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Submission #336903

# Submission time Handle Problem Language Result Execution time Memory
336903 2020-12-17T08:31:26 Z dolphingarlic Star Trek (CEOI20_startrek) C++14
78 / 100
 1000 ms 15324 KB 
#include <bits/stdc++.h>
typedef long long ll;
using namespace std;

const ll MOD = 1e9 + 7;

vector<int> graph[100001];
ll win_as_root[100001], critical[100001];

ll expo(ll base, ll pow) {
    ll ans = 1;
    while (pow) {
        if (pow & 1) ans = ans * base % MOD;
        pow >>= 1, base = base * base % MOD;
    }
    return ans;
}

void dfs1(int node = 1, int parent = 0) {
    for (int i : graph[node]) if (i != parent) {
        dfs1(i, node);
        win_as_root[node] += (win_as_root[i] == 0);
    }
    if (!win_as_root[node]) critical[node] = 1;
    for (int i : graph[node]) if (i != parent) {
        if ((win_as_root[node] == 1 && !win_as_root[i]) || !win_as_root[node])
            critical[node] += critical[i];
    }
}

void dfs2(int node = 1, int parent = 0, bool par_win = true, ll par_crit = 0) {
    win_as_root[node] += !par_win;
    ll all_crit = 0, lose_crit = 0;

    critical[node] = (win_as_root[node] == 0);
    all_crit += par_crit;
    if (!par_win) lose_crit += par_crit;
    if ((win_as_root[node] == 1 && !par_win) || !win_as_root[node])
        critical[node] += par_crit;
    for (int i : graph[node]) if (i != parent) {
        all_crit += critical[i];
        if (!win_as_root[i]) lose_crit += critical[i];
        if ((win_as_root[node] == 1 && !win_as_root[i]) || !win_as_root[node])
            critical[node] += critical[i];
    }

    for (int i : graph[node]) if (i != parent) {
        if (win_as_root[node] - (win_as_root[i] == 0) == 0)
            dfs2(i, node, false, all_crit - critical[i] + 1);
        else if (win_as_root[node] - (win_as_root[i] == 0) == 1)
            dfs2(i, node, true, lose_crit - (win_as_root[i] ? 0 : critical[i]));
        else
            dfs2(i, node, true, 0);
    }
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    ll n, d;
    cin >> n >> d;
    for (int i = 1; i < n; i++) {
        int u, v;
        cin >> u >> v;
        graph[u].push_back(v);
        graph[v].push_back(u);
    }
    dfs1();
    dfs2();

    ll lose_cnt = 0, e_val = 0;
    for (int i = 1; i <= n; i++) {
        if (win_as_root[i]) e_val += critical[i];
        else lose_cnt++, e_val -= critical[i];
    }
    e_val = (e_val % MOD + MOD) % MOD;

    ll dp = 0;
    for (int i = 0; i < d; i++)
        dp = (dp + expo(e_val, i) * expo(n, 2 * (d - i - 1)) % MOD) % MOD;
    dp = dp * lose_cnt % MOD;
    if (win_as_root[1])
        cout << (expo(n, 2 * d) - critical[1] * dp % MOD + MOD) % MOD;
    else
        cout << critical[1] * dp % MOD;
    return 0;
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2668 KB Output is correct
2 Correct 3 ms 2804 KB Output is correct

Subtask #2
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 4 ms 2668 KB Output is correct
3 Execution timed out 1081 ms 2688 KB Time limit exceeded
4 Halted 0 ms 0 KB -

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2700 KB Output is correct
2 Correct 2 ms 2668 KB Output is correct
3 Correct 2 ms 2668 KB Output is correct
4 Correct 2 ms 2668 KB Output is correct
5 Correct 2 ms 2668 KB Output is correct
6 Correct 2 ms 2668 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2700 KB Output is correct
2 Correct 2 ms 2668 KB Output is correct
3 Correct 2 ms 2668 KB Output is correct
4 Correct 2 ms 2668 KB Output is correct
5 Correct 2 ms 2668 KB Output is correct
6 Correct 2 ms 2668 KB Output is correct
7 Correct 2 ms 2796 KB Output is correct
8 Correct 2 ms 2796 KB Output is correct
9 Correct 3 ms 2796 KB Output is correct
10 Correct 2 ms 2796 KB Output is correct
11 Correct 2 ms 2796 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2700 KB Output is correct
2 Correct 2 ms 2668 KB Output is correct
3 Correct 2 ms 2668 KB Output is correct
4 Correct 2 ms 2668 KB Output is correct
5 Correct 2 ms 2668 KB Output is correct
6 Correct 2 ms 2668 KB Output is correct
7 Correct 2 ms 2796 KB Output is correct
8 Correct 2 ms 2796 KB Output is correct
9 Correct 3 ms 2796 KB Output is correct
10 Correct 2 ms 2796 KB Output is correct
11 Correct 2 ms 2796 KB Output is correct
12 Correct 78 ms 11048 KB Output is correct
13 Correct 103 ms 15324 KB Output is correct
14 Correct 80 ms 7548 KB Output is correct
15 Correct 105 ms 7672 KB Output is correct
16 Correct 80 ms 7424 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2700 KB Output is correct
2 Correct 2 ms 2668 KB Output is correct
3 Correct 2 ms 2668 KB Output is correct
4 Correct 2 ms 2668 KB Output is correct
5 Correct 2 ms 2668 KB Output is correct
6 Correct 2 ms 2668 KB Output is correct
7 Correct 2 ms 2796 KB Output is correct
8 Correct 2 ms 2796 KB Output is correct
9 Correct 3 ms 2796 KB Output is correct
10 Correct 2 ms 2796 KB Output is correct
11 Correct 2 ms 2796 KB Output is correct
12 Correct 3 ms 2668 KB Output is correct
13 Correct 3 ms 2796 KB Output is correct
14 Correct 2 ms 2668 KB Output is correct
15 Correct 4 ms 2668 KB Output is correct
16 Correct 2 ms 2668 KB Output is correct
17 Correct 2 ms 2668 KB Output is correct
18 Correct 2 ms 2668 KB Output is correct
19 Correct 2 ms 2668 KB Output is correct
20 Correct 2 ms 2668 KB Output is correct
21 Correct 2 ms 2796 KB Output is correct
22 Correct 3 ms 2796 KB Output is correct
23 Correct 2 ms 2796 KB Output is correct
24 Correct 3 ms 2796 KB Output is correct
25 Correct 3 ms 2796 KB Output is correct
26 Correct 17 ms 2796 KB Output is correct
27 Correct 18 ms 2796 KB Output is correct
28 Correct 22 ms 2668 KB Output is correct
29 Correct 19 ms 2796 KB Output is correct
30 Correct 12 ms 2796 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2700 KB Output is correct
2 Correct 2 ms 2668 KB Output is correct
3 Correct 2 ms 2668 KB Output is correct
4 Correct 2 ms 2668 KB Output is correct
5 Correct 2 ms 2668 KB Output is correct
6 Correct 2 ms 2668 KB Output is correct
7 Correct 2 ms 2796 KB Output is correct
8 Correct 2 ms 2796 KB Output is correct
9 Correct 3 ms 2796 KB Output is correct
10 Correct 2 ms 2796 KB Output is correct
11 Correct 2 ms 2796 KB Output is correct
12 Correct 78 ms 11048 KB Output is correct
13 Correct 103 ms 15324 KB Output is correct
14 Correct 80 ms 7548 KB Output is correct
15 Correct 105 ms 7672 KB Output is correct
16 Correct 80 ms 7424 KB Output is correct
17 Correct 3 ms 2668 KB Output is correct
18 Correct 3 ms 2796 KB Output is correct
19 Correct 2 ms 2668 KB Output is correct
20 Correct 4 ms 2668 KB Output is correct
21 Correct 2 ms 2668 KB Output is correct
22 Correct 2 ms 2668 KB Output is correct
23 Correct 2 ms 2668 KB Output is correct
24 Correct 2 ms 2668 KB Output is correct
25 Correct 2 ms 2668 KB Output is correct
26 Correct 2 ms 2796 KB Output is correct
27 Correct 3 ms 2796 KB Output is correct
28 Correct 2 ms 2796 KB Output is correct
29 Correct 3 ms 2796 KB Output is correct
30 Correct 3 ms 2796 KB Output is correct
31 Correct 17 ms 2796 KB Output is correct
32 Correct 18 ms 2796 KB Output is correct
33 Correct 22 ms 2668 KB Output is correct
34 Correct 19 ms 2796 KB Output is correct
35 Correct 12 ms 2796 KB Output is correct
36 Correct 87 ms 10992 KB Output is correct
37 Correct 89 ms 15212 KB Output is correct
38 Correct 58 ms 7528 KB Output is correct
39 Correct 74 ms 7404 KB Output is correct
40 Correct 87 ms 7404 KB Output is correct
41 Correct 98 ms 13164 KB Output is correct
42 Correct 87 ms 14060 KB Output is correct
43 Correct 63 ms 7016 KB Output is correct
44 Correct 81 ms 7404 KB Output is correct
45 Correct 92 ms 7404 KB Output is correct

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2668 KB Output is correct
2 Correct 3 ms 2804 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 4 ms 2668 KB Output is correct
5 Execution timed out 1081 ms 2688 KB Time limit exceeded
6 Halted 0 ms 0 KB -