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Submission #1089036

# Submission time Handle Problem Language Result Execution time Memory
1089036 2024-09-15T19:30:36 Z fve5 Star Trek (CEOI20_startrek) C++17
50 / 100
 1000 ms 15444 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 {
    bool win;
    int forceable;

    void merge_child(const Info &ch) {
        if (win) {
            if (!ch.win) {
                forceable = 0;
            }
        } else {
            if (ch.win) {
                forceable += ch.forceable;
            } else {
                win = true;
                forceable = ch.forceable;
            }
        }
    }

    Info() : win(false), forceable(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] = Info();
            for (auto ch: adj[par])
                if (ch != node)
                    dp[par].merge_child(dp[ch]);

            dp[node].merge_child(dp[par]);
        }

        if (dp[node].win) {
            w++;

            (trans[0][0] += dp[node].forceable) %= MOD;
            (trans[1][0] += N - dp[node].forceable) %= MOD;
            (trans[1][1] += N) %= MOD;
        } else {
            l++;

            (trans[0][0] += N - dp[node].forceable) %= MOD;
            (trans[1][0] += dp[node].forceable) %= MOD;
            (trans[0][1] += N) %= MOD;
        }

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

        if (par != -1) {
            dp[node] = Info();
            for (auto ch: adj[node])
                if (ch != par)
                    dp[node].merge_child(dp[ch]);

            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; 

    long long ans = 0;
    if (dp[0].win) {
        (ans += (long long)(N - dp[0].forceable) * l_tot) %= MOD;
        (ans += (long long)N * w_tot) %= MOD;
    } else {
        (ans += (long long)dp[0].forceable * 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';
}

Subtask #1
0.0 / 0.0

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

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 456 KB Output is correct
3 Correct 0 ms 456 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 372 KB Output is correct
3 Correct 1 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 0 ms 348 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 372 KB Output is correct
3 Correct 1 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 0 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 372 KB Output is correct
3 Correct 1 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 0 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 39 ms 11344 KB Output is correct
13 Correct 43 ms 15444 KB Output is correct
14 Execution timed out 1079 ms 7640 KB Time limit exceeded
15 Halted 0 ms 0 KB -

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 372 KB Output is correct
3 Correct 1 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 0 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 0 ms 344 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 0 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 0 ms 348 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 0 ms 348 KB Output is correct
21 Correct 1 ms 464 KB Output is correct
22 Correct 1 ms 604 KB Output is correct
23 Correct 1 ms 344 KB Output is correct
24 Correct 0 ms 344 KB Output is correct
25 Correct 0 ms 348 KB Output is correct
26 Correct 1 ms 344 KB Output is correct
27 Correct 0 ms 604 KB Output is correct
28 Correct 0 ms 348 KB Output is correct
29 Correct 1 ms 348 KB Output is correct
30 Correct 0 ms 348 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 372 KB Output is correct
3 Correct 1 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 0 ms 348 KB Output is correct
7 Correct 1 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 39 ms 11344 KB Output is correct
13 Correct 43 ms 15444 KB Output is correct
14 Execution timed out 1079 ms 7640 KB Time limit exceeded
15 Halted 0 ms 0 KB -

Subtask #8
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 456 KB Output is correct
5 Correct 0 ms 456 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 372 KB Output is correct
10 Correct 1 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 0 ms 348 KB Output is correct
14 Correct 1 ms 348 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 39 ms 11344 KB Output is correct
20 Correct 43 ms 15444 KB Output is correct
21 Execution timed out 1079 ms 7640 KB Time limit exceeded
22 Halted 0 ms 0 KB -