Submission #1151325

#	Time	Username	Problem	Language	Result	Execution time	Memory
1151325		vladilius	Star Trek (CEOI20_startrek)	C++20	45 / 100	67 ms	32328 KiB

startrek

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
#define pb push_back
#define ff first
#define ss second
const int mod = 1e9 + 7;

int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    
    int n; ll d; cin>>n>>d;
    vector<int> g[n + 1];
    for (int i = 1; i < n; i++){
        int u, v; cin>>u>>v;
        g[u].pb(v);
        g[v].pb(u);
    }
    
    if (n == 2){
        int out = 4, pr = 4; d--;
        while (d > 0){
            if (d & 1){
                out = (1LL * out * pr) % mod;
            }
            pr = (1LL * pr * pr) % mod;
            d >>= 1;
        }
        cout<<out<<"\n";
        return 0;
    }
    
    vector<int> h(n + 1), p(n + 1);
    function<void(int, int)> dfs = [&](int v, int pr){
        h[v] = 1; p[v] = pr;
        for (int i: g[v]){
            if (i == pr) continue;
            dfs(i, v);
            h[v] = min(h[v], h[i]);
        }
        h[v] = !h[v];
    };
    dfs(1, 0);
    
    vector<vector<bool>> dp(n + 1, vector<bool>(2));
    function<void(int)> fill = [&](int v){
        int s = 0, x = 0;
        for (int i: g[v]){
            if (i == p[v]) continue;
            if (!h[i]){
                s++;
                x = i;
            }
        }
        for (int i: g[v]){
            if (i == p[v]) continue;
            dp[i][0] = dp[v][1];
            if (!s || (s == 1 && i == x)){
                dp[i][1] = dp[v][0];
            }
            else {
                dp[i][1] = dp[v][1];
            }
            fill(i);
        }
    };
    dp[1][0] = 0; dp[1][1] = 1;
    fill(1);
    
    vector<int> c1(n + 1), c0(n + 1);
    int cc1 = 0, cc0 = 0;
    for (int i = 1; i <= n; i++){
        if (dp[i][1]) cc1++;
        else cc0++;
    }

    vector<int> f(n + 1), t = h;
    function<void(int)> rr = [&](int v){
        c1[v] = cc1; c0[v] = cc0;
        f[v] = t[v];
        int s = 0, x = 0;
        for (int i: g[v]){
            if (!t[i]){
                s++;
                x = i;
            }
        }
        for (int i: g[v]){
            if (i == p[v]) continue;

            int i0 = dp[i][0], i1 = dp[i][1];
            dp[i][0] = 0; dp[i][1] = 1;

            int S = 0, X = 0;
            for (int j: g[i]){
                if (!h[j]){
                    S++;
                    X = j;
                }
            }
            
            int v0 = dp[v][0], v1 = dp[v][1];
            dp[v][0] = dp[i][1];
            if (!S || (S == 1 && v == X)){
                dp[v][1] = dp[i][0];
            }
            else {
                dp[v][1] = dp[i][1];
            }
            
            int tv = t[v], ti = t[i];
            if (s == 1 && i == x){
                t[v] = 0;
            }
            t[i] = 1;
            for (int j: g[i]){
                t[i] = min(t[i], t[j]);
            }
            t[i] = !t[i];
            
            rr(i);
            
            t[v] = tv; t[i] = ti;
            dp[i][0] = i0; dp[i][1] = i1;
            dp[v][0] = v0; dp[v][1] = v1;
        }
    };
    rr(1);
    
    int S0 = 0, S1 = 0;
    for (int i = 1; i <= n; i++){
        S0 = (S0 + c0[i]) % mod;
        S1 = (S1 + c1[i]) % mod;
    }
    
    int h0 = 0, h1 = 0, s0 = 0, s1 = 0;
    for (int i = 1; i <= n; i++){
        if (f[i]){
            h1++;
            s1++;
        }
        else {
            h0++;
            s0++;
        }
    }

    int out = f[1];
    for (int i = 1; i <= d; i++){
        out = (1LL * c1[1] * s0) % mod;
        if (f[1]) out = (out + 1LL * s1 * n) % mod;
        int x = s0, y = s1;
        s0 = (1LL * x * S0 + 1LL * y * n * h0) % mod;
        s1 = (1LL * x * S1 + 1LL * y * n * h1) % mod;
    }
    cout<<out<<"\n";
}

• Subtask 1: 0 / 0
• Subtask 2: 7 / 7
• Subtask 3: 8 / 8
• Subtask 4: 15 / 15
• Subtask 5: 15 / 15
• Subtask 6: 0 / 20
• Subtask 7: 0 / 20
• Subtask 8: 0 / 15