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Submission #597050

# Submission time Handle Problem Language Result Execution time Memory
597050 2022-07-15T12:31:05 Z jiahng Star Trek (CEOI20_startrek) C++14
45 / 100
 125 ms 56904 KB 
#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;

        dp[i] -= dp[x];
        dp[x] = dpx; dp[i] = dpi;
        dp[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 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 28500 KB Output is correct
2 Incorrect 15 ms 28564 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 28540 KB Output is correct
2 Correct 13 ms 28500 KB Output is correct
3 Correct 13 ms 28516 KB Output is correct
4 Correct 13 ms 28500 KB Output is correct
5 Correct 14 ms 28472 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 28460 KB Output is correct
2 Correct 14 ms 28468 KB Output is correct
3 Correct 15 ms 28500 KB Output is correct
4 Correct 16 ms 28500 KB Output is correct
5 Correct 18 ms 28500 KB Output is correct
6 Correct 15 ms 28500 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 28460 KB Output is correct
2 Correct 14 ms 28468 KB Output is correct
3 Correct 15 ms 28500 KB Output is correct
4 Correct 16 ms 28500 KB Output is correct
5 Correct 18 ms 28500 KB Output is correct
6 Correct 15 ms 28500 KB Output is correct
7 Correct 15 ms 28628 KB Output is correct
8 Correct 17 ms 28756 KB Output is correct
9 Correct 14 ms 28664 KB Output is correct
10 Correct 14 ms 28660 KB Output is correct
11 Correct 15 ms 28548 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 28460 KB Output is correct
2 Correct 14 ms 28468 KB Output is correct
3 Correct 15 ms 28500 KB Output is correct
4 Correct 16 ms 28500 KB Output is correct
5 Correct 18 ms 28500 KB Output is correct
6 Correct 15 ms 28500 KB Output is correct
7 Correct 15 ms 28628 KB Output is correct
8 Correct 17 ms 28756 KB Output is correct
9 Correct 14 ms 28664 KB Output is correct
10 Correct 14 ms 28660 KB Output is correct
11 Correct 15 ms 28548 KB Output is correct
12 Correct 106 ms 47756 KB Output is correct
13 Correct 124 ms 56904 KB Output is correct
14 Correct 125 ms 40008 KB Output is correct
15 Correct 108 ms 39932 KB Output is correct
16 Correct 99 ms 40148 KB Output is correct

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 28460 KB Output is correct
2 Correct 14 ms 28468 KB Output is correct
3 Correct 15 ms 28500 KB Output is correct
4 Correct 16 ms 28500 KB Output is correct
5 Correct 18 ms 28500 KB Output is correct
6 Correct 15 ms 28500 KB Output is correct
7 Correct 15 ms 28628 KB Output is correct
8 Correct 17 ms 28756 KB Output is correct
9 Correct 14 ms 28664 KB Output is correct
10 Correct 14 ms 28660 KB Output is correct
11 Correct 15 ms 28548 KB Output is correct
12 Correct 17 ms 28524 KB Output is correct
13 Incorrect 14 ms 28628 KB Output isn't correct
14 Halted 0 ms 0 KB -

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 28460 KB Output is correct
2 Correct 14 ms 28468 KB Output is correct
3 Correct 15 ms 28500 KB Output is correct
4 Correct 16 ms 28500 KB Output is correct
5 Correct 18 ms 28500 KB Output is correct
6 Correct 15 ms 28500 KB Output is correct
7 Correct 15 ms 28628 KB Output is correct
8 Correct 17 ms 28756 KB Output is correct
9 Correct 14 ms 28664 KB Output is correct
10 Correct 14 ms 28660 KB Output is correct
11 Correct 15 ms 28548 KB Output is correct
12 Correct 106 ms 47756 KB Output is correct
13 Correct 124 ms 56904 KB Output is correct
14 Correct 125 ms 40008 KB Output is correct
15 Correct 108 ms 39932 KB Output is correct
16 Correct 99 ms 40148 KB Output is correct
17 Correct 17 ms 28524 KB Output is correct
18 Incorrect 14 ms 28628 KB Output isn't correct
19 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 28500 KB Output is correct
2 Incorrect 15 ms 28564 KB Output isn't correct
3 Halted 0 ms 0 KB -