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Submission #495508

# Submission time Handle Problem Language Result Execution time Memory
495508 2021-12-19T07:59:04 Z LittleCube Star Trek (CEOI20_startrek) C++14
100 / 100
 144 ms 19424 KB 
#include <bits/stdc++.h>
#define ll long long
#define pii pair<int, int>
#define pll pair<ll, ll>
#define F first
#define S second
using namespace std;

const ll MOD = 1000000007;

ll N, D, dp[100005], pre[100005], subtree[100005], crit[100005], L, K, dpL[100005], Npow[100005];
vector<int> E[100005];

void dfs(int k)
{
    for (int i : E[k])
        if (i != pre[k])
        {
            pre[i] = k;
            dfs(i);
            if (dp[i] == 0)
                dp[k]++;
        }
}

ll fastpow(ll b, ll p)
{
    ll a = 1;
    while (p > 0)
    {
        if (p & 1)
            a = a * b % MOD;
        b = b * b % MOD;
        p >>= 1;
    }
    return a;
}

void dfs2(int k, bool w)
{
    //cout << "dfs2 " << k << '\n';
    if (w && dp[k] == 1)
        for (int i : E[k])
        {
            if (i != pre[k])
            {
                if (dp[i] == 0)
                {
                    dfs2(i, false);
                    subtree[k] += subtree[i];
                }
                else
                    dfs2(i, true);
            }
        }
    else if (w)
        for (int i : E[k])
        {
            if (i != pre[k])
                dfs2(i, dp[i] != 0);
        }
    else if (!w)
    {
        subtree[k]++;
        for (int i : E[k])
            if (i != pre[k])
            {
                dfs2(i, true);
                subtree[k] += subtree[i];
            }
    }
}

void reroot(int k)
{
    //cout << "reroot " << k << '\n';
    //for (int i = 1; i <= N; i++)
    //    cout << subtree[i] << " \n"[i == N];
    //for (int i = 1; i <= N; i++)
    //    cout << dp[i] << " \n"[i == N];
    int sum = 0;
    if (dp[k] == 0)
        crit[k] = 1;
    for (int i : E[k])
    {
        if (dp[k] == 1 && dp[i] == 0)
            crit[k] += subtree[i];
        else if (dp[k] == 0)
            crit[k] += subtree[i];

        if (dp[k] == 2 && dp[i] == 0)
            sum += subtree[i];
        else if (dp[k] == 1 && dp[i] == 1)
            sum += subtree[i];
    }
    swap(subtree[k], crit[k]);
    for (int i : E[k])
        if (i != pre[k])
        {
            if (dp[k] == 1 && dp[i] == 0)
            {
                ll tmp = sum + 1;
                swap(tmp, subtree[k]);
                dp[k]--, dp[i]++;
                reroot(i);
                dp[k]++;
                swap(tmp, subtree[k]);
            }
            else if (dp[k] >= 2 && dp[i] == 0)
            {
                ll tmp = (dp[k] == 2 ? sum - subtree[i] : 0);
                swap(tmp, subtree[k]);
                dp[k]--;
                reroot(i);
                dp[k]++;
                swap(tmp, subtree[k]);
            }
            else if (dp[k] == 0)
            {
                ll tmp = subtree[k] - subtree[i];
                swap(tmp, subtree[k]);
                dp[i]++;
                reroot(i);
                swap(tmp, subtree[k]);
            }
            else
                reroot(i);
        }
    swap(subtree[k], crit[k]);
}

signed main()
{
    cin >> N >> D;
    for (int i = 1; i < N; i++)
    {
        int u, v;
        cin >> u >> v;
        E[u].emplace_back(v);
        E[v].emplace_back(u);
    }

    dfs(1);
    dfs2(1, dp[1] != 0);
    reroot(1);
    //for (int i = 1; i <= N; i++)
    //    cout << crit[i] << " \n"[i == N];
    //for (int i = 1; i <= N; i++)
    //    cout << dp[i] << " \n"[i == N];
    for (int i = 1; i <= N; i++)
        if (dp[i] == 0)
            L++, K = (K - crit[i] + MOD) % MOD;
        else
            K = (K + crit[i] + MOD) % MOD;
    ll res = L * (((fastpow(N, D * 2) - fastpow(K, D) + MOD) % MOD) * fastpow((N * N - K + MOD) % MOD, MOD - 2) % MOD) % MOD;
    if (dp[1] == 0)
        cout << (res * crit[1]) % MOD << '\n';
    else
        cout << (fastpow(N, D * 2) - (res * crit[1] % MOD) + MOD) % MOD << '\n';
}
/*
7 1
1 2
2 3
3 4
4 5
5 6
6 7
*/

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2636 KB Output is correct
2 Correct 1 ms 2636 KB Output is correct
3 Correct 1 ms 2636 KB Output is correct
4 Correct 1 ms 2640 KB Output is correct
5 Correct 1 ms 2640 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2648 KB Output is correct
4 Correct 1 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2648 KB Output is correct
4 Correct 1 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 2 ms 2764 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 2 ms 2636 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2648 KB Output is correct
4 Correct 1 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 2 ms 2764 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 2 ms 2636 KB Output is correct
12 Correct 111 ms 13228 KB Output is correct
13 Correct 137 ms 18264 KB Output is correct
14 Correct 85 ms 9064 KB Output is correct
15 Correct 95 ms 8944 KB Output is correct
16 Correct 91 ms 8900 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2648 KB Output is correct
4 Correct 1 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 2 ms 2764 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 2 ms 2636 KB Output is correct
12 Correct 1 ms 2636 KB Output is correct
13 Correct 2 ms 2636 KB Output is correct
14 Correct 1 ms 2636 KB Output is correct
15 Correct 1 ms 2584 KB Output is correct
16 Correct 2 ms 2636 KB Output is correct
17 Correct 1 ms 2636 KB Output is correct
18 Correct 2 ms 2636 KB Output is correct
19 Correct 2 ms 2636 KB Output is correct
20 Correct 2 ms 2636 KB Output is correct
21 Correct 2 ms 2764 KB Output is correct
22 Correct 2 ms 2764 KB Output is correct
23 Correct 3 ms 2636 KB Output is correct
24 Correct 2 ms 2636 KB Output is correct
25 Correct 2 ms 2636 KB Output is correct
26 Correct 2 ms 2764 KB Output is correct
27 Correct 2 ms 2764 KB Output is correct
28 Correct 3 ms 2636 KB Output is correct
29 Correct 2 ms 2636 KB Output is correct
30 Correct 2 ms 2636 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2648 KB Output is correct
4 Correct 1 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 2 ms 2764 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 2 ms 2636 KB Output is correct
12 Correct 111 ms 13228 KB Output is correct
13 Correct 137 ms 18264 KB Output is correct
14 Correct 85 ms 9064 KB Output is correct
15 Correct 95 ms 8944 KB Output is correct
16 Correct 91 ms 8900 KB Output is correct
17 Correct 1 ms 2636 KB Output is correct
18 Correct 2 ms 2636 KB Output is correct
19 Correct 1 ms 2636 KB Output is correct
20 Correct 1 ms 2584 KB Output is correct
21 Correct 2 ms 2636 KB Output is correct
22 Correct 1 ms 2636 KB Output is correct
23 Correct 2 ms 2636 KB Output is correct
24 Correct 2 ms 2636 KB Output is correct
25 Correct 2 ms 2636 KB Output is correct
26 Correct 2 ms 2764 KB Output is correct
27 Correct 2 ms 2764 KB Output is correct
28 Correct 3 ms 2636 KB Output is correct
29 Correct 2 ms 2636 KB Output is correct
30 Correct 2 ms 2636 KB Output is correct
31 Correct 2 ms 2764 KB Output is correct
32 Correct 2 ms 2764 KB Output is correct
33 Correct 3 ms 2636 KB Output is correct
34 Correct 2 ms 2636 KB Output is correct
35 Correct 2 ms 2636 KB Output is correct
36 Correct 114 ms 13144 KB Output is correct
37 Correct 128 ms 18236 KB Output is correct
38 Correct 88 ms 9044 KB Output is correct
39 Correct 102 ms 8904 KB Output is correct
40 Correct 102 ms 8932 KB Output is correct
41 Correct 128 ms 15784 KB Output is correct
42 Correct 93 ms 16928 KB Output is correct
43 Correct 64 ms 8328 KB Output is correct
44 Correct 95 ms 8940 KB Output is correct
45 Correct 96 ms 8852 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 1 ms 2636 KB Output is correct
4 Correct 1 ms 2636 KB Output is correct
5 Correct 1 ms 2636 KB Output is correct
6 Correct 1 ms 2640 KB Output is correct
7 Correct 1 ms 2640 KB Output is correct
8 Correct 1 ms 2636 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 2 ms 2648 KB Output is correct
11 Correct 1 ms 2636 KB Output is correct
12 Correct 2 ms 2636 KB Output is correct
13 Correct 2 ms 2636 KB Output is correct
14 Correct 3 ms 2764 KB Output is correct
15 Correct 2 ms 2764 KB Output is correct
16 Correct 2 ms 2636 KB Output is correct
17 Correct 2 ms 2636 KB Output is correct
18 Correct 2 ms 2636 KB Output is correct
19 Correct 111 ms 13228 KB Output is correct
20 Correct 137 ms 18264 KB Output is correct
21 Correct 85 ms 9064 KB Output is correct
22 Correct 95 ms 8944 KB Output is correct
23 Correct 91 ms 8900 KB Output is correct
24 Correct 1 ms 2636 KB Output is correct
25 Correct 2 ms 2636 KB Output is correct
26 Correct 1 ms 2636 KB Output is correct
27 Correct 1 ms 2584 KB Output is correct
28 Correct 2 ms 2636 KB Output is correct
29 Correct 1 ms 2636 KB Output is correct
30 Correct 2 ms 2636 KB Output is correct
31 Correct 2 ms 2636 KB Output is correct
32 Correct 2 ms 2636 KB Output is correct
33 Correct 2 ms 2764 KB Output is correct
34 Correct 2 ms 2764 KB Output is correct
35 Correct 3 ms 2636 KB Output is correct
36 Correct 2 ms 2636 KB Output is correct
37 Correct 2 ms 2636 KB Output is correct
38 Correct 2 ms 2764 KB Output is correct
39 Correct 2 ms 2764 KB Output is correct
40 Correct 3 ms 2636 KB Output is correct
41 Correct 2 ms 2636 KB Output is correct
42 Correct 2 ms 2636 KB Output is correct
43 Correct 114 ms 13144 KB Output is correct
44 Correct 128 ms 18236 KB Output is correct
45 Correct 88 ms 9044 KB Output is correct
46 Correct 102 ms 8904 KB Output is correct
47 Correct 102 ms 8932 KB Output is correct
48 Correct 128 ms 15784 KB Output is correct
49 Correct 93 ms 16928 KB Output is correct
50 Correct 64 ms 8328 KB Output is correct
51 Correct 95 ms 8940 KB Output is correct
52 Correct 96 ms 8852 KB Output is correct
53 Correct 144 ms 19424 KB Output is correct
54 Correct 115 ms 17520 KB Output is correct
55 Correct 63 ms 8556 KB Output is correct
56 Correct 107 ms 14392 KB Output is correct
57 Correct 108 ms 10156 KB Output is correct
58 Correct 102 ms 10092 KB Output is correct
59 Correct 94 ms 10024 KB Output is correct
60 Correct 97 ms 10072 KB Output is correct