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Submission #1007918

# Submission time Handle Problem Language Result Execution time Memory
1007918 2024-06-25T19:05:40 Z NValchanov Star Trek (CEOI20_startrek) C++17
100 / 100
 44 ms 19536 KB 
#include <bits/stdc++.h>

#define endl '\n'

using namespace std;

typedef long long ll;

const int MAXN = 1e5 + 10;
const ll MAXD = 1e18 + 10;
const ll MOD = 1e9 + 7;

struct matrix
{
    int n;
    vector < vector < ll > > m;

    matrix()
    {
        n = 0;
        m.clear();
    }

    matrix(int n)
    {
        this->n = n;
        m.resize(n);
        for(int i = 0; i < n; i++)
        {
            m[i].resize(n, 0LL);
        }
    }

    int size()
    {
        return n;
    }

    friend matrix operator*(matrix a, matrix b)
    {
        int sz = a.size();
        matrix result(sz);

        for(int k = 0; k < sz; k++)
        {
            for(int i = 0; i < sz; i++)
            {
                for(int j = 0; j < sz; j++)
                {
                    result.m[i][j] = (result.m[i][j] + (a.m[i][k] * b.m[k][j]) % MOD) % MOD;
                }
            }
        }

        return result;
    }
};

ll binpow(ll a, ll b)
{
    ll result = 1LL;

    while(b)
    {
        if(b & 1)
            result = (result * a) % MOD;

        a = (a * a) % MOD;
        b /= 2;
    }

    return result;
}

matrix binpow(matrix a, ll b)
{
    int sz = a.size();
    matrix result(sz);
    result.m[0][0] = result.m[1][1] = 1LL;

    while(b)
    {
        if(b & 1)
            result = result * a;
            
        a = a * a;
        b /= 2;
    }

    return result;
}

vector < ll > mult(vector < ll > a, matrix b)
{
    vector < ll > result = {0LL, 0LL};
    for(int i = 0; i < 2; i++)
    {
        for(int j = 0; j < 2; j++)
        {
            result[j] = (result[j] + (b.m[i][j] * a[i]) % MOD) % MOD;
        }
    }

    return result;
}

ll n;
ll d;
vector < ll > adj[MAXN];
ll dp[MAXN];
ll dpt[MAXN];
ll dph[MAXN];
ll crit[MAXN];
ll win[MAXN];
ll lose[MAXN];

ll cntwin;
ll cntlose;
ll pot;

void read()
{
    cin >> n >> d;
    for(int i = 1; i <= n - 1; i++)
    {
        int u, v;
        cin >> u >> v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
}

void dfs(int u, int par)
{
    for(int v : adj[u])
    {
        if(v == par)
            continue;
        
        dfs(v, u);

        if(!dpt[v])
            dpt[u]++;
    }
}

void find_crit(int u, int par)
{
    if(!dpt[u])
        crit[u] = 1;

    for(int v : adj[u])
    {
        if(v == par)
            continue;
        
        find_crit(v, u);

        if(dpt[v])
            win[u] += crit[v];
        else
            lose[u] += crit[v];

        if(dpt[u] == 1 && !dpt[v])
            crit[u] += crit[v];

        if(!dpt[u] && dpt[v])
            crit[u] += crit[v];
    }
}

void change(int u, int v)
{
    if(!dpt[v])
    {
        dpt[u]--;
        lose[u] -= crit[v];
    }
    else
    {
        win[u] -= crit[v];
    }

    if(dpt[u] > 1)
        crit[u] = 0;
    else if(dpt[u] == 1)
        crit[u] = lose[u];
    else
        crit[u] = win[u] + 1;

    
    if(!dpt[u])
    {
        dpt[v]++;
        lose[v] += crit[u];
    }
    else
    {
        win[v] += crit[u];
    }

    if(dpt[v] > 1)
        crit[v] = 0;
    else if(dpt[v] == 1)
        crit[v] = lose[v];
    else
        crit[v] = win[v] + 1;
}

void reroot(int u, int par)
{
    dp[u] = dpt[u];
    dph[u] = crit[u];

    for(int v : adj[u])
    {
        if(v == par)
            continue;

        change(u, v);

        reroot(v, u);
        
        change(v, u);
    }
}

void find_win_lose()
{
    dfs(1, 0);
    find_crit(1, 0);
    reroot(1, 0);

    for(int i = 1; i <= n; i++)
    {
        if(!dp[i])
        {
            pot++;
            cntlose = (cntlose + dph[i]) % MOD;
        }
        else
        {
            cntwin = (cntwin + dph[i]) % MOD;
        }
    }
    // cout << "DPH : " << endl;
    // for(int i = 1; i <= n; i++)
    // {
    //     cout << dph[i] << " ";
    // }
    // cout << endl << endl;
    // cout << "DP : " << endl;
    // for(int i = 1; i <= n; i++)
    // {
    //     cout << dp[i] << " ";
    // }
    // cout << endl;
}

void solve()
{
    matrix mat(2);

    mat.m[0][0] = (cntwin - cntlose + MOD) % MOD;
    mat.m[0][1] = 0LL;
    mat.m[1][0] = 1LL;
    mat.m[1][1] = (n * n) % MOD;

    vector < ll > tmp = {pot, (pot * (n * n) % MOD) % MOD};

    tmp = mult(tmp, binpow(mat, d - 1LL));

    ll ans = 0LL;

    if(dp[1])
        ans = (dph[1] * tmp[0]) % MOD;
    else
        ans = (binpow(n, 2LL * d) - (dph[1] * tmp[0]) % MOD + MOD) % MOD;

    ans = (binpow(n, 2LL * d) - ans + MOD) % MOD;

    cout << ans << endl;
}

int main()
{
    ios_base :: sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    read();
    find_win_lose();
    solve();

    return 0;
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5212 KB Output is correct
2 Correct 1 ms 5212 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5208 KB Output is correct
2 Correct 1 ms 5212 KB Output is correct
3 Correct 1 ms 5212 KB Output is correct
4 Correct 1 ms 5212 KB Output is correct
5 Correct 1 ms 5212 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5212 KB Output is correct
2 Correct 1 ms 5212 KB Output is correct
3 Correct 1 ms 5212 KB Output is correct
4 Correct 1 ms 5212 KB Output is correct
5 Correct 1 ms 5212 KB Output is correct
6 Correct 1 ms 5212 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5212 KB Output is correct
2 Correct 1 ms 5212 KB Output is correct
3 Correct 1 ms 5212 KB Output is correct
4 Correct 1 ms 5212 KB Output is correct
5 Correct 1 ms 5212 KB Output is correct
6 Correct 1 ms 5212 KB Output is correct
7 Correct 1 ms 5212 KB Output is correct
8 Correct 1 ms 5224 KB Output is correct
9 Correct 1 ms 5212 KB Output is correct
10 Correct 1 ms 5212 KB Output is correct
11 Correct 1 ms 5212 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5212 KB Output is correct
2 Correct 1 ms 5212 KB Output is correct
3 Correct 1 ms 5212 KB Output is correct
4 Correct 1 ms 5212 KB Output is correct
5 Correct 1 ms 5212 KB Output is correct
6 Correct 1 ms 5212 KB Output is correct
7 Correct 1 ms 5212 KB Output is correct
8 Correct 1 ms 5224 KB Output is correct
9 Correct 1 ms 5212 KB Output is correct
10 Correct 1 ms 5212 KB Output is correct
11 Correct 1 ms 5212 KB Output is correct
12 Correct 42 ms 14220 KB Output is correct
13 Correct 42 ms 18256 KB Output is correct
14 Correct 24 ms 10828 KB Output is correct
15 Correct 34 ms 10752 KB Output is correct
16 Correct 31 ms 10828 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5212 KB Output is correct
2 Correct 1 ms 5212 KB Output is correct
3 Correct 1 ms 5212 KB Output is correct
4 Correct 1 ms 5212 KB Output is correct
5 Correct 1 ms 5212 KB Output is correct
6 Correct 1 ms 5212 KB Output is correct
7 Correct 1 ms 5212 KB Output is correct
8 Correct 1 ms 5224 KB Output is correct
9 Correct 1 ms 5212 KB Output is correct
10 Correct 1 ms 5212 KB Output is correct
11 Correct 1 ms 5212 KB Output is correct
12 Correct 1 ms 5212 KB Output is correct
13 Correct 1 ms 5212 KB Output is correct
14 Correct 1 ms 5212 KB Output is correct
15 Correct 1 ms 5212 KB Output is correct
16 Correct 1 ms 5212 KB Output is correct
17 Correct 1 ms 5212 KB Output is correct
18 Correct 1 ms 5212 KB Output is correct
19 Correct 1 ms 5212 KB Output is correct
20 Correct 1 ms 5468 KB Output is correct
21 Correct 2 ms 5212 KB Output is correct
22 Correct 1 ms 5212 KB Output is correct
23 Correct 1 ms 5212 KB Output is correct
24 Correct 1 ms 5212 KB Output is correct
25 Correct 1 ms 5212 KB Output is correct
26 Correct 2 ms 5212 KB Output is correct
27 Correct 1 ms 5212 KB Output is correct
28 Correct 1 ms 5212 KB Output is correct
29 Correct 1 ms 5212 KB Output is correct
30 Correct 2 ms 5208 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5212 KB Output is correct
2 Correct 1 ms 5212 KB Output is correct
3 Correct 1 ms 5212 KB Output is correct
4 Correct 1 ms 5212 KB Output is correct
5 Correct 1 ms 5212 KB Output is correct
6 Correct 1 ms 5212 KB Output is correct
7 Correct 1 ms 5212 KB Output is correct
8 Correct 1 ms 5224 KB Output is correct
9 Correct 1 ms 5212 KB Output is correct
10 Correct 1 ms 5212 KB Output is correct
11 Correct 1 ms 5212 KB Output is correct
12 Correct 42 ms 14220 KB Output is correct
13 Correct 42 ms 18256 KB Output is correct
14 Correct 24 ms 10828 KB Output is correct
15 Correct 34 ms 10752 KB Output is correct
16 Correct 31 ms 10828 KB Output is correct
17 Correct 1 ms 5212 KB Output is correct
18 Correct 1 ms 5212 KB Output is correct
19 Correct 1 ms 5212 KB Output is correct
20 Correct 1 ms 5212 KB Output is correct
21 Correct 1 ms 5212 KB Output is correct
22 Correct 1 ms 5212 KB Output is correct
23 Correct 1 ms 5212 KB Output is correct
24 Correct 1 ms 5212 KB Output is correct
25 Correct 1 ms 5468 KB Output is correct
26 Correct 2 ms 5212 KB Output is correct
27 Correct 1 ms 5212 KB Output is correct
28 Correct 1 ms 5212 KB Output is correct
29 Correct 1 ms 5212 KB Output is correct
30 Correct 1 ms 5212 KB Output is correct
31 Correct 2 ms 5212 KB Output is correct
32 Correct 1 ms 5212 KB Output is correct
33 Correct 1 ms 5212 KB Output is correct
34 Correct 1 ms 5212 KB Output is correct
35 Correct 2 ms 5208 KB Output is correct
36 Correct 36 ms 15440 KB Output is correct
37 Correct 44 ms 19496 KB Output is correct
38 Correct 26 ms 11860 KB Output is correct
39 Correct 34 ms 12112 KB Output is correct
40 Correct 38 ms 12116 KB Output is correct
41 Correct 37 ms 17488 KB Output is correct
42 Correct 37 ms 18264 KB Output is correct
43 Correct 21 ms 11052 KB Output is correct
44 Correct 33 ms 12124 KB Output is correct
45 Correct 32 ms 12124 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5212 KB Output is correct
2 Correct 1 ms 5212 KB Output is correct
3 Correct 1 ms 5208 KB Output is correct
4 Correct 1 ms 5212 KB Output is correct
5 Correct 1 ms 5212 KB Output is correct
6 Correct 1 ms 5212 KB Output is correct
7 Correct 1 ms 5212 KB Output is correct
8 Correct 1 ms 5212 KB Output is correct
9 Correct 1 ms 5212 KB Output is correct
10 Correct 1 ms 5212 KB Output is correct
11 Correct 1 ms 5212 KB Output is correct
12 Correct 1 ms 5212 KB Output is correct
13 Correct 1 ms 5212 KB Output is correct
14 Correct 1 ms 5212 KB Output is correct
15 Correct 1 ms 5224 KB Output is correct
16 Correct 1 ms 5212 KB Output is correct
17 Correct 1 ms 5212 KB Output is correct
18 Correct 1 ms 5212 KB Output is correct
19 Correct 42 ms 14220 KB Output is correct
20 Correct 42 ms 18256 KB Output is correct
21 Correct 24 ms 10828 KB Output is correct
22 Correct 34 ms 10752 KB Output is correct
23 Correct 31 ms 10828 KB Output is correct
24 Correct 1 ms 5212 KB Output is correct
25 Correct 1 ms 5212 KB Output is correct
26 Correct 1 ms 5212 KB Output is correct
27 Correct 1 ms 5212 KB Output is correct
28 Correct 1 ms 5212 KB Output is correct
29 Correct 1 ms 5212 KB Output is correct
30 Correct 1 ms 5212 KB Output is correct
31 Correct 1 ms 5212 KB Output is correct
32 Correct 1 ms 5468 KB Output is correct
33 Correct 2 ms 5212 KB Output is correct
34 Correct 1 ms 5212 KB Output is correct
35 Correct 1 ms 5212 KB Output is correct
36 Correct 1 ms 5212 KB Output is correct
37 Correct 1 ms 5212 KB Output is correct
38 Correct 2 ms 5212 KB Output is correct
39 Correct 1 ms 5212 KB Output is correct
40 Correct 1 ms 5212 KB Output is correct
41 Correct 1 ms 5212 KB Output is correct
42 Correct 2 ms 5208 KB Output is correct
43 Correct 36 ms 15440 KB Output is correct
44 Correct 44 ms 19496 KB Output is correct
45 Correct 26 ms 11860 KB Output is correct
46 Correct 34 ms 12112 KB Output is correct
47 Correct 38 ms 12116 KB Output is correct
48 Correct 37 ms 17488 KB Output is correct
49 Correct 37 ms 18264 KB Output is correct
50 Correct 21 ms 11052 KB Output is correct
51 Correct 33 ms 12124 KB Output is correct
52 Correct 32 ms 12124 KB Output is correct
53 Correct 41 ms 19536 KB Output is correct
54 Correct 44 ms 18004 KB Output is correct
55 Correct 24 ms 10448 KB Output is correct
56 Correct 36 ms 15444 KB Output is correct
57 Correct 30 ms 12372 KB Output is correct
58 Correct 33 ms 12116 KB Output is correct
59 Correct 34 ms 11860 KB Output is correct
60 Correct 32 ms 12032 KB Output is correct