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Submission #975328

# Submission time Handle Problem Language Result Execution time Memory
975328 2024-05-04T19:15:56 Z efedmrlr Star Trek (CEOI20_startrek) C++17
100 / 100
 51 ms 15600 KB 
#include <bits/stdc++.h>

#define lli long long int
#define ld long double
#define pb push_back
#define MP make_pair
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define REP(i, n) for(int i = 0; (i) < (n); (i)++)

using namespace std;

void fastio() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
}

const int N = 1e5 + 5;
const int INF = 1e9 + 500;
const int MOD = 1e9 + 7;
const int B = 2;
int add(int x, int y) {
    if(x + y >= MOD) return x + y - MOD;
    return x + y;
}
int mult(int x, int y) {
    return (int)((1ll * x * y) % MOD);
}
int subt(int x, int y) {
    if(x - y < 0) return x - y + MOD;
    return x - y;
}
int fp(int x, lli y) {
    int ret = 1;
    while(y > 0ll) {
        if(y & 1ll) {
            ret = mult(ret, x);
        }
        x = mult(x, x);
        y /= 2ll;
    }
    return ret;
}

struct Matrix {
    array<array<int, B>, B> mat;
    Matrix() {
        REP(i, B) REP(j, B) mat[i][j] = 0;
    }
    void print() {
        REP(i, B) {
            REP(j, B) {
                cout << mat[i][j] << " ";
            }
            cout << "\n";
        }
        cout << "\n\n";
    }
};
Matrix mult(Matrix x, Matrix y) {
    Matrix ret;
    REP(i, 2) REP(j, 2) REP(k, 2) {
        ret.mat[i][j] = add(ret.mat[i][j], mult(x.mat[i][k], y.mat[k][j]));
    }
    return ret;
}
array<int, B> mult(array<int, B> x, Matrix y) {
    array<int, B> ret = {0, 0};
    REP(i, 2) {
        REP(j, 2) {
            ret[j] = add(ret[j], mult(y.mat[i][j], x[i])); 
        }
    }
    return ret;
}
Matrix fp(Matrix x, lli y) {
    Matrix ret;
    REP(i, B) ret.mat[i][i] = 1;
    while(y > 0ll) {
        if(y & 1) {
            ret = mult(ret, x);
        }
        y /= 2ll;
        x = mult(x, x);
    }
    return ret;
}
int n;
lli d;
vector<vector<int> > adj(N, vector<int>());
vector<int> dp(N, 0), dpr(N, 0);
vector<int> dpcrit(N, 0), dpc(N, 0);
vector<int> wc(N, 0), lc(N, 0);
int L = 0;
int CL = 0, CW = 0;
void dfs1(int node, int par) {
    for(auto c : adj[node]) {
        if(c == par) continue;
        dfs1(c, node);
        if(!dpr[c]) dpr[node]++;
    }

}
void dfs2(int node, int par) {
    if(!dpr[node]) {
        dpcrit[node] = 1;
    }
    for(auto c : adj[node]) {
        if(c == par) continue;
        dfs2(c, node);
        if(dpr[c]) wc[node] += dpcrit[c];
        else lc[node] += dpcrit[c];
        if(dpr[node] == 1 && !dpr[c]) {
            dpcrit[node] += dpcrit[c];
        } 
        if(!dpr[node] && dpr[c]) {
            dpcrit[node] += dpcrit[c];
        }
    }
    
}
void change_root(int p, int x) {
    if(!dpr[x]) {
        dpr[p]--;
        lc[p] -= dpcrit[x];
    }
    else {
        wc[p] -= dpcrit[x];
    }
    if(dpr[p] >= 2) {
        dpcrit[p] = 0;
    }
    else if(dpr[p] == 1) {
        dpcrit[p] = lc[p];
    }
    else {
        dpcrit[p] = wc[p] + 1;
    }

    if(!dpr[p]) {
        dpr[x]++;
        lc[x] += dpcrit[p];
    }
    else {
        wc[x] += dpcrit[p];
    }
    if(dpr[x] >= 2) {
        dpcrit[x] = 0;
    }
    else if(dpr[x] == 1) {
        dpcrit[x] = lc[x];
    }
    else {
        dpcrit[x] = wc[x] + 1;
    }

}

void reroot(int node, int par) {
    dp[node] = dpr[node];
    dpc[node] = dpcrit[node];
    for(auto c : adj[node]) {
        if(c == par) continue;
        change_root(node, c);
        reroot(c, node);
        change_root(c, node); 
    }

}

void solve() {
    cin >> n >> d;
    REP(i, n - 1) {
        int u, v;
        cin >> u >> v;
        adj[u].pb(v);
        adj[v].pb(u);
    }
    dfs1(1, 0);
    dfs2(1, 0);
    // for(int i = 1; i <= n; i++) {
    //     cout << "i:" << i << " dpr:" << dpr[i] << " crit:" << dpcrit[i] << "\n";
    // }
    reroot(1, 0);
    // for(int i = 1; i <= n; i++) {
    //     cout << "i:" << i << " dp:" << dp[i] << " c:" << dpc[i] << "\n";
    // }
    for(int i = 1; i <= n; i++) {
        if(!dp[i]) {
            L++;
            CL = add(CL, dpc[i]);
        }
        else {
            CW = add(CW, dpc[i]);
        }
    }
    // cout << "L:" << L << " CL:" << CL << " CW:" << CW << "\n";
    // int LD = L, LDN = 0;
    // for(int i = 1; i < d; i++) {
    //     LDN = add(mult(LD, subt(CW, CL)), mult(L, fp(n, 2ll * i)));
    //     swap(LD, LDN);
    // }

    Matrix rel;
    rel.mat[0] = {subt(CW, CL), 0};
    rel.mat[1] = {1, mult(n, n)};
    array<int, B> st = {L, mult(L, mult(n, n))};
    // rel.print();
    st = mult(st, fp(rel, d - 1));
    // REP(i, B) {
    //     cout << st[i] << " ";
    // }
    // cout << " AAA\n";
    int ans = 0;
    if(dp[1]) {
        ans = mult(dpc[1], st[0]);
    }
    else {
        ans = subt(fp(n, 2ll * d), mult(dpc[1], st[0]));
    }
    ans = subt(fp(n, 2ll * d), ans);
    cout << ans << "\n";
}

signed main() {
    fastio();
    solve();
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4956 KB Output is correct
2 Correct 3 ms 4956 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4956 KB Output is correct
2 Correct 3 ms 4956 KB Output is correct
3 Correct 3 ms 4952 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 2 ms 4956 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4956 KB Output is correct
2 Correct 3 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 3 ms 5208 KB Output is correct
6 Correct 3 ms 4976 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4956 KB Output is correct
2 Correct 3 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 3 ms 5208 KB Output is correct
6 Correct 3 ms 4976 KB Output is correct
7 Correct 3 ms 5212 KB Output is correct
8 Correct 3 ms 5212 KB Output is correct
9 Correct 3 ms 4956 KB Output is correct
10 Correct 3 ms 4956 KB Output is correct
11 Correct 3 ms 4956 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4956 KB Output is correct
2 Correct 3 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 3 ms 5208 KB Output is correct
6 Correct 3 ms 4976 KB Output is correct
7 Correct 3 ms 5212 KB Output is correct
8 Correct 3 ms 5212 KB Output is correct
9 Correct 3 ms 4956 KB Output is correct
10 Correct 3 ms 4956 KB Output is correct
11 Correct 3 ms 4956 KB Output is correct
12 Correct 39 ms 11044 KB Output is correct
13 Correct 46 ms 14420 KB Output is correct
14 Correct 28 ms 8404 KB Output is correct
15 Correct 38 ms 8592 KB Output is correct
16 Correct 41 ms 8284 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4956 KB Output is correct
2 Correct 3 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 3 ms 5208 KB Output is correct
6 Correct 3 ms 4976 KB Output is correct
7 Correct 3 ms 5212 KB Output is correct
8 Correct 3 ms 5212 KB Output is correct
9 Correct 3 ms 4956 KB Output is correct
10 Correct 3 ms 4956 KB Output is correct
11 Correct 3 ms 4956 KB Output is correct
12 Correct 2 ms 4956 KB Output is correct
13 Correct 3 ms 5172 KB Output is correct
14 Correct 4 ms 4956 KB Output is correct
15 Correct 2 ms 4956 KB Output is correct
16 Correct 3 ms 4956 KB Output is correct
17 Correct 2 ms 5176 KB Output is correct
18 Correct 2 ms 4956 KB Output is correct
19 Correct 3 ms 4956 KB Output is correct
20 Correct 3 ms 4956 KB Output is correct
21 Correct 3 ms 5180 KB Output is correct
22 Correct 3 ms 5212 KB Output is correct
23 Correct 3 ms 4956 KB Output is correct
24 Correct 3 ms 4956 KB Output is correct
25 Correct 3 ms 4956 KB Output is correct
26 Correct 3 ms 5212 KB Output is correct
27 Correct 3 ms 5212 KB Output is correct
28 Correct 3 ms 5364 KB Output is correct
29 Correct 3 ms 4956 KB Output is correct
30 Correct 3 ms 4956 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4956 KB Output is correct
2 Correct 3 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 2 ms 4956 KB Output is correct
5 Correct 3 ms 5208 KB Output is correct
6 Correct 3 ms 4976 KB Output is correct
7 Correct 3 ms 5212 KB Output is correct
8 Correct 3 ms 5212 KB Output is correct
9 Correct 3 ms 4956 KB Output is correct
10 Correct 3 ms 4956 KB Output is correct
11 Correct 3 ms 4956 KB Output is correct
12 Correct 39 ms 11044 KB Output is correct
13 Correct 46 ms 14420 KB Output is correct
14 Correct 28 ms 8404 KB Output is correct
15 Correct 38 ms 8592 KB Output is correct
16 Correct 41 ms 8284 KB Output is correct
17 Correct 2 ms 4956 KB Output is correct
18 Correct 3 ms 5172 KB Output is correct
19 Correct 4 ms 4956 KB Output is correct
20 Correct 2 ms 4956 KB Output is correct
21 Correct 3 ms 4956 KB Output is correct
22 Correct 2 ms 5176 KB Output is correct
23 Correct 2 ms 4956 KB Output is correct
24 Correct 3 ms 4956 KB Output is correct
25 Correct 3 ms 4956 KB Output is correct
26 Correct 3 ms 5180 KB Output is correct
27 Correct 3 ms 5212 KB Output is correct
28 Correct 3 ms 4956 KB Output is correct
29 Correct 3 ms 4956 KB Output is correct
30 Correct 3 ms 4956 KB Output is correct
31 Correct 3 ms 5212 KB Output is correct
32 Correct 3 ms 5212 KB Output is correct
33 Correct 3 ms 5364 KB Output is correct
34 Correct 3 ms 4956 KB Output is correct
35 Correct 3 ms 4956 KB Output is correct
36 Correct 50 ms 12112 KB Output is correct
37 Correct 51 ms 15600 KB Output is correct
38 Correct 35 ms 9448 KB Output is correct
39 Correct 37 ms 9536 KB Output is correct
40 Correct 36 ms 9308 KB Output is correct
41 Correct 41 ms 13916 KB Output is correct
42 Correct 43 ms 14684 KB Output is correct
43 Correct 25 ms 8920 KB Output is correct
44 Correct 44 ms 9560 KB Output is correct
45 Correct 38 ms 9296 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4956 KB Output is correct
2 Correct 3 ms 4956 KB Output is correct
3 Correct 2 ms 4956 KB Output is correct
4 Correct 3 ms 4956 KB Output is correct
5 Correct 3 ms 4952 KB Output is correct
6 Correct 2 ms 4956 KB Output is correct
7 Correct 2 ms 4956 KB Output is correct
8 Correct 3 ms 4956 KB Output is correct
9 Correct 3 ms 4956 KB Output is correct
10 Correct 2 ms 4956 KB Output is correct
11 Correct 2 ms 4956 KB Output is correct
12 Correct 3 ms 5208 KB Output is correct
13 Correct 3 ms 4976 KB Output is correct
14 Correct 3 ms 5212 KB Output is correct
15 Correct 3 ms 5212 KB Output is correct
16 Correct 3 ms 4956 KB Output is correct
17 Correct 3 ms 4956 KB Output is correct
18 Correct 3 ms 4956 KB Output is correct
19 Correct 39 ms 11044 KB Output is correct
20 Correct 46 ms 14420 KB Output is correct
21 Correct 28 ms 8404 KB Output is correct
22 Correct 38 ms 8592 KB Output is correct
23 Correct 41 ms 8284 KB Output is correct
24 Correct 2 ms 4956 KB Output is correct
25 Correct 3 ms 5172 KB Output is correct
26 Correct 4 ms 4956 KB Output is correct
27 Correct 2 ms 4956 KB Output is correct
28 Correct 3 ms 4956 KB Output is correct
29 Correct 2 ms 5176 KB Output is correct
30 Correct 2 ms 4956 KB Output is correct
31 Correct 3 ms 4956 KB Output is correct
32 Correct 3 ms 4956 KB Output is correct
33 Correct 3 ms 5180 KB Output is correct
34 Correct 3 ms 5212 KB Output is correct
35 Correct 3 ms 4956 KB Output is correct
36 Correct 3 ms 4956 KB Output is correct
37 Correct 3 ms 4956 KB Output is correct
38 Correct 3 ms 5212 KB Output is correct
39 Correct 3 ms 5212 KB Output is correct
40 Correct 3 ms 5364 KB Output is correct
41 Correct 3 ms 4956 KB Output is correct
42 Correct 3 ms 4956 KB Output is correct
43 Correct 50 ms 12112 KB Output is correct
44 Correct 51 ms 15600 KB Output is correct
45 Correct 35 ms 9448 KB Output is correct
46 Correct 37 ms 9536 KB Output is correct
47 Correct 36 ms 9308 KB Output is correct
48 Correct 41 ms 13916 KB Output is correct
49 Correct 43 ms 14684 KB Output is correct
50 Correct 25 ms 8920 KB Output is correct
51 Correct 44 ms 9560 KB Output is correct
52 Correct 38 ms 9296 KB Output is correct
53 Correct 51 ms 15444 KB Output is correct
54 Correct 49 ms 14164 KB Output is correct
55 Correct 22 ms 8408 KB Output is correct
56 Correct 38 ms 12116 KB Output is correct
57 Correct 48 ms 9548 KB Output is correct
58 Correct 43 ms 9308 KB Output is correct
59 Correct 35 ms 9436 KB Output is correct
60 Correct 37 ms 9400 KB Output is correct