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Submission #1072028

# Submission time Handle Problem Language Result Execution time Memory
1072028 2024-08-23T13:31:34 Z shmax Fountain Parks (IOI21_parks) C++17
55 / 100
 3500 ms 96176 KB 
#include "parks.h"
#include <bits/stdc++.h>

using namespace std;
using i32 = int;
#define int long long
#define len(x) (int)(x.size())
template<typename T>
using vec = vector<T>;

struct DSU {
public:
    DSU() : _n(0) {}

    explicit DSU(int n) : _n(n), parent_or_size(n, -1) {}

    int unite(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }

    bool one(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }

    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }

    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
                std::remove_if(result.begin(), result.end(),
                               [&](const std::vector<int> &v) { return v.empty(); }),
                result.end());
        return result;
    }

private:
    int _n;
    // root node: -1 * component size
    // otherwise: parent
    std::vector<int> parent_or_size;
};


i32 construct_roads(std::vector<i32> _x, std::vector<i32> _y) {
    int n = len(_x);
    map<pair<int, int>, int> mp;
    for (int i = 0; i < n; i++) {
        mp[{_x[i], _y[i]}] = i;
    }
    mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
    vec<pair<int, int>> edges;
    for (int i = 0; i < n; i++) {
        vec<pair<int, int>> moves = {{-2, 0},
                                     {2,  0},
                                     {0,  -2},
                                     {0,  2}};
        for (auto [dx, dy]: moves) {
            int nx = _x[i] + dx;
            int ny = _y[i] + dy;
            if (!mp.count({nx, ny})) continue;
            edges.push_back({i, mp[{nx, ny}]});
        }
    }
    for (int times = 0; times < 10; times++) {
        DSU dsu(n);

        shuffle(edges.begin(), edges.end(), rnd);

        vec<pair<int, int>> used_edges;
        for (auto [a, b]: edges) {
            if (dsu.one(a, b)) continue;
            dsu.unite(a, b);
            used_edges.emplace_back(a, b);
        }
        if (dsu.size(0) != n) return 0;
        map<pair<int, int>, int> benches;
        vec<pair<int, int>> benches_pos;
        int idx = 0;
        for (auto [a, b]: used_edges) {
            auto [x1, y1] = pair<int, int>{_x[a], _y[a]};
            auto [x2, y2] = pair<int, int>{_x[b], _y[b]};
            if (x1 == x2) {
                if (!benches.count({x1 - 1, (y1 + y2) / 2}))
                    benches[{x1 - 1, (y1 + y2) / 2}] = idx++, benches_pos.emplace_back(x1 - 1, (y1 + y2) / 2);
                if (!benches.count({x1 + 1, (y1 + y2) / 2}))
                    benches[{x1 + 1, (y1 + y2) / 2}] = idx++, benches_pos.emplace_back(x1 + 1, (y1 + y2) / 2);
            } else {
                if (!benches.count({(x1 + x2) / 2, y1 - 1}))
                    benches[{(x1 + x2) / 2, y1 - 1}] = idx++, benches_pos.emplace_back((x1 + x2) / 2, y1 - 1);
                if (!benches.count({(x1 + x2) / 2, y1 + 1}))
                    benches[{(x1 + x2) / 2, y1 + 1}] = idx++, benches_pos.emplace_back((x1 + x2) / 2, y1 + 1);
            }
        }
        vec<vec<int>> g(n - 1 + len(benches));
        int idt = 0;
        for (auto [a, b]: used_edges) {
            auto [x1, y1] = pair<int, int>{_x[a], _y[a]};
            auto [x2, y2] = pair<int, int>{_x[b], _y[b]};
            if (x1 == x2) {
                g[idt].push_back(n - 1 + benches[{x1 - 1, (y1 + y2) / 2}]);
                g[idt].push_back(n - 1 + benches[{x1 + 1, (y1 + y2) / 2}]);
            } else {
                g[idt].push_back(n - 1 + benches[{(x1 + x2) / 2, y1 - 1}]);
                g[idt].push_back(n - 1 + benches[{(x1 + x2) / 2, y1 + 1}]);
            }
            idt++;
        }

//        matching
//        shuffle
        for (int i = 0; i < n - 1; i++) {
            shuffle(g[i].begin(), g[i].end(), rnd);
        }
        vec<int> match(n - 1 + len(benches), -1);
        vec<bool> used(n - 1 + len(benches), false);
        function<bool(int)> dfs = [&](int v) -> bool {
            if (used[v]) return false;
            used[v] = true;
            for (auto u: g[v]) {
                if (match[u] == -1 || dfs(match[u])) {
                    match[u] = v;
                    match[v] = u;
                    return true;
                }
            }
            return false;
        };

        bool flag = true;
        do {
            flag = false;
            fill(used.begin(), used.end(), false);
            for (int i = 0; i < n - 1; i++) {
                if (match[i] == -1) {
                    if (dfs(i)) {
                        flag = true;
                    }
                }
            }
        } while (flag);

        int cnt = 0;
        for (int i = 0; i < n - 1; i++) {
            if (match[i] != -1) cnt++;
        }

        if (cnt == n - 1) {
            vec<i32> x_benches, y_benches;
            vec<i32> u, v;
            for (int i = 0; i < n - 1; i++) {
                x_benches.push_back(benches_pos[match[i] - n + 1].first);
                y_benches.push_back(benches_pos[match[i] - n + 1].second);
                u.push_back(used_edges[i].first);
                v.push_back(used_edges[i].second);
            }
            build(u, v, x_benches, y_benches);
            return 1;
        }


    }

    return 0;
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 316 ms 48508 KB Output is correct
10 Correct 20 ms 5080 KB Output is correct
11 Correct 124 ms 25304 KB Output is correct
12 Correct 46 ms 7368 KB Output is correct
13 Correct 52 ms 7272 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 2 ms 600 KB Output is correct
16 Correct 312 ms 47068 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 316 ms 48508 KB Output is correct
10 Correct 20 ms 5080 KB Output is correct
11 Correct 124 ms 25304 KB Output is correct
12 Correct 46 ms 7368 KB Output is correct
13 Correct 52 ms 7272 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 2 ms 600 KB Output is correct
16 Correct 312 ms 47068 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 344 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 344 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 874 ms 80212 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 2 ms 860 KB Output is correct
26 Correct 3 ms 860 KB Output is correct
27 Correct 4 ms 1116 KB Output is correct
28 Correct 259 ms 32016 KB Output is correct
29 Correct 383 ms 49084 KB Output is correct
30 Correct 584 ms 66556 KB Output is correct
31 Correct 768 ms 79008 KB Output is correct
32 Correct 0 ms 348 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 1 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 0 ms 348 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 0 ms 348 KB Output is correct
41 Correct 0 ms 348 KB Output is correct
42 Correct 0 ms 348 KB Output is correct
43 Correct 2 ms 600 KB Output is correct
44 Correct 4 ms 860 KB Output is correct
45 Correct 306 ms 40132 KB Output is correct
46 Correct 571 ms 60344 KB Output is correct
47 Correct 490 ms 60720 KB Output is correct

Subtask #3
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 316 ms 48508 KB Output is correct
10 Correct 20 ms 5080 KB Output is correct
11 Correct 124 ms 25304 KB Output is correct
12 Correct 46 ms 7368 KB Output is correct
13 Correct 52 ms 7272 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 2 ms 600 KB Output is correct
16 Correct 312 ms 47068 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 344 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 344 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 874 ms 80212 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 2 ms 860 KB Output is correct
26 Correct 3 ms 860 KB Output is correct
27 Correct 4 ms 1116 KB Output is correct
28 Correct 259 ms 32016 KB Output is correct
29 Correct 383 ms 49084 KB Output is correct
30 Correct 584 ms 66556 KB Output is correct
31 Correct 768 ms 79008 KB Output is correct
32 Correct 0 ms 348 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 1 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 0 ms 348 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 0 ms 348 KB Output is correct
41 Correct 0 ms 348 KB Output is correct
42 Correct 0 ms 348 KB Output is correct
43 Correct 2 ms 600 KB Output is correct
44 Correct 4 ms 860 KB Output is correct
45 Correct 306 ms 40132 KB Output is correct
46 Correct 571 ms 60344 KB Output is correct
47 Correct 490 ms 60720 KB Output is correct
48 Correct 0 ms 348 KB Output is correct
49 Correct 0 ms 348 KB Output is correct
50 Correct 0 ms 348 KB Output is correct
51 Correct 1 ms 348 KB Output is correct
52 Correct 1 ms 348 KB Output is correct
53 Correct 0 ms 348 KB Output is correct
54 Correct 1 ms 344 KB Output is correct
55 Execution timed out 3601 ms 70420 KB Time limit exceeded
56 Halted 0 ms 0 KB -

Subtask #4
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 316 ms 48508 KB Output is correct
10 Correct 20 ms 5080 KB Output is correct
11 Correct 124 ms 25304 KB Output is correct
12 Correct 46 ms 7368 KB Output is correct
13 Correct 52 ms 7272 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 2 ms 600 KB Output is correct
16 Correct 312 ms 47068 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 348 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 679 ms 80536 KB Output is correct
21 Correct 708 ms 76480 KB Output is correct
22 Correct 678 ms 75960 KB Output is correct
23 Correct 586 ms 81584 KB Output is correct
24 Correct 217 ms 17492 KB Output is correct
25 Correct 371 ms 31960 KB Output is correct
26 Correct 309 ms 31812 KB Output is correct
27 Correct 698 ms 94252 KB Output is correct
28 Correct 740 ms 93944 KB Output is correct
29 Correct 767 ms 95272 KB Output is correct
30 Correct 757 ms 94256 KB Output is correct
31 Correct 1 ms 348 KB Output is correct
32 Correct 35 ms 5876 KB Output is correct
33 Correct 102 ms 9024 KB Output is correct
34 Correct 645 ms 75920 KB Output is correct
35 Correct 12 ms 2012 KB Output is correct
36 Correct 70 ms 8060 KB Output is correct
37 Correct 155 ms 16064 KB Output is correct
38 Correct 251 ms 30916 KB Output is correct
39 Correct 336 ms 42168 KB Output is correct
40 Correct 463 ms 57004 KB Output is correct
41 Correct 594 ms 66364 KB Output is correct
42 Correct 761 ms 75760 KB Output is correct
43 Correct 1 ms 348 KB Output is correct
44 Correct 0 ms 348 KB Output is correct
45 Correct 0 ms 348 KB Output is correct
46 Correct 0 ms 348 KB Output is correct
47 Correct 0 ms 348 KB Output is correct
48 Correct 1 ms 348 KB Output is correct
49 Correct 0 ms 348 KB Output is correct
50 Correct 0 ms 344 KB Output is correct
51 Correct 0 ms 348 KB Output is correct
52 Correct 0 ms 344 KB Output is correct
53 Correct 1 ms 348 KB Output is correct
54 Correct 2 ms 604 KB Output is correct
55 Correct 3 ms 860 KB Output is correct
56 Correct 314 ms 40624 KB Output is correct
57 Correct 485 ms 61060 KB Output is correct
58 Correct 518 ms 58940 KB Output is correct
59 Correct 0 ms 348 KB Output is correct
60 Correct 1 ms 348 KB Output is correct
61 Correct 1 ms 348 KB Output is correct
62 Correct 693 ms 93500 KB Output is correct
63 Correct 747 ms 95172 KB Output is correct
64 Correct 731 ms 96176 KB Output is correct
65 Correct 6 ms 860 KB Output is correct
66 Correct 8 ms 1504 KB Output is correct
67 Correct 327 ms 39864 KB Output is correct
68 Correct 566 ms 61364 KB Output is correct
69 Correct 719 ms 81080 KB Output is correct

Subtask #5
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 316 ms 48508 KB Output is correct
10 Correct 20 ms 5080 KB Output is correct
11 Correct 124 ms 25304 KB Output is correct
12 Correct 46 ms 7368 KB Output is correct
13 Correct 52 ms 7272 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 2 ms 600 KB Output is correct
16 Correct 312 ms 47068 KB Output is correct
17 Correct 792 ms 93916 KB Output is correct
18 Correct 732 ms 94760 KB Output is correct
19 Correct 781 ms 77116 KB Output is correct
20 Correct 825 ms 78524 KB Output is correct
21 Correct 720 ms 77744 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 90 ms 12248 KB Output is correct
24 Correct 27 ms 3488 KB Output is correct
25 Correct 116 ms 12692 KB Output is correct
26 Correct 208 ms 19056 KB Output is correct
27 Correct 331 ms 39324 KB Output is correct
28 Correct 415 ms 50864 KB Output is correct
29 Correct 516 ms 61620 KB Output is correct
30 Correct 636 ms 68876 KB Output is correct
31 Correct 720 ms 78268 KB Output is correct
32 Correct 696 ms 82952 KB Output is correct
33 Correct 666 ms 93620 KB Output is correct
34 Correct 5 ms 1240 KB Output is correct
35 Correct 9 ms 1748 KB Output is correct
36 Correct 295 ms 40236 KB Output is correct
37 Correct 491 ms 60832 KB Output is correct
38 Correct 714 ms 80128 KB Output is correct

Subtask #6
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 344 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 316 ms 48508 KB Output is correct
10 Correct 20 ms 5080 KB Output is correct
11 Correct 124 ms 25304 KB Output is correct
12 Correct 46 ms 7368 KB Output is correct
13 Correct 52 ms 7272 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 2 ms 600 KB Output is correct
16 Correct 312 ms 47068 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 0 ms 344 KB Output is correct
19 Correct 0 ms 348 KB Output is correct
20 Correct 1 ms 344 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 348 KB Output is correct
23 Correct 874 ms 80212 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 2 ms 860 KB Output is correct
26 Correct 3 ms 860 KB Output is correct
27 Correct 4 ms 1116 KB Output is correct
28 Correct 259 ms 32016 KB Output is correct
29 Correct 383 ms 49084 KB Output is correct
30 Correct 584 ms 66556 KB Output is correct
31 Correct 768 ms 79008 KB Output is correct
32 Correct 0 ms 348 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 1 ms 348 KB Output is correct
35 Correct 0 ms 348 KB Output is correct
36 Correct 0 ms 348 KB Output is correct
37 Correct 0 ms 348 KB Output is correct
38 Correct 0 ms 348 KB Output is correct
39 Correct 0 ms 348 KB Output is correct
40 Correct 0 ms 348 KB Output is correct
41 Correct 0 ms 348 KB Output is correct
42 Correct 0 ms 348 KB Output is correct
43 Correct 2 ms 600 KB Output is correct
44 Correct 4 ms 860 KB Output is correct
45 Correct 306 ms 40132 KB Output is correct
46 Correct 571 ms 60344 KB Output is correct
47 Correct 490 ms 60720 KB Output is correct
48 Correct 0 ms 348 KB Output is correct
49 Correct 0 ms 348 KB Output is correct
50 Correct 0 ms 348 KB Output is correct
51 Correct 1 ms 348 KB Output is correct
52 Correct 1 ms 348 KB Output is correct
53 Correct 0 ms 348 KB Output is correct
54 Correct 1 ms 344 KB Output is correct
55 Execution timed out 3601 ms 70420 KB Time limit exceeded
56 Halted 0 ms 0 KB -