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답안 #792335

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
792335 2023-07-25T01:25:05 Z skittles1412 Sky Walking (IOI19_walk) C++17
57 / 100
 4000 ms 844312 KB 
#include "bits/extc++.h"

using namespace std;

template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
    cerr << t;
    ((cerr << " | " << u), ...);
    cerr << endl;
}

#ifdef DEBUG
#define dbg(...)                                              \
    cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]: "; \
    dbgh(__VA_ARGS__)
#else
#define dbg(...)
#define cerr   \
    if (false) \
    cerr
#endif

using ll = long long;

#define endl "\n"
#define long int64_t
#define sz(x) int(std::size(x))

template <typename T>
using min_pq = priority_queue<T, vector<T>, greater<T>>;

template <typename A, typename B>
ostream& operator<<(ostream& out, const pair<A, B>& p) {
    return out << "(" << p.first << ", " << p.second << ")";
}

template <typename Cb>
struct CmpByKey {
    Cb cb;

    CmpByKey(const Cb& cb) : cb(cb) {}

    template <typename T>
    bool operator()(const T& a, const T& b) const {
        return cb(a) < cb(b);
    }
};

template <typename T>
struct Comp {
    map<T, int> mp;

    int operator()(const T& t) {
        auto [it, inserted] = mp.emplace(t, -1);
        if (inserted) {
            it->second = sz(mp) - 1;
        }
        return it->second;
    }
};

template <typename T, typename Cmp = less<T>>
vector<T> sorted(vector<T> arr, Cmp cmp = Cmp()) {
    sort(begin(arr), end(arr), cmp);
    return arr;
}

template <typename S>
long dijkstra(const vector<tuple<S, S, long>>& edges, S src, S dest) {
    dbg("A");
    int n = 2 * sz(edges) + 10;

    Comp<S> comp;
    vector<pair<int, long>> graph[n];

    for (auto& [u, v, w] : edges) {
        int cu = comp(u), cv = comp(v);
        graph[cu].emplace_back(cv, w);
        graph[cv].emplace_back(cu, w);
    }

    long dist[n];
    memset(dist, 0x3f, sizeof(dist));

    min_pq<pair<long, int>> pq;
    auto push = [&](int u, long d) -> void {
        if (d >= dist[u]) {
            return;
        }
        dist[u] = d;
        pq.emplace(d, u);
    };

    int c_src = comp(src), c_dest = comp(dest);

    push(c_src, 0);

    while (sz(pq)) {
        auto [d, u] = pq.top();
        pq.pop();

        if (u == c_dest) {
            return d;
        }
        if (d != dist[u]) {
            continue;
        }

        for (auto& [v, w] : graph[u]) {
            push(v, d + w);
        }
    }

    return -1;
}

namespace s1 {

long solve(vector<pair<int, int>> arr,
           vector<array<int, 3>> walk,
           int src,
           int dest) {
    map<int, vector<pair<int, int>>> evts;
    for (auto& [x, h] : arr) {
        evts[-h].emplace_back(x, -1);
    }
    for (auto& [ql, qr, h] : walk) {
        evts[-h].emplace_back(ql, qr);
    }

    vector<array<int, 3>> d_walk;
    {
        set<int> pos;
        for (auto& [nh, ev] : evts) {
            int h = -nh;

            for (auto& [x, ty] : ev) {
                if (ty == -1) {
                    dbg(h, x);
                    pos.insert(x);
                }
            }

            for (auto& [ql, qr] : ev) {
                if (qr == -1) {
                    continue;
                }
                dbg(h, ql, qr);

                auto it = pos.lower_bound(ql);
                while (true) {
                    int cl = *it;
                    ++it;
                    int cr = *it;
                    d_walk.push_back({cl, cr, h});

                    dbg("A", *it, qr);
                    assert(*it <= qr);
                    if (*it == qr) {
                        break;
                    }
                }
            }
        }
    }

    for (auto& [ql, qr, h] : d_walk) {
        dbg(ql, qr, h);
    }

    using S = pair<int, int>;

    S s_src {src, 0}, s_dest {dest, 0};
    vector<S> states {s_src, s_dest};
    for (auto& [ql, qr, h] : d_walk) {
        states.emplace_back(ql, h);
        states.emplace_back(qr, h);
    }

    sort(begin(states), end(states));
    states.erase(unique(begin(states), end(states)), states.end());

    map<int, vector<int>> buildings;
    for (auto& [x, y] : states) {
        buildings[x].push_back(y);
    }

    vector<tuple<S, S, long>> edges;

    for (auto& [x, ys] : buildings) {
        sort(begin(ys), end(ys));
        for (int i = 0; i + 1 < sz(ys); i++) {
            edges.emplace_back(S(x, ys[i]), S(x, ys[i + 1]), ys[i + 1] - ys[i]);
        }
    }

    for (auto& [ql, qr, h] : d_walk) {
        edges.emplace_back(S(ql, h), S(qr, h), qr - ql);
    }

    for (auto& [u, v, w] : edges) {
        dbg(u, v, w);
    }

    return dijkstra(edges, s_src, s_dest);
}

}  // namespace s1

namespace s2 {

template <typename Cb>
void add_edges(vector<array<int, 4>> arr, const Cb& cb) {
    for (auto& [_ql, qr, _i, _] : arr) {
        // [] -> [)
        qr++;
    }

    int n = sz(arr);

    map<pair<int, int>, int> mp;

    auto split = [&](int ind) -> void {
        auto it = mp.lower_bound({ind + 1, -1});
        if (it == mp.begin()) {
            return;
        }
        --it;
        auto [cql, cqr] = it->first;

        if (cql < ind && ind < cqr) {
            int cv = it->second;
            mp.erase(it);
            mp[{cql, ind}] = cv;
            mp[{ind, cqr}] = cv;
        }
    };

    for (auto& [ql, qr, qi, _] : arr) {
        split(ql);
        split(qr);

        for (auto it = mp.lower_bound({ql, -1}); it != mp.end();
             it = mp.erase(it)) {
            auto [cql, cqr] = it->first;
            if (qr <= cql) {
                break;
            }

            assert(ql <= cql && cqr <= qr);
            cb(qi, it->second);
        }

        mp[{ql, qr}] = qi;
    }
}

long solve(vector<pair<int, int>> arr,
           vector<array<int, 3>> walk,
           int src,
           int dest) {
    map<int, int> x_to_h;
    for (auto& [x, h] : arr) {
        x_to_h[x] = h;
    }
    int src_h = x_to_h[src], dest_h = x_to_h[dest];
    assert(src_h && dest_h);

    int c_src = sz(walk), c_dest = sz(walk) + 1;
    walk.push_back({src, src, 0});
    walk.push_back({dest, dest, 0});

    using S = pair<int, int>;

    vector<tuple<S, S, long>> edges;

    auto add_edge = [&](const S& s1, const S& s2) -> void {
        auto& [x1, y1] = s1;
        auto& [x2, y2] = s2;
        assert(x1 == x2 || y1 == y2);
        dbg(s1, s2);
        edges.emplace_back(s1, s2, abs(x1 - x2) + abs(y1 - y2));
    };

    vector<array<int, 4>> n_walk;
    for (int i = 0; i < sz(walk); i++) {
        auto& [ql, qr, qh] = walk[i];
        n_walk.push_back({ql, qr, i, qh});
    }

    vector<S> w_segs[sz(walk)];

    vector<array<int, 5>> queries;

    auto inter = [&](int l1, int r1, int l2, int r2) -> bool {
        if (l1 > l2) {
            swap(l1, l2);
            swap(r1, r2);
        }
        return l2 <= r1;
    };

    auto go = [&](int u, int v, int x) -> void {
        int h1 = walk[u][2], h2 = walk[v][2];
        w_segs[u].emplace_back(x, h1);
        w_segs[v].emplace_back(x, h2);

        add_edge(S {x, h1}, S {x, h2});
    };
    auto go_query = [&](int cql, int cqr, int mh, int u, int v) -> void {
        set<int> pos;
        for (auto& [x, h] : arr) {
            if (mh <= h) {
                pos.insert(x);
            }
        }
        auto go_c = [&](int x) -> void {
            if (cql <= x && x <= cqr) {
                dbg(u, v, x);
                go(u, v, x);
            }
        };
        auto f_nearest = [&](int base) -> void {
            auto it = pos.lower_bound(base);
            if (it != pos.end()) {
                go_c(*it);
            }
            if (it != pos.begin()) {
                go_c(*(--it));
            }
        };
        f_nearest(cql);
        f_nearest(cqr);
        f_nearest(src);
        f_nearest(dest);
    };
    auto cb_edge = [&](int u, int v) -> void {
        auto [l1, r1, h1] = walk[u];
        auto [l2, r2, h2] = walk[v];
        if (!inter(l1, r1, l2, r2)) {
            return;
        }

        int cql = max(l1, l2), cqr = min(r1, r2);
        queries.push_back({cql, cqr, max(h1, h2), u, v});
    };

    for (int i = 0; i < sz(walk); i++) {
        cb_edge(i, c_src);
        cb_edge(i, c_dest);
    }

    add_edges(
        sorted(n_walk, CmpByKey([&](const auto& a) -> int { return a[3]; })),
        cb_edge);
    add_edges(
        sorted(n_walk, CmpByKey([&](const auto& a) -> int { return -a[3]; })),
        cb_edge);

    map<int, vector<pair<bool, int>>> mp;
    for (auto& [x, h] : arr) {
        mp[-h].emplace_back(true, x);
    }
    for (int i = 0; i < sz(queries); i++) {
        mp[-queries[i][2]].emplace_back(false, i);
    }

    set<int> pos;

    for (auto& [nh, e] : mp) {
        for (auto& [ty, x] : e) {
            if (ty) {
                pos.insert(x);
            }
        }

        for (auto& [ty, qi] : e) {
            if (ty) {
                continue;
            }
            auto& [cql, cqr, _h, u, v] = queries[qi];

            vector<int> ccache;
            auto go_c = [&](int x) -> void {
                if (cql <= x && x <= cqr) {
                    ccache.push_back(x);
                }
            };
            auto f_nearest = [&](int base) -> void {
                auto it = pos.lower_bound(base);
                if (it != pos.end()) {
                    go_c(*it);
                }
                if (it != pos.begin()) {
                    go_c(*(--it));
                }
            };

            f_nearest(cql);
            f_nearest(cqr);
            f_nearest(src);
            f_nearest(dest);

            sort(begin(ccache), end(ccache));
            ccache.erase(unique(begin(ccache), end(ccache)), ccache.end());
            for (auto& a : ccache) {
                go(u, v, a);
            }
        }
    }

    for (auto& a : w_segs) {
        sort(begin(a), end(a));
        a.erase(unique(begin(a), end(a)), a.end());

        for (int i = 0; i + 1 < sz(a); i++) {
            add_edge(a[i], a[i + 1]);
        }
    }

    sort(begin(edges), end(edges));
    edges.erase(unique(begin(edges), end(edges)), edges.end());

    return dijkstra(edges, S {src, 0}, S {dest, 0});
}

}  // namespace s2

ll min_distance(vector<int> arr_x,
                vector<int> arr_h,
                vector<int> walk_l,
                vector<int> walk_r,
                vector<int> walk_y,
                int src,
                int dest) {
    int n = sz(arr_x), m = sz(walk_l);

    vector<pair<int, int>> arr(n);
    for (int i = 0; i < n; i++) {
        arr[i] = {arr_x[i], arr_h[i]};
    }

    vector<array<int, 3>> walk(m);
    for (int i = 0; i < m; i++) {
        walk[i] = {arr_x[walk_l[i]], arr_x[walk_r[i]], walk_y[i]};
    }

    src = arr_x[src];
    dest = arr_x[dest];

    return s2::solve(arr, walk, src, dest);
}

Compilation message

walk.cpp: In function 'int64_t s1::solve(std::vector<std::pair<int, int> >, std::vector<std::array<int, 3> >, int, int)':
walk.cpp:167:16: warning: unused structured binding declaration [-Wunused-variable]
  167 |     for (auto& [ql, qr, h] : d_walk) {
      |                ^~~~~~~~~~~
walk.cpp:201:16: warning: unused structured binding declaration [-Wunused-variable]
  201 |     for (auto& [u, v, w] : edges) {
      |                ^~~~~~~~~
walk.cpp: In function 'int64_t s2::solve(std::vector<std::pair<int, int> >, std::vector<std::array<int, 3> >, int, int)':
walk.cpp:310:10: warning: variable 'go_query' set but not used [-Wunused-but-set-variable]
  310 |     auto go_query = [&](int cql, int cqr, int mh, int u, int v) -> void {
      |          ^~~~~~~~
walk.cpp: In instantiation of 'void s2::add_edges(std::vector<std::array<int, 4> >, const Cb&) [with Cb = s2::solve(std::vector<std::pair<int, int> >, std::vector<std::array<int, 3> >, int, int)::<lambda(int, int)>]':
walk.cpp:355:16:   required from here
walk.cpp:219:9: warning: unused variable 'n' [-Wunused-variable]
  219 |     int n = sz(arr);
      |         ^

Subtask #1
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 468 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 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 1 ms 340 KB Output is correct
17 Correct 1 ms 468 KB Output is correct

Subtask #2
14.0 / 14.0

# 결과 실행 시간 메모리 Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1503 ms 345088 KB Output is correct
4 Correct 1884 ms 344332 KB Output is correct
5 Correct 1230 ms 263224 KB Output is correct
6 Correct 1105 ms 227356 KB Output is correct
7 Correct 1256 ms 263228 KB Output is correct
8 Correct 1675 ms 383660 KB Output is correct
9 Correct 1678 ms 313260 KB Output is correct
10 Correct 2054 ms 391872 KB Output is correct
11 Correct 1209 ms 228992 KB Output is correct
12 Correct 748 ms 104024 KB Output is correct
13 Correct 2052 ms 388372 KB Output is correct
14 Correct 590 ms 96244 KB Output is correct
15 Correct 593 ms 96540 KB Output is correct
16 Correct 558 ms 104116 KB Output is correct
17 Correct 577 ms 99612 KB Output is correct
18 Correct 638 ms 169244 KB Output is correct
19 Correct 18 ms 5180 KB Output is correct
20 Correct 226 ms 48912 KB Output is correct
21 Correct 651 ms 103892 KB Output is correct
22 Correct 543 ms 89844 KB Output is correct
23 Correct 619 ms 132204 KB Output is correct
24 Correct 549 ms 96888 KB Output is correct
25 Correct 559 ms 98116 KB Output is correct

Subtask #3
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 307 ms 53748 KB Output is correct
2 Correct 2054 ms 485600 KB Output is correct
3 Correct 2380 ms 511832 KB Output is correct
4 Correct 2549 ms 523020 KB Output is correct
5 Correct 3114 ms 545344 KB Output is correct
6 Correct 2527 ms 480808 KB Output is correct
7 Correct 1154 ms 230524 KB Output is correct
8 Correct 666 ms 95920 KB Output is correct
9 Correct 2630 ms 450856 KB Output is correct
10 Correct 783 ms 170924 KB Output is correct
11 Correct 23 ms 7628 KB Output is correct

Subtask #4
18.0 / 18.0

# 결과 실행 시간 메모리 Grader output
1 Correct 307 ms 53748 KB Output is correct
2 Correct 2054 ms 485600 KB Output is correct
3 Correct 2380 ms 511832 KB Output is correct
4 Correct 2549 ms 523020 KB Output is correct
5 Correct 3114 ms 545344 KB Output is correct
6 Correct 2527 ms 480808 KB Output is correct
7 Correct 1154 ms 230524 KB Output is correct
8 Correct 666 ms 95920 KB Output is correct
9 Correct 2630 ms 450856 KB Output is correct
10 Correct 783 ms 170924 KB Output is correct
11 Correct 23 ms 7628 KB Output is correct
12 Correct 2372 ms 513156 KB Output is correct
13 Correct 2512 ms 534624 KB Output is correct
14 Correct 3142 ms 557168 KB Output is correct
15 Correct 1654 ms 322148 KB Output is correct
16 Correct 1934 ms 378624 KB Output is correct
17 Correct 2335 ms 453804 KB Output is correct
18 Correct 1646 ms 322208 KB Output is correct
19 Correct 1988 ms 378140 KB Output is correct
20 Correct 1324 ms 276452 KB Output is correct
21 Correct 134 ms 29792 KB Output is correct
22 Correct 1642 ms 394872 KB Output is correct
23 Correct 1508 ms 350572 KB Output is correct
24 Correct 879 ms 187816 KB Output is correct
25 Correct 1392 ms 315100 KB Output is correct
26 Correct 527 ms 94856 KB Output is correct
27 Correct 3184 ms 554520 KB Output is correct
28 Correct 2443 ms 539252 KB Output is correct
29 Correct 2676 ms 490076 KB Output is correct
30 Correct 1205 ms 239404 KB Output is correct
31 Correct 2446 ms 460788 KB Output is correct
32 Correct 682 ms 138168 KB Output is correct
33 Correct 667 ms 129288 KB Output is correct
34 Correct 651 ms 148660 KB Output is correct
35 Correct 965 ms 198900 KB Output is correct
36 Correct 730 ms 131156 KB Output is correct
37 Correct 647 ms 105672 KB Output is correct
38 Correct 545 ms 91788 KB Output is correct
39 Correct 633 ms 134140 KB Output is correct
40 Correct 597 ms 98980 KB Output is correct
41 Correct 554 ms 100164 KB Output is correct

Subtask #5
0 / 43.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 468 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 340 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 1 ms 340 KB Output is correct
17 Correct 1 ms 468 KB Output is correct
18 Correct 0 ms 212 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 1503 ms 345088 KB Output is correct
21 Correct 1884 ms 344332 KB Output is correct
22 Correct 1230 ms 263224 KB Output is correct
23 Correct 1105 ms 227356 KB Output is correct
24 Correct 1256 ms 263228 KB Output is correct
25 Correct 1675 ms 383660 KB Output is correct
26 Correct 1678 ms 313260 KB Output is correct
27 Correct 2054 ms 391872 KB Output is correct
28 Correct 1209 ms 228992 KB Output is correct
29 Correct 748 ms 104024 KB Output is correct
30 Correct 2052 ms 388372 KB Output is correct
31 Correct 590 ms 96244 KB Output is correct
32 Correct 593 ms 96540 KB Output is correct
33 Correct 558 ms 104116 KB Output is correct
34 Correct 577 ms 99612 KB Output is correct
35 Correct 638 ms 169244 KB Output is correct
36 Correct 18 ms 5180 KB Output is correct
37 Correct 226 ms 48912 KB Output is correct
38 Correct 651 ms 103892 KB Output is correct
39 Correct 543 ms 89844 KB Output is correct
40 Correct 619 ms 132204 KB Output is correct
41 Correct 549 ms 96888 KB Output is correct
42 Correct 559 ms 98116 KB Output is correct
43 Correct 307 ms 53748 KB Output is correct
44 Correct 2054 ms 485600 KB Output is correct
45 Correct 2380 ms 511832 KB Output is correct
46 Correct 2549 ms 523020 KB Output is correct
47 Correct 3114 ms 545344 KB Output is correct
48 Correct 2527 ms 480808 KB Output is correct
49 Correct 1154 ms 230524 KB Output is correct
50 Correct 666 ms 95920 KB Output is correct
51 Correct 2630 ms 450856 KB Output is correct
52 Correct 783 ms 170924 KB Output is correct
53 Correct 23 ms 7628 KB Output is correct
54 Correct 2372 ms 513156 KB Output is correct
55 Correct 2512 ms 534624 KB Output is correct
56 Correct 3142 ms 557168 KB Output is correct
57 Correct 1654 ms 322148 KB Output is correct
58 Correct 1934 ms 378624 KB Output is correct
59 Correct 2335 ms 453804 KB Output is correct
60 Correct 1646 ms 322208 KB Output is correct
61 Correct 1988 ms 378140 KB Output is correct
62 Correct 1324 ms 276452 KB Output is correct
63 Correct 134 ms 29792 KB Output is correct
64 Correct 1642 ms 394872 KB Output is correct
65 Correct 1508 ms 350572 KB Output is correct
66 Correct 879 ms 187816 KB Output is correct
67 Correct 1392 ms 315100 KB Output is correct
68 Correct 527 ms 94856 KB Output is correct
69 Correct 3184 ms 554520 KB Output is correct
70 Correct 2443 ms 539252 KB Output is correct
71 Correct 2676 ms 490076 KB Output is correct
72 Correct 1205 ms 239404 KB Output is correct
73 Correct 2446 ms 460788 KB Output is correct
74 Correct 682 ms 138168 KB Output is correct
75 Correct 667 ms 129288 KB Output is correct
76 Correct 651 ms 148660 KB Output is correct
77 Correct 965 ms 198900 KB Output is correct
78 Correct 730 ms 131156 KB Output is correct
79 Correct 647 ms 105672 KB Output is correct
80 Correct 545 ms 91788 KB Output is correct
81 Correct 633 ms 134140 KB Output is correct
82 Correct 597 ms 98980 KB Output is correct
83 Correct 554 ms 100164 KB Output is correct
84 Correct 261 ms 46052 KB Output is correct
85 Correct 2365 ms 529540 KB Output is correct
86 Correct 3720 ms 706016 KB Output is correct
87 Correct 150 ms 38660 KB Output is correct
88 Correct 226 ms 56064 KB Output is correct
89 Correct 136 ms 38784 KB Output is correct
90 Correct 93 ms 21076 KB Output is correct
91 Correct 3 ms 1204 KB Output is correct
92 Correct 70 ms 20324 KB Output is correct
93 Correct 867 ms 199156 KB Output is correct
94 Correct 134 ms 31840 KB Output is correct
95 Correct 1755 ms 419776 KB Output is correct
96 Correct 1558 ms 354468 KB Output is correct
97 Correct 930 ms 190364 KB Output is correct
98 Correct 1487 ms 316128 KB Output is correct
99 Execution timed out 4062 ms 844312 KB Time limit exceeded
100 Halted 0 ms 0 KB -