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Submission #1089042

# Submission time Handle Problem Language Result Execution time Memory
1089042 2024-09-15T19:45:00 Z fve5 Star Trek (CEOI20_startrek) C++17
100 / 100
 43 ms 16532 KB 
#include <bits/stdc++.h>
using namespace std;

constexpr int MOD = 1e9 + 7;

struct Mat {
    int mat[2][2] = {};

    int* operator[](const int &idx) { return mat[idx]; }

    Mat operator*(Mat &o) {
        Mat ans;
        for (int i = 0; i < 2; i++)
            for (int j = 0; j < 2; j++)
                for (int k = 0; k < 2; k++)
                    (ans[i][k] += ((long long)mat[i][j] * o[j][k]) % MOD) %= MOD;
        return ans;
    }

    Mat operator^(const long long &exp) {
        Mat ans = { .mat = {{1, 0}, {0, 1}} };
        Mat base = *this;

        for (long long e = exp; e; e >>= 1) {
            if (e & 1) ans = base * ans;
            base = base * base;
        }

        return ans;
    }
};

struct Info {
    int total_children, won_children, forceable_w, forceable_l;

    pair<bool, int> get_data() const {
        int lost_children = total_children - won_children;
        if (lost_children == 0) {
            return {false, forceable_w};
        } else if (lost_children == 1) {
            return {true, forceable_l};
        } else {
            return {true, 0};
        }
    }

    void merge_child(const Info &ch) {
        auto [w, f] = ch.get_data();
        total_children++;
        won_children += w;
        
        if (w) forceable_w += f;
        else forceable_l += f;
    }

    void demerge_child(const Info &ch) {
        auto [w, f] = ch.get_data();
        total_children--;
        won_children -= w;

        if (w) forceable_w -= f;
        else forceable_l -= f;
    }

    Info() : total_children(0), won_children(0), forceable_l(0), forceable_w(1) { }
};

int solve(int N, long long D, const vector<vector<int>> &adj) {
    vector<Info> dp(N);
    int w = 0, l = 0;
    Mat trans;

    auto dfs1 = [&](auto &&dfs1, int node, int par = -1) -> void {
        dp[node] = Info();

        for (auto child: adj[node]) {
            if (child == par) continue;
            
            dfs1(dfs1, child, node);
            dp[node].merge_child(dp[child]);
        }
    };

    auto dfs2 = [&](auto &&dfs2, int node, int par = -1) -> void {
        if (par != -1) {
            dp[par].demerge_child(dp[node]);
            dp[node].merge_child(dp[par]);
        }

        auto [ww, ff] = dp[node].get_data();

        if (ww) {
            w++;

            (trans[0][0] += ff) %= MOD;
            (trans[1][0] += N - ff) %= MOD;
            (trans[1][1] += N) %= MOD;
        } else {
            l++;

            (trans[0][0] += N - ff) %= MOD;
            (trans[1][0] += ff) %= MOD;
            (trans[0][1] += N) %= MOD;
        }

        for (auto ch: adj[node])
            if (ch != par)
                dfs2(dfs2, ch, node);

        if (par != -1) {
            dp[node].demerge_child(dp[par]);
            dp[par].merge_child(dp[node]);
        }
    };

    dfs1(dfs1, 0);
    dfs2(dfs2, 0);

    Mat final = trans ^ (D - 1);
    int w_tot = ((long long)w * final[1][1] + (long long)l * final[1][0]) % MOD;
    int l_tot = ((long long)w * final[0][1] + (long long)l * final[0][0]) % MOD; 

    auto [ww, ff] = dp[0].get_data();
    long long ans = 0;
    if (ww) {
        (ans += (long long)(N - ff) * l_tot) %= MOD;
        (ans += (long long)N * w_tot) %= MOD;
    } else {
        (ans += (long long)ff * l_tot) %= MOD;
    }

    return ans;
}

int main() {
    ios_base::sync_with_stdio(false); cin.tie(nullptr);
    
    int N; cin >> N;
    long long D; cin >> D;
    vector<vector<int>> adj(N);
    for (int i = 0; i < N - 1; i++) {
        int u, v; cin >> u >> v;
        adj[u - 1].push_back(v - 1);
        adj[v - 1].push_back(u - 1);
    }

    cout << solve(N, D, adj) << '\n';
}

Compilation message

startrek.cpp: In constructor 'Info::Info()':
startrek.cpp:34:52: warning: 'Info::forceable_l' will be initialized after [-Wreorder]
   34 |     int total_children, won_children, forceable_w, forceable_l;
      |                                                    ^~~~~~~~~~~
startrek.cpp:34:39: warning:   'int Info::forceable_w' [-Wreorder]
   34 |     int total_children, won_children, forceable_w, forceable_l;
      |                                       ^~~~~~~~~~~
startrek.cpp:65:5: warning:   when initialized here [-Wreorder]
   65 |     Info() : total_children(0), won_children(0), forceable_l(0), forceable_w(1) { }
      |     ^~~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 344 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 344 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 456 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 344 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 456 KB Output is correct
12 Correct 32 ms 11744 KB Output is correct
13 Correct 43 ms 15848 KB Output is correct
14 Correct 23 ms 8408 KB Output is correct
15 Correct 32 ms 8540 KB Output is correct
16 Correct 31 ms 8532 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 344 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 456 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 0 ms 452 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 0 ms 600 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 0 ms 456 KB Output is correct
21 Correct 0 ms 348 KB Output is correct
22 Correct 0 ms 604 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 0 ms 348 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 0 ms 600 KB Output is correct
28 Correct 0 ms 348 KB Output is correct
29 Correct 1 ms 348 KB Output is correct
30 Correct 1 ms 348 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 344 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 1 ms 604 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 456 KB Output is correct
12 Correct 32 ms 11744 KB Output is correct
13 Correct 43 ms 15848 KB Output is correct
14 Correct 23 ms 8408 KB Output is correct
15 Correct 32 ms 8540 KB Output is correct
16 Correct 31 ms 8532 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 0 ms 452 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 0 ms 600 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 0 ms 456 KB Output is correct
26 Correct 0 ms 348 KB Output is correct
27 Correct 0 ms 604 KB Output is correct
28 Correct 1 ms 348 KB Output is correct
29 Correct 1 ms 348 KB Output is correct
30 Correct 0 ms 348 KB Output is correct
31 Correct 0 ms 348 KB Output is correct
32 Correct 0 ms 600 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 1 ms 348 KB Output is correct
35 Correct 1 ms 348 KB Output is correct
36 Correct 34 ms 12236 KB Output is correct
37 Correct 38 ms 16212 KB Output is correct
38 Correct 27 ms 8576 KB Output is correct
39 Correct 30 ms 8540 KB Output is correct
40 Correct 31 ms 8540 KB Output is correct
41 Correct 34 ms 14200 KB Output is correct
42 Correct 37 ms 15044 KB Output is correct
43 Correct 21 ms 7640 KB Output is correct
44 Correct 30 ms 8540 KB Output is correct
45 Correct 32 ms 8528 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 344 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 1 ms 344 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 1 ms 604 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 0 ms 456 KB Output is correct
19 Correct 32 ms 11744 KB Output is correct
20 Correct 43 ms 15848 KB Output is correct
21 Correct 23 ms 8408 KB Output is correct
22 Correct 32 ms 8540 KB Output is correct
23 Correct 31 ms 8532 KB Output is correct
24 Correct 0 ms 348 KB Output is correct
25 Correct 1 ms 348 KB Output is correct
26 Correct 1 ms 348 KB Output is correct
27 Correct 0 ms 452 KB Output is correct
28 Correct 1 ms 348 KB Output is correct
29 Correct 1 ms 348 KB Output is correct
30 Correct 0 ms 600 KB Output is correct
31 Correct 1 ms 348 KB Output is correct
32 Correct 0 ms 456 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 0 ms 604 KB Output is correct
35 Correct 1 ms 348 KB Output is correct
36 Correct 1 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 600 KB Output is correct
40 Correct 0 ms 348 KB Output is correct
41 Correct 1 ms 348 KB Output is correct
42 Correct 1 ms 348 KB Output is correct
43 Correct 34 ms 12236 KB Output is correct
44 Correct 38 ms 16212 KB Output is correct
45 Correct 27 ms 8576 KB Output is correct
46 Correct 30 ms 8540 KB Output is correct
47 Correct 31 ms 8540 KB Output is correct
48 Correct 34 ms 14200 KB Output is correct
49 Correct 37 ms 15044 KB Output is correct
50 Correct 21 ms 7640 KB Output is correct
51 Correct 30 ms 8540 KB Output is correct
52 Correct 32 ms 8528 KB Output is correct
53 Correct 41 ms 16532 KB Output is correct
54 Correct 35 ms 14672 KB Output is correct
55 Correct 19 ms 6872 KB Output is correct
56 Correct 31 ms 12192 KB Output is correct
57 Correct 28 ms 8540 KB Output is correct
58 Correct 29 ms 8528 KB Output is correct
59 Correct 34 ms 8576 KB Output is correct
60 Correct 36 ms 8648 KB Output is correct