Submission #597052

#	Time	Username	Problem	Language	Result	Execution time	Memory
597052		jiahng	Star Trek (CEOI20_startrek)	C++14	100 / 100	142 ms	57284 KiB

startrek

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
#define int ll
typedef pair<int,int> pi;
typedef vector <int> vi;
typedef vector <pi> vpi;
typedef pair<pi, ll> pii;
typedef set <ll> si;
typedef long double ld;
#define f first
#define s second
#define mp make_pair
#define FOR(i,s,e) for(int i=s;i<=int(e);++i)
#define DEC(i,s,e) for(int i=s;i>=int(e);--i)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
#define aFOR(i,x) for (auto i: x)
#define mem(x,i) memset(x,i,sizeof x)
#define fast ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0)
#define maxn 400010
#define INF (ll)(1e9+10)
#define MOD 1000000007
typedef pair <vi, int> pvi;
typedef pair <int,pi> ipi;
typedef vector <pii> vpii;
typedef pair <pi,pi> pipi;

int N,D,a,b;
vi adj[maxn];
int qexp(int a,int b){
	int ans = 1;
	while (b){
		//~ cout << a << ' ' << b << ' ' << ans << '\n';
		if (b & 1) (ans *= a) %= MOD;
		(a *= a) %= MOD;
		b >>= 1;
	}
	return ans;
}
bool state[maxn];
int dp[maxn], num[maxn];
set <int> st[maxn];
int sm[maxn];
void dfs(int x,int p){
    state[x] = 0; dp[x] = num[x] = 0;
    aFOR(i,adj[x]) if (i != p){
        dfs(i,x);
        if (!state[i]){
            num[x]++; st[x].insert(i);state[x] = 1;
        }
        sm[x] += dp[i];
    }
    if (num[x] == 1){
        aFOR(i, adj[x]) if (i != p && !state[i]) dp[x] = dp[i];
    }else if (num[x] == 0){
        aFOR(i,adj[x]) if (i != p) dp[x] += dp[i];
    }
    if (!state[x]) dp[x]++;
}
bool win[maxn];
int crit[maxn];
void reroot(int x,int p){
    crit[x] = dp[x];
    win[x] = state[x];
    aFOR(i,adj[x]) if (i != p){
        int statex = state[x], statei = state[i], numx = num[x], numi = num[i], dpx = dp[x], dpi = dp[i];
        if (!state[i]) num[x]--;
        
        state[x] = (num[x] > 0);
        if (!state[x]) st[i].insert(x);

        if (!state[i]) st[x].erase(i);
        if (!state[x]) num[i]++;
        state[i] = (num[i] > 0);
        
        sm[x] -= dp[i];
        dp[x] = 0;
        if (num[x] == 1) dp[x] = dp[*st[x].begin()];
        else if (num[x] == 0) dp[x] = sm[x];
        if (!state[x]) dp[x]++;

        sm[i] += dp[x];

        dp[i] = 0;
        if (num[i] == 1) dp[i] = dp[*st[i].begin()];
        else if (num[i] == 0) dp[i] = sm[i];

        if (!state[i]) dp[i]++;

        reroot(i,x);

        if (!state[x]) st[i].erase(x);
        state[x] = statex; state[i] = statei;
        if (!state[i]) st[x].insert(i);
        num[x] = numx; num[i] = numi;

        sm[i] -= dp[x];
        dp[x] = dpx; dp[i] = dpi;
        sm[x] += dp[i];
    }
}

int32_t main(){
    fast;
    cin >> N >> D;
    FOR(i,1,N-1){
        cin >> a >> b; adj[a].pb(b); adj[b].pb(a);
    }
    dfs(1,-1);
    reroot(1,-1);

    int E = 0;
    FOR(i,1,N){
        if (win[i]) E += crit[i];
        else E -= crit[i];
        //cout << crit[i] << ' ';
    }
    //cout << '\n';
    int L = 0;
    FOR(i,1,N) if (!win[i]) L++;

    //cout << L << ' ' << E << '\n';
    D--;
    int invN = qexp(N, MOD - 2);
    int EN2 = (E * ((invN * invN) % MOD)) % MOD;
    int N2D = qexp(N, 2*D);
    int LD1 = (((((L * N2D) % MOD) * (qexp(EN2, D) - 1)) % MOD) * qexp(EN2 - 1, MOD - 2)) % MOD;
    (LD1 += (qexp(E, D) * L) % MOD) %= MOD;
    D++;
    //cout << LD1 << ' ';
    int ans;
    if (win[1]) ans = (crit[1] * LD1) % MOD;
    else ans = qexp(N, 2*D) - (crit[1] * LD1) % MOD;
    ans = qexp(N, 2*D) - ans;
    ans %= MOD; ans += MOD; ans %= MOD;

    cout << ans;
}

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