            query_sketches.back().curr_first += delta;
            query_sketches.back().curr_last += delta;
        }
    }
}

long long arrival_time(long long q)
{
    auto it = std::lower_bound(query_sketches.begin(), query_sketches.end(), q, [](const sketch &s, long long q2)
                               { return s.orig_last < q2; });
    if (it->curr_first == it->curr_last)
    {
        return it->curr_first;
    }
    return it->curr_first + (q - it->orig_first);
}

Subtask #0
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 212 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 452 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 980 KB Output is correct
10 Correct 1 ms 980 KB Output is correct
11 Correct 1 ms 980 KB Output is correct
12 Correct 1 ms 852 KB Output is correct
13 Correct 1 ms 980 KB Output is correct
14 Correct 1 ms 852 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 1 ms 468 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 1 ms 468 KB Output is correct
20 Correct 1 ms 468 KB Output is correct
21 Correct 0 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 0 ms 340 KB Output is correct
25 Correct 0 ms 468 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 0 ms 468 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 0 ms 340 KB Output is correct
30 Correct 1 ms 340 KB Output is correct
31 Correct 0 ms 340 KB Output is correct
32 Correct 1 ms 1232 KB Output is correct
33 Correct 1 ms 1232 KB Output is correct
34 Correct 1 ms 1232 KB Output is correct
35 Correct 1 ms 1232 KB Output is correct
36 Correct 1 ms 1232 KB Output is correct
37 Correct 1 ms 1232 KB Output is correct
38 Correct 0 ms 212 KB Output is correct
39 Correct 0 ms 212 KB Output is correct
40 Correct 1 ms 852 KB Output is correct

Subtask #4
26.0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 1 ms 980 KB Output is correct
17 Correct 1 ms 980 KB Output is correct
18 Correct 1 ms 980 KB Output is correct
19 Correct 1 ms 852 KB Output is correct
20 Correct 1 ms 980 KB Output is correct
21 Correct 1 ms 852 KB Output is correct
22 Correct 1 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 1 ms 468 KB Output is correct
25 Correct 1 ms 468 KB Output is correct
26 Correct 1 ms 468 KB Output is correct
27 Correct 1 ms 468 KB Output is correct
28 Correct 0 ms 340 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 1 ms 468 KB Output is correct
31 Correct 0 ms 340 KB Output is correct
32 Correct 0 ms 468 KB Output is correct
33 Correct 1 ms 340 KB Output is correct
34 Correct 0 ms 468 KB Output is correct
35 Correct 1 ms 340 KB Output is correct
36 Correct 0 ms 340 KB Output is correct
37 Correct 1 ms 340 KB Output is correct
38 Correct 0 ms 340 KB Output is correct
39 Correct 1 ms 1232 KB Output is correct
40 Correct 1 ms 1232 KB Output is correct
41 Correct 1 ms 1232 KB Output is correct
42 Correct 1 ms 1232 KB Output is correct
43 Correct 1 ms 1232 KB Output is correct
44 Correct 1 ms 1232 KB Output is correct
45 Correct 0 ms 212 KB Output is correct
46 Correct 0 ms 212 KB Output is correct
47 Correct 1 ms 852 KB Output is correct
48 Correct 19 ms 6444 KB Output is correct
49 Correct 18 ms 8696 KB Output is correct
50 Correct 19 ms 10356 KB Output is correct
51 Correct 20 ms 7892 KB Output is correct
52 Correct 18 ms 8720 KB Output is correct
53 Correct 19 ms 8660 KB Output is correct
54 Correct 27 ms 7792 KB Output is correct
55 Correct 13 ms 2708 KB Output is correct
56 Correct 20 ms 8148 KB Output is correct
57 Correct 24 ms 7716 KB Output is correct
58 Correct 27 ms 8192 KB Output is correct
59 Correct 19 ms 7968 KB Output is correct
60 Correct 28 ms 8152 KB Output is correct
61 Correct 20 ms 8216 KB Output is correct
62 Correct 2 ms 468 KB Output is correct
63 Correct 2 ms 468 KB Output is correct
64 Correct 12 ms 4820 KB Output is correct
65 Correct 11 ms 4688 KB Output is correct
66 Correct 29 ms 26196 KB Output is correct
67 Correct 27 ms 9936 KB Output is correct
68 Correct 20 ms 10388 KB Output is correct
69 Correct 83 ms 72448 KB Output is correct
70 Correct 89 ms 72456 KB Output is correct
71 Correct 91 ms 72436 KB Output is correct
72 Correct 131 ms 71100 KB Output is correct
73 Correct 85 ms 72480 KB Output is correct
74 Correct 84 ms 72400 KB Output is correct
75 Correct 1 ms 352 KB Output is correct
76 Correct 2 ms 340 KB Output is correct
77 Correct 2 ms 340 KB Output is correct
78 Correct 41 ms 47864 KB Output is correct

Subtask #5
35.0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 1 ms 468 KB Output is correct
20 Correct 1 ms 468 KB Output is correct
21 Correct 1 ms 468 KB Output is correct
22 Correct 1 ms 452 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 212 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 1 ms 980 KB Output is correct
28 Correct 1 ms 980 KB Output is correct
29 Correct 1 ms 980 KB Output is correct
30 Correct 1 ms 852 KB Output is correct
31 Correct 1 ms 980 KB Output is correct
32 Correct 1 ms 852 KB Output is correct
33 Correct 1 ms 468 KB Output is correct
34 Correct 1 ms 468 KB Output is correct
35 Correct 1 ms 468 KB Output is correct
36 Correct 1 ms 468 KB Output is correct
37 Correct 1 ms 468 KB Output is correct
38 Correct 1 ms 468 KB Output is correct
39 Correct 0 ms 340 KB Output is correct
40 Correct 1 ms 340 KB Output is correct
41 Correct 1 ms 468 KB Output is correct
42 Correct 0 ms 340 KB Output is correct
43 Correct 0 ms 468 KB Output is correct
44 Correct 1 ms 340 KB Output is correct
45 Correct 0 ms 468 KB Output is correct
46 Correct 1 ms 340 KB Output is correct
47 Correct 0 ms 340 KB Output is correct
48 Correct 1 ms 340 KB Output is correct
49 Correct 0 ms 340 KB Output is correct
50 Correct 1 ms 1232 KB Output is correct
51 Correct 1 ms 1232 KB Output is correct
52 Correct 1 ms 1232 KB Output is correct
53 Correct 1 ms 1232 KB Output is correct
54 Correct 1 ms 1232 KB Output is correct
55 Correct 1 ms 1232 KB Output is correct
56 Correct 0 ms 212 KB Output is correct
57 Correct 0 ms 212 KB Output is correct
58 Correct 1 ms 852 KB Output is correct
59 Correct 19 ms 6444 KB Output is correct
60 Correct 18 ms 8696 KB Output is correct
61 Correct 19 ms 10356 KB Output is correct
62 Correct 20 ms 7892 KB Output is correct
63 Correct 18 ms 8720 KB Output is correct
64 Correct 19 ms 8660 KB Output is correct
65 Correct 27 ms 7792 KB Output is correct
66 Correct 13 ms 2708 KB Output is correct
67 Correct 20 ms 8148 KB Output is correct
68 Correct 24 ms 7716 KB Output is correct
69 Correct 27 ms 8192 KB Output is correct
70 Correct 19 ms 7968 KB Output is correct
71 Correct 28 ms 8152 KB Output is correct
72 Correct 20 ms 8216 KB Output is correct
73 Correct 2 ms 468 KB Output is correct
74 Correct 2 ms 468 KB Output is correct
75 Correct 12 ms 4820 KB Output is correct
76 Correct 11 ms 4688 KB Output is correct
77 Correct 29 ms 26196 KB Output is correct
78 Correct 27 ms 9936 KB Output is correct
79 Correct 20 ms 10388 KB Output is correct
80 Correct 83 ms 72448 KB Output is correct
81 Correct 89 ms 72456 KB Output is correct
82 Correct 91 ms 72436 KB Output is correct
83 Correct 131 ms 71100 KB Output is correct
84 Correct 85 ms 72480 KB Output is correct
85 Correct 84 ms 72400 KB Output is correct
86 Correct 1 ms 352 KB Output is correct
87 Correct 2 ms 340 KB Output is correct
88 Correct 2 ms 340 KB Output is correct
89 Correct 41 ms 47864 KB Output is correct
90 Correct 49 ms 7268 KB Output is correct
91 Correct 235 ms 26008 KB Output is correct
92 Correct 241 ms 25784 KB Output is correct
93 Correct 232 ms 26092 KB Output is correct
94 Correct 248 ms 25908 KB Output is correct
95 Correct 235 ms 26056 KB Output is correct
96 Correct 275 ms 26104 KB Output is correct
97 Correct 41 ms 3556 KB Output is correct
98 Correct 238 ms 25808 KB Output is correct
99 Correct 266 ms 26396 KB Output is correct
100 Correct 237 ms 26004 KB Output is correct
101 Correct 286 ms 25804 KB Output is correct
102 Correct 234 ms 25832 KB Output is correct
103 Correct 259 ms 26040 KB Output is correct
104 Correct 220 ms 25028 KB Output is correct
105 Correct 235 ms 27368 KB Output is correct
106 Correct 301 ms 36152 KB Output is correct
107 Correct 266 ms 30140 KB Output is correct
108 Correct 264 ms 30040 KB Output is correct
109 Correct 253 ms 30044 KB Output is correct
110 Correct 273 ms 30112 KB Output is correct
111 Correct 447 ms 80308 KB Output is correct
112 Correct 453 ms 80308 KB Output is correct
113 Correct 519 ms 80188 KB Output is correct
114 Correct 451 ms 58204 KB Output is correct
115 Correct 515 ms 80308 KB Output is correct
116 Correct 465 ms 80304 KB Output is correct
117 Correct 189 ms 27972 KB Output is correct
118 Correct 252 ms 28020 KB Output is correct
119 Correct 188 ms 27024 KB Output is correct
120 Correct 190 ms 27960 KB Output is correct
121 Correct 197 ms 28976 KB Output is correct
122 Correct 314 ms 55616 KB Output is correct
123 Correct 466 ms 58232 KB Output is correct
124 Correct 535 ms 47804 KB Output is correct
125 Correct 460 ms 46660 KB Output is correct