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답안 #459170

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
459170 2021-08-08T09:20:02 Z AmShZ Star Trek (CEOI20_startrek) C++11
100 / 100
 116 ms 18464 KB 
//khodaya khodet komak kon
# include <bits/stdc++.h>

using namespace std;

typedef long long                                        ll;
typedef long double                                      ld;
typedef pair <int, int>                                  pii;
typedef pair <pii, int>                                  ppi;
typedef pair <int, pii>                                  pip;
typedef pair <pii, pii>                                  ppp;
typedef pair <ll, ll>                                    pll;

# define A                                               first
# define B                                               second
# define endl                                            '\n'
# define sep                                             ' '
# define all(x)                                          x.begin(), x.end()
# define kill(x)                                         return cout << x << endl, 0
# define SZ(x)                                           int(x.size())
# define lc                                              id << 1
# define rc                                              id << 1 | 1
# define fast_io                                         ios::sync_with_stdio(0);cin.tie(0); cout.tie(0);

ll power(ll a, ll b, ll md) {return (!b ? 1 : (b & 1 ? a * power(a * a % md, b / 2, md) % md : power(a * a % md, b / 2, md) % md));}

const int xn = 1e5 + 10;
const int xm = - 20 + 10;
const int sq = 320;
const int inf = 1e9 + 10;
const ll INF = 1e18 + 10;
const ld eps = 1e-15;
const int mod = 1e9 + 7;//998244353;
const int base = 257;

int n, dp[2][xn], sz[2][xn], par[xn], ans;
bool f[2][xn];
ll D;
vector <int> adj[xn];

void DFS(int v, int p = - 1){
	sz[0][v] = 1;
	int ted = 0;
	for (int u : adj[v]){
		if (u == p)
			continue;
		par[u] = v;
		DFS(u, v);
		f[0][v] |= !(f[0][u]);
		sz[0][v] += sz[0][u];
		ted += !f[0][u];
	}
	dp[0][v] = sz[0][v];
	for (int u : adj[v])
		if (u != p && ted == !f[0][u])
			dp[0][v] -= dp[0][u];
}
void DFS2(int v, int p = - 1){
	int ted = !f[1][v];
	for (int u : adj[v])
		if (u != p)
			ted += !f[0][u], sz[1][v] += sz[0][u];
	++ sz[1][v];
	int sum0 = 0, sum1 = 0;
	for (int u : adj[v]){
		if (u == p)
			continue;
		sz[1][u] = sz[1][v] - sz[0][u];
		dp[1][u] = sz[1][u];
		dp[1][u] = n - sz[0][u];
		f[1][u] = (0 < ted - !f[0][u]);
		if (f[0][u])
			sum1 += dp[0][u];
		else
			sum0 += dp[0][u];
	}
	if (f[1][v])
		sum1 += dp[1][v];
	else
		sum0 += dp[1][v];
	for (int u : adj[v]){
		if (u == p)
			continue;
		if (f[0][u])
			sum1 -= dp[0][u];
		else
			sum0 -= dp[0][u];
		if (ted - !f[0][u] == 0)
			dp[1][u] -= sum1;
		else if (ted - !f[0][u] == 1)
			dp[1][u] -= sum0;
		if (f[0][u])
			sum1 += dp[0][u];
		else
			sum0 += dp[0][u];
		DFS2(u, v);
	}
}

struct matrix{
    int a[2][2];
    matrix operator * (const matrix &t){
        matrix r;
        for (int i = 0; i < 2; ++ i)
        	for (int j = 0; j < 2; ++ j)
        		r.a[i][j] = 0;
        for (int i = 0; i < 2; ++ i)
        	for (int j = 0; j < 2; ++ j)
        		for (int k = 0; k < 2; ++ k)
        			r.a[i][k] = (r.a[i][k] + 1ll * a[i][j] * t.a[!j][k] % mod) % mod;
        return r;
    }
};
matrix Pow(matrix a, ll b){
    matrix res = a;
    if (b < 0)
    	return res;
    for (; b; b = b >> 1){
        if (b & 1)
            res = res * a;
        a = a * a;
    }
    return res;
}

int main(){
	fast_io;

	cin >> n >> D;
	for (int i = 0; i < n - 1; ++ i){
		int v, u;
		cin >> v >> u;
		adj[v].push_back(u);
		adj[u].push_back(v);
	}
	DFS(1);
	f[1][1] = 1;
	DFS2(1);
	matrix M;
	for (int i = 0; i < 2; ++ i)
		for (int j = 0; j < 2; ++ j)
			M.a[i][j] = 0;
	pii last;
	for (int v = 1; v <= n; ++ v){
		bool fl = !f[1][v];
		int ted = !f[1][v];
		for (int u : adj[v]){
			if (u == par[v])
				continue;
			fl |= !f[0][u];
			ted += !f[0][u];
		}
		int val = n;
		if (ted == !f[1][v])
			val -= dp[1][v];
		for (int u : adj[v])
			if (u != par[v] && ted == !f[0][u])
				val -= dp[0][u];
		M.a[1][1] = (M.a[1][1] + val) % mod;
		M.a[0][1] = (M.a[0][1] + n - val) % mod;
		if (fl)
			M.a[1][0] = (M.a[1][0] + n) % mod;
		else
			M.a[0][0] = (M.a[0][0] + n) % mod;
		if (v == 1)
			last = {fl, val};
	}
	M = Pow(M, D - 1);
	if (last.A)
		ans = (ans + 1ll * n * M.a[1][0] % mod) % mod;
	ans = (ans + 1ll * last.B * M.a[0][0] % mod) % mod;
	ans = 1ll * ans * power(n, mod - 2, mod) % mod;
	cout << ans << endl;

	return 0;
}

Subtask #1
0.0 / 0.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct

Subtask #2
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct

Subtask #3
8.0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct

Subtask #4
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 2 ms 2764 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 2 ms 2636 KB Output is correct

Subtask #5
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 2 ms 2764 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 2 ms 2636 KB Output is correct
12 Correct 98 ms 12244 KB Output is correct
13 Correct 99 ms 17240 KB Output is correct
14 Correct 62 ms 8128 KB Output is correct
15 Correct 71 ms 7876 KB Output is correct
16 Correct 92 ms 7904 KB Output is correct

Subtask #6
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 2 ms 2764 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 2 ms 2636 KB Output is correct
12 Correct 2 ms 2636 KB Output is correct
13 Correct 3 ms 2636 KB Output is correct
14 Correct 2 ms 2668 KB Output is correct
15 Correct 2 ms 2636 KB Output is correct
16 Correct 2 ms 2636 KB Output is correct
17 Correct 2 ms 2704 KB Output is correct
18 Correct 2 ms 2636 KB Output is correct
19 Correct 2 ms 2680 KB Output is correct
20 Correct 2 ms 2672 KB Output is correct
21 Correct 3 ms 2764 KB Output is correct
22 Correct 3 ms 2764 KB Output is correct
23 Correct 2 ms 2636 KB Output is correct
24 Correct 2 ms 2636 KB Output is correct
25 Correct 3 ms 2636 KB Output is correct
26 Correct 2 ms 2764 KB Output is correct
27 Correct 3 ms 2764 KB Output is correct
28 Correct 2 ms 2672 KB Output is correct
29 Correct 2 ms 2636 KB Output is correct
30 Correct 2 ms 2636 KB Output is correct

Subtask #7
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 3 ms 2764 KB Output is correct
8 Correct 2 ms 2764 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 2 ms 2636 KB Output is correct
12 Correct 98 ms 12244 KB Output is correct
13 Correct 99 ms 17240 KB Output is correct
14 Correct 62 ms 8128 KB Output is correct
15 Correct 71 ms 7876 KB Output is correct
16 Correct 92 ms 7904 KB Output is correct
17 Correct 2 ms 2636 KB Output is correct
18 Correct 3 ms 2636 KB Output is correct
19 Correct 2 ms 2668 KB Output is correct
20 Correct 2 ms 2636 KB Output is correct
21 Correct 2 ms 2636 KB Output is correct
22 Correct 2 ms 2704 KB Output is correct
23 Correct 2 ms 2636 KB Output is correct
24 Correct 2 ms 2680 KB Output is correct
25 Correct 2 ms 2672 KB Output is correct
26 Correct 3 ms 2764 KB Output is correct
27 Correct 3 ms 2764 KB Output is correct
28 Correct 2 ms 2636 KB Output is correct
29 Correct 2 ms 2636 KB Output is correct
30 Correct 3 ms 2636 KB Output is correct
31 Correct 2 ms 2764 KB Output is correct
32 Correct 3 ms 2764 KB Output is correct
33 Correct 2 ms 2672 KB Output is correct
34 Correct 2 ms 2636 KB Output is correct
35 Correct 2 ms 2636 KB Output is correct
36 Correct 102 ms 13416 KB Output is correct
37 Correct 81 ms 18464 KB Output is correct
38 Correct 65 ms 9100 KB Output is correct
39 Correct 116 ms 9144 KB Output is correct
40 Correct 86 ms 9080 KB Output is correct
41 Correct 78 ms 15936 KB Output is correct
42 Correct 88 ms 17116 KB Output is correct
43 Correct 50 ms 8304 KB Output is correct
44 Correct 74 ms 9272 KB Output is correct
45 Correct 78 ms 9032 KB Output is correct

Subtask #8
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2636 KB Output is correct
2 Correct 2 ms 2636 KB Output is correct
3 Correct 2 ms 2636 KB Output is correct
4 Correct 2 ms 2636 KB Output is correct
5 Correct 2 ms 2636 KB Output is correct
6 Correct 2 ms 2636 KB Output is correct
7 Correct 2 ms 2636 KB Output is correct
8 Correct 2 ms 2636 KB Output is correct
9 Correct 2 ms 2636 KB Output is correct
10 Correct 2 ms 2636 KB Output is correct
11 Correct 2 ms 2636 KB Output is correct
12 Correct 2 ms 2636 KB Output is correct
13 Correct 2 ms 2636 KB Output is correct
14 Correct 3 ms 2764 KB Output is correct
15 Correct 2 ms 2764 KB Output is correct
16 Correct 2 ms 2636 KB Output is correct
17 Correct 2 ms 2636 KB Output is correct
18 Correct 2 ms 2636 KB Output is correct
19 Correct 98 ms 12244 KB Output is correct
20 Correct 99 ms 17240 KB Output is correct
21 Correct 62 ms 8128 KB Output is correct
22 Correct 71 ms 7876 KB Output is correct
23 Correct 92 ms 7904 KB Output is correct
24 Correct 2 ms 2636 KB Output is correct
25 Correct 3 ms 2636 KB Output is correct
26 Correct 2 ms 2668 KB Output is correct
27 Correct 2 ms 2636 KB Output is correct
28 Correct 2 ms 2636 KB Output is correct
29 Correct 2 ms 2704 KB Output is correct
30 Correct 2 ms 2636 KB Output is correct
31 Correct 2 ms 2680 KB Output is correct
32 Correct 2 ms 2672 KB Output is correct
33 Correct 3 ms 2764 KB Output is correct
34 Correct 3 ms 2764 KB Output is correct
35 Correct 2 ms 2636 KB Output is correct
36 Correct 2 ms 2636 KB Output is correct
37 Correct 3 ms 2636 KB Output is correct
38 Correct 2 ms 2764 KB Output is correct
39 Correct 3 ms 2764 KB Output is correct
40 Correct 2 ms 2672 KB Output is correct
41 Correct 2 ms 2636 KB Output is correct
42 Correct 2 ms 2636 KB Output is correct
43 Correct 102 ms 13416 KB Output is correct
44 Correct 81 ms 18464 KB Output is correct
45 Correct 65 ms 9100 KB Output is correct
46 Correct 116 ms 9144 KB Output is correct
47 Correct 86 ms 9080 KB Output is correct
48 Correct 78 ms 15936 KB Output is correct
49 Correct 88 ms 17116 KB Output is correct
50 Correct 50 ms 8304 KB Output is correct
51 Correct 74 ms 9272 KB Output is correct
52 Correct 78 ms 9032 KB Output is correct
53 Correct 79 ms 18464 KB Output is correct
54 Correct 83 ms 16440 KB Output is correct
55 Correct 57 ms 7768 KB Output is correct
56 Correct 87 ms 13400 KB Output is correct
57 Correct 70 ms 9108 KB Output is correct
58 Correct 75 ms 9156 KB Output is correct
59 Correct 88 ms 9028 KB Output is correct
60 Correct 65 ms 9104 KB Output is correct