oj.uz

Submission #800040

# Submission time Handle Problem Language Result Execution time Memory
800040 2023-08-01T09:33:54 Z jakobrs Radio Towers (IOI22_towers) C++17
23 / 100
 4000 ms 26364 KB 
#include <algorithm>
#include <optional>
#include <unordered_set>
#include <vector>
#include <map>
#include <queue>

int n;
std::vector<int> h;

int max_idx;
std::map<int, int> data;

void init(int N, std::vector<int> H) {
    n = N;
    h = H;

    max_idx = 0;
    for (int i = 1; i < N; i++) {
        if (H[i] > H[max_idx]) {
            max_idx = i;
        }
    }

    int towers = 0;

    struct D {
        int prev;
        int max_to_prev;
        int next;
        int max_to_next;
    };
    std::vector<D> adj;

    for (int i = 0; i < N; i++) {
        towers += 1;
        int max_to_prev = H[i];
        int max_to_next = H[i];
        if (i != 0) max_to_prev = std::max(max_to_prev, H[i - 1]);
        if (i + 1 != N) max_to_next = std::max(max_to_next, H[i + 1]);
        adj.push_back({.prev = i - 1,
                       .max_to_prev = max_to_prev,
                       .next = i + 1 == N ? -1 : i + 1,
                       .max_to_next = max_to_next});
    }

    struct PQItem {
        int priority;
        int from;
        int to;

        bool operator<(const PQItem &rhs) const {
            return priority > rhs.priority;
        }
    };

    std::vector<bool> active(adj.size(), true);
    std::priority_queue<PQItem> pq;
    for (int i = 1; i < adj.size(); i++) {
        pq.push({.priority = 0, .from = i - 1, .to = i});
    }

    while (!pq.empty()) {
        auto [priority, from, to] = pq.top();
        pq.pop();

        if (!active[from] || !active[to]) continue;

        data.emplace(priority, towers);

        if (H[from] > H[to]) {
            int max = adj[to].max_to_prev =
                std::max(adj[from].max_to_prev, adj[to].max_to_prev);
            adj[to].prev = adj[from].prev;
            if (adj[to].prev != -1) {
                adj[adj[to].prev].next = to;
                pq.push({.priority = max - std::max(H[adj[to].prev], H[to]),
                         .from = adj[to].prev,
                         .to = to});
            }
            towers -= 1;
            active[from] = false;
        } else {
            int max = adj[from].max_to_next =
                std::max(adj[from].max_to_next, adj[to].max_to_next);
            adj[from].next = adj[to].next;
            if (adj[from].next != -1) {
                adj[adj[from].next].prev = from;
                pq.push({.priority = max - std::max(H[from], H[adj[from].next]),
                         .from = from,
                         .to = adj[from].next});
            }
            towers -= 1;
            active[to] = false;
        }
    }

    data.emplace(2'000'000'000, towers);
}

template <typename Node>
struct SegmentTree {
    std::vector<Node> nodes;
    int offset;

    explicit SegmentTree(int sz) : nodes(2 * sz), offset(sz) {}

    void update(int idx, const Node &node) {
        idx += offset;
        nodes[idx] = node;

        while (idx /= 2) {
            nodes[idx] = nodes[2 * idx] * nodes[2 * idx + 1];
        }
    }

    Node query(int l, int r) const {
        Node left, right;

        l += offset;
        r += offset;

        while (l < r) {
            if (l & 1) left = left * nodes[l++];
            if (r & 1) right = nodes[--r] * right;

            l >>= 1;
            r >>= 1;
        }

        return left * right;
    }
};

int d;

struct LeftNode {
    int a, b, min, max;

    LeftNode() : a(-1), b(-1), min(2'000'000'000), max(-2'000'000'000) {}
    LeftNode(int a) : a(-1), b(-1), min(a), max(a) {}
    LeftNode(int a, int b, int min, int max) : a(a), b(b), min(min), max(max) {}

    LeftNode operator*(const LeftNode &rhs) const {
        std::pair<int, int> c1 = {b, a};
        std::pair<int, int> c2 = {rhs.b, rhs.a};
        std::pair<int, int> c3 = {-1, -1};
        if (rhs.max >= 0 && rhs.max - min >= d) {
            c3 = {rhs.max, min};
        }

        std::pair<int, int> best = std::max(std::max(c1, c2), c3);

        return {best.second, best.first, std::min(min, rhs.min),
                std::max(max, rhs.max)};
    }
};
struct RightNode {
    int a, b, min, max;

    RightNode() : a(-1), b(-1), min(2'000'000'000), max(-2'000'000'000) {}
    RightNode(int a) : a(-1), b(-1), min(a), max(a) {}
    RightNode(int a, int b, int min, int max)
        : a(a), b(b), min(min), max(max) {}

    RightNode operator*(const RightNode &rhs) const {
        std::pair<int, int> c1 = {b, a};
        std::pair<int, int> c2 = {rhs.b, rhs.a};
        std::pair<int, int> c3 = {-1, -1};
        if (max >= 0 && max - rhs.min >= d) {
            c3 = {max, rhs.min};
        }

        std::pair<int, int> best = std::max(std::max(c1, c2), c3);

        return {best.second, best.first, std::min(min, rhs.min),
                std::max(max, rhs.max)};
    }
};

struct PrecomputedData {
    std::unordered_set<int> included_s;
    std::vector<int> prefix_sums, prev, next;

    SegmentTree<LeftNode> left_st;
    SegmentTree<RightNode> right_st;
};

std::optional<PrecomputedData> precomputed;

int max_towers(int L, int R, int D) {
    if (L == R) return 1;
    R += 1;

    precomputed.reset();
    if (!precomputed) {
        d = D;
        std::vector<int> included{h[0]};
        int intermediary = h[0];
        for (int i = 1; i < n; i++) {
            if (h[i] > intermediary) {
                intermediary = h[i];
            } else if (intermediary - included.back() < D) {
                if (h[i] < included.back()) {
                    included.pop_back();
                    included.push_back(h[i]);
                    intermediary = h[i];
                }
            } else if (intermediary - h[i] >= D) {
                included.push_back(h[i]);
                intermediary = h[i];
            }
        }

        std::unordered_set<int> included_s(included.begin(), included.end());

        std::vector<int> prev, next;
        int prev_val = -1;
        for (int i = 0; i < n; i++) {
            if (included_s.count(h[i])) {
                prev_val = i;
            }
            prev.push_back(prev_val);
        }
        int next_val = -1;
        for (int i = n - 1; i >= 0; i--) {
            if (included_s.count(h[i])) {
                next_val = i;
            }
            next.push_back(next_val);
        }
        std::reverse(next.begin(), next.end());
        std::vector<int> prefix_sums{1};
        prefix_sums.reserve(n + 1);
        for (int i = 0; i < n; i++) {
            prefix_sums.push_back(prefix_sums.back() + included_s.count(h[i]));
        }

        int o = 1;
        while (o < n) o *= 2;

        SegmentTree<LeftNode> left_st(o);
        SegmentTree<RightNode> right_st(o);

        for (int i = 0; i < n; i++) {
            left_st.update(i, LeftNode(h[i]));
            right_st.update(i, RightNode(h[i]));
        }

        precomputed = std::make_optional(PrecomputedData{
            included_s, prefix_sums, prev, next, left_st, right_st});
    }

    if (L == 0 && R + 1 == n) {
        return data.lower_bound(D)->second;
    }

    if (D != d) {
        if (R - 1 <= max_idx) {
            return 1;
        }
        if (L >= max_idx) {
            return 1;
        }

        int a = h[L];
        int b = h[R - 1];
        int c = h[max_idx];

        if (c - a >= D && c - b >= D) {
            return 2;
        } else {
            return 1;
        }
    }

    int total = precomputed->prefix_sums[R] - precomputed->prefix_sums[L];

    int next = precomputed->next[L];
    auto q0 = precomputed->left_st.query(L, next);
    if (q0.b - h[next] >= D) {
        total += 1;
    }

    int prev = precomputed->prev[R - 1];
    auto q1 = precomputed->right_st.query(prev + 1, R);
    if (q1.b - h[prev] >= D) {
        total += 1;
    }

    return std::max(total, 1);
}

Compilation message

towers.cpp: In function 'void init(int, std::vector<int>)':
towers.cpp:59:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<init(int, std::vector<int>)::D>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   59 |     for (int i = 1; i < adj.size(); i++) {
      |                     ~~^~~~~~~~~~~~

Subtask #1
0 / 4.0

# Verdict Execution time Memory Grader output
1 Execution timed out 4046 ms 10532 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 336 KB Output is correct
2 Correct 2 ms 592 KB Output is correct
3 Correct 1 ms 592 KB Output is correct
4 Correct 2 ms 720 KB Output is correct
5 Correct 1 ms 592 KB Output is correct
6 Correct 2 ms 592 KB Output is correct
7 Correct 2 ms 592 KB Output is correct
8 Correct 1 ms 592 KB Output is correct
9 Correct 1 ms 620 KB Output is correct
10 Correct 1 ms 592 KB Output is correct
11 Correct 1 ms 592 KB Output is correct
12 Correct 0 ms 208 KB Output is correct
13 Correct 1 ms 592 KB Output is correct
14 Correct 1 ms 592 KB Output is correct
15 Correct 2 ms 604 KB Output is correct
16 Correct 2 ms 720 KB Output is correct
17 Correct 2 ms 720 KB Output is correct
18 Correct 1 ms 592 KB Output is correct
19 Correct 1 ms 592 KB Output is correct
20 Correct 2 ms 592 KB Output is correct
21 Correct 2 ms 720 KB Output is correct
22 Correct 2 ms 720 KB Output is correct
23 Correct 1 ms 592 KB Output is correct
24 Correct 1 ms 592 KB Output is correct
25 Correct 1 ms 336 KB Output is correct
26 Correct 1 ms 592 KB Output is correct
27 Correct 2 ms 592 KB Output is correct
28 Correct 1 ms 592 KB Output is correct
29 Correct 2 ms 592 KB Output is correct
30 Correct 1 ms 592 KB Output is correct
31 Correct 1 ms 592 KB Output is correct
32 Correct 1 ms 592 KB Output is correct
33 Correct 1 ms 592 KB Output is correct
34 Correct 1 ms 592 KB Output is correct
35 Correct 2 ms 592 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 336 KB Output is correct
2 Correct 2 ms 592 KB Output is correct
3 Correct 1 ms 592 KB Output is correct
4 Correct 2 ms 720 KB Output is correct
5 Correct 1 ms 592 KB Output is correct
6 Correct 2 ms 592 KB Output is correct
7 Correct 2 ms 592 KB Output is correct
8 Correct 1 ms 592 KB Output is correct
9 Correct 1 ms 620 KB Output is correct
10 Correct 1 ms 592 KB Output is correct
11 Correct 1 ms 592 KB Output is correct
12 Correct 0 ms 208 KB Output is correct
13 Correct 1 ms 592 KB Output is correct
14 Correct 1 ms 592 KB Output is correct
15 Correct 2 ms 604 KB Output is correct
16 Correct 2 ms 720 KB Output is correct
17 Correct 2 ms 720 KB Output is correct
18 Correct 1 ms 592 KB Output is correct
19 Correct 1 ms 592 KB Output is correct
20 Correct 2 ms 592 KB Output is correct
21 Correct 2 ms 720 KB Output is correct
22 Correct 2 ms 720 KB Output is correct
23 Correct 1 ms 592 KB Output is correct
24 Correct 1 ms 592 KB Output is correct
25 Correct 1 ms 336 KB Output is correct
26 Correct 1 ms 592 KB Output is correct
27 Correct 2 ms 592 KB Output is correct
28 Correct 1 ms 592 KB Output is correct
29 Correct 2 ms 592 KB Output is correct
30 Correct 1 ms 592 KB Output is correct
31 Correct 1 ms 592 KB Output is correct
32 Correct 1 ms 592 KB Output is correct
33 Correct 1 ms 592 KB Output is correct
34 Correct 1 ms 592 KB Output is correct
35 Correct 2 ms 592 KB Output is correct
36 Correct 55 ms 13196 KB Output is correct
37 Correct 78 ms 21980 KB Output is correct
38 Correct 91 ms 23220 KB Output is correct
39 Correct 77 ms 22376 KB Output is correct
40 Correct 91 ms 25520 KB Output is correct
41 Correct 86 ms 24124 KB Output is correct
42 Correct 91 ms 26316 KB Output is correct
43 Correct 57 ms 20160 KB Output is correct
44 Correct 62 ms 20156 KB Output is correct
45 Correct 61 ms 20168 KB Output is correct
46 Correct 64 ms 20156 KB Output is correct
47 Correct 94 ms 24128 KB Output is correct
48 Correct 91 ms 26248 KB Output is correct
49 Correct 93 ms 26304 KB Output is correct
50 Correct 67 ms 20184 KB Output is correct
51 Correct 70 ms 20156 KB Output is correct
52 Correct 87 ms 24148 KB Output is correct
53 Correct 90 ms 26364 KB Output is correct
54 Correct 90 ms 26256 KB Output is correct
55 Correct 67 ms 20204 KB Output is correct
56 Correct 62 ms 20096 KB Output is correct
57 Correct 81 ms 22204 KB Output is correct
58 Correct 83 ms 22936 KB Output is correct
59 Correct 85 ms 23484 KB Output is correct
60 Correct 91 ms 26272 KB Output is correct
61 Correct 92 ms 25740 KB Output is correct
62 Correct 87 ms 24548 KB Output is correct
63 Correct 89 ms 25688 KB Output is correct
64 Correct 56 ms 20184 KB Output is correct
65 Correct 62 ms 20160 KB Output is correct
66 Correct 72 ms 20292 KB Output is correct
67 Correct 63 ms 20176 KB Output is correct

Subtask #4
0 / 14.0

# Verdict Execution time Memory Grader output
1 Execution timed out 4035 ms 24260 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #5
0 / 17.0

# Verdict Execution time Memory Grader output
1 Execution timed out 4088 ms 6252 KB Time limit exceeded
2 Halted 0 ms 0 KB -

Subtask #6
0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 336 KB Output is correct
2 Correct 2 ms 592 KB Output is correct
3 Correct 1 ms 592 KB Output is correct
4 Correct 2 ms 720 KB Output is correct
5 Correct 1 ms 592 KB Output is correct
6 Correct 2 ms 592 KB Output is correct
7 Correct 2 ms 592 KB Output is correct
8 Correct 1 ms 592 KB Output is correct
9 Correct 1 ms 620 KB Output is correct
10 Correct 1 ms 592 KB Output is correct
11 Correct 1 ms 592 KB Output is correct
12 Correct 0 ms 208 KB Output is correct
13 Correct 1 ms 592 KB Output is correct
14 Correct 1 ms 592 KB Output is correct
15 Correct 2 ms 604 KB Output is correct
16 Correct 2 ms 720 KB Output is correct
17 Correct 2 ms 720 KB Output is correct
18 Correct 1 ms 592 KB Output is correct
19 Correct 1 ms 592 KB Output is correct
20 Correct 2 ms 592 KB Output is correct
21 Correct 2 ms 720 KB Output is correct
22 Correct 2 ms 720 KB Output is correct
23 Correct 1 ms 592 KB Output is correct
24 Correct 1 ms 592 KB Output is correct
25 Correct 1 ms 336 KB Output is correct
26 Correct 1 ms 592 KB Output is correct
27 Correct 2 ms 592 KB Output is correct
28 Correct 1 ms 592 KB Output is correct
29 Correct 2 ms 592 KB Output is correct
30 Correct 1 ms 592 KB Output is correct
31 Correct 1 ms 592 KB Output is correct
32 Correct 1 ms 592 KB Output is correct
33 Correct 1 ms 592 KB Output is correct
34 Correct 1 ms 592 KB Output is correct
35 Correct 2 ms 592 KB Output is correct
36 Correct 55 ms 13196 KB Output is correct
37 Correct 78 ms 21980 KB Output is correct
38 Correct 91 ms 23220 KB Output is correct
39 Correct 77 ms 22376 KB Output is correct
40 Correct 91 ms 25520 KB Output is correct
41 Correct 86 ms 24124 KB Output is correct
42 Correct 91 ms 26316 KB Output is correct
43 Correct 57 ms 20160 KB Output is correct
44 Correct 62 ms 20156 KB Output is correct
45 Correct 61 ms 20168 KB Output is correct
46 Correct 64 ms 20156 KB Output is correct
47 Correct 94 ms 24128 KB Output is correct
48 Correct 91 ms 26248 KB Output is correct
49 Correct 93 ms 26304 KB Output is correct
50 Correct 67 ms 20184 KB Output is correct
51 Correct 70 ms 20156 KB Output is correct
52 Correct 87 ms 24148 KB Output is correct
53 Correct 90 ms 26364 KB Output is correct
54 Correct 90 ms 26256 KB Output is correct
55 Correct 67 ms 20204 KB Output is correct
56 Correct 62 ms 20096 KB Output is correct
57 Correct 81 ms 22204 KB Output is correct
58 Correct 83 ms 22936 KB Output is correct
59 Correct 85 ms 23484 KB Output is correct
60 Correct 91 ms 26272 KB Output is correct
61 Correct 92 ms 25740 KB Output is correct
62 Correct 87 ms 24548 KB Output is correct
63 Correct 89 ms 25688 KB Output is correct
64 Correct 56 ms 20184 KB Output is correct
65 Correct 62 ms 20160 KB Output is correct
66 Correct 72 ms 20292 KB Output is correct
67 Correct 63 ms 20176 KB Output is correct
68 Execution timed out 4035 ms 24260 KB Time limit exceeded
69 Halted 0 ms 0 KB -

Subtask #7
0 / 23.0

# Verdict Execution time Memory Grader output
1 Execution timed out 4046 ms 10532 KB Time limit exceeded
2 Halted 0 ms 0 KB -