oj.uz

Submission #660041

# Submission time Handle Problem Language Result Execution time Memory
660041 2022-11-20T09:18:26 Z highway_to_hell Star Trek (CEOI20_startrek) C++14
100 / 100
 532 ms 114972 KB 
#include<bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define endl '\n'
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int mod = 1e9 + 7;
int add(int a, int b) {
	a += b;
	if (a >= mod) a -= mod;
	if (a < 0) a += mod;
	return a;
}
int mul(int a, int b) {
	return 1ll*a*b%mod;
}

const int N = 1e5 + 50, LG = 60;
int n, pw[LG];
ll d;
vector<int> adj[N];
pii dpdw[N], dpup[N], dp[LG][N][2], out[N][2], tmp[N][2]; 

void dfs(int u, int p) {
	int cnt, sum, sbd;
	cnt = sum = sbd = 0;
	for (int v:adj[u]) {
		if(v == p) continue;
		dfs(v, u);
		sum = add(sum, dpdw[v].S);
		sbd = add(sbd, dpdw[v].F*dpdw[v].S);
		cnt += dpdw[v].F;
	}
	dpdw[u].F = !cnt;
	if (cnt >= 2) return;
	dpdw[u].S = (cnt? sbd:sum+1);
}

void sfd(int u, int p) {
	int cnt, sum, sbd;
	cnt = dpup[u].F;
	sum = dpup[u].S;
	sbd = dpup[u].F*dpup[u].S;
	for (int v:adj[u]) {
		if (v == p) continue;
		sum = add(sum, dpdw[v].S);
		sbd = add(sbd, dpdw[v].F*dpdw[v].S);
		cnt += dpdw[v].F;
	}
	for (int v:adj[u]) {
		if (v == p) continue;
		sum = add(sum, -dpdw[v].S);
		sbd = add(sbd, -dpdw[v].F*dpdw[v].S);
		cnt -= dpdw[v].F;
		
		dpup[v].F = !cnt;
		if (cnt < 2) dpup[v].S = (cnt? sbd:sum+1);

		sum = add(sum, dpdw[v].S);
		sbd = add(sbd, dpdw[v].F*dpdw[v].S);
		cnt += dpdw[v].F;

		sfd(v, u);
	}
}

void solve() {
	cin >> n >> d;
	d++;
	for (int i = 1; i <= n-1; i++) {
		int u, v;
		cin >> u >> v;
		adj[u].push_back(v);
		adj[v].push_back(u);
	}
	pw[0] = mul(n, n);
	for (int k = 1; k < LG; k++) {
		pw[k] = mul(pw[k-1], pw[k-1]);
	}

	dfs(1, 0);
	sfd(1, 0);
	for (int u = 1; u <= n; u++) {
		if (dpdw[u].F) {
			dp[0][u][dpup[u].F^1] = {1, (dpup[u].F? dpup[u].S : add(dpdw[u].S, dpup[u].S))};
		}
		else {
			dp[0][u][0] = {1, (dpup[u].F ? 0 : dpdw[u].S)};
		}
	}
	for (int k = 1; k < LG; k++) {
		int sum = 0;
		int sa = 0, sb = 0;
		for (int u = 1; u <= n; u++) {
			sum = add(sum, dp[k-1][u][1].F);
			sa = add(sa, dp[k-1][u][0].S);
			sb = add(sb, dp[k-1][u][1].S);
		}
		for (int u = 1; u <= n; u++) {
			dp[k][u][0].F = add(dp[k][u][0].F, mul(dp[k-1][u][0].F, pw[k-1]));
			dp[k][u][0].F = add(dp[k][u][0].F, -mul(dp[k-1][u][0].S, sum));
			dp[k][u][0].F = add(dp[k][u][0].F, mul(dp[k-1][u][1].S, sum));
			dp[k][u][0].S = add(mul(dp[k-1][u][0].S, sa), mul(dp[k-1][u][1].S, sb));

			dp[k][u][1].F = add(dp[k][u][1].F, mul(dp[k-1][u][1].F, pw[k-1]));
			dp[k][u][1].F = add(dp[k][u][1].F, -mul(dp[k-1][u][1].S, sum));
			dp[k][u][1].F = add(dp[k][u][1].F, mul(dp[k-1][u][0].S, sum));
			dp[k][u][1].S = add(mul(dp[k-1][u][1].S, sa), mul(dp[k-1][u][0].S, sb));
		}
	}

	bool flg = 0;
	for (int k = 0; k < LG; k++) {
		if (!(d>>k&1)) continue;
		if (!flg) {
			for (int u = 1; u <= n; u++) {
				out[u][0] = dp[k][u][0];
				out[u][1] = dp[k][u][1];
			}
			flg = 1;
			continue;
		}
		int sum = 0;
		int sa = 0, sb = 0;
		for (int u = 1; u <= n; u++) {
			sum = add(sum, dp[k][u][1].F);
			sa = add(sa, dp[k][u][0].S);
			sb = add(sb, dp[k][u][1].S);
		}
		for (int u = 1; u <= n; u++) {
			tmp[u][0] = tmp[u][1] = {0, 0};

			tmp[u][0].F = add(tmp[u][0].F, mul(out[u][0].F, pw[k]));
			tmp[u][0].F = add(tmp[u][0].F, -mul(out[u][0].S, sum));
			tmp[u][0].F = add(tmp[u][0].F, mul(out[u][1].S, sum));
			tmp[u][0].S = add(mul(out[u][0].S, sa), mul(out[u][1].S, sb));

			tmp[u][1].F = add(tmp[u][1].F, mul(out[u][1].F, pw[k]));
			tmp[u][1].F = add(tmp[u][1].F, -mul(out[u][1].S, sum));
			tmp[u][1].F = add(tmp[u][1].F, mul(out[u][0].S, sum));
			tmp[u][1].S = add(mul(out[u][1].S, sa), mul(out[u][0].S, sb));

			out[u][0] = tmp[u][0];
			out[u][1] = tmp[u][1];
		}
	}
	cout << out[1][0].F << endl;
}

int main() {
	ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	solve();
	return 0;
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 3028 KB Output is correct
2 Correct 5 ms 4052 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 3028 KB Output is correct
2 Correct 2 ms 3028 KB Output is correct
3 Correct 2 ms 3028 KB Output is correct
4 Correct 1 ms 3028 KB Output is correct
5 Correct 2 ms 3028 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 3028 KB Output is correct
2 Correct 2 ms 3156 KB Output is correct
3 Correct 2 ms 3156 KB Output is correct
4 Correct 2 ms 3156 KB Output is correct
5 Correct 2 ms 3156 KB Output is correct
6 Correct 2 ms 3156 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 3028 KB Output is correct
2 Correct 2 ms 3156 KB Output is correct
3 Correct 2 ms 3156 KB Output is correct
4 Correct 2 ms 3156 KB Output is correct
5 Correct 2 ms 3156 KB Output is correct
6 Correct 2 ms 3156 KB Output is correct
7 Correct 4 ms 4052 KB Output is correct
8 Correct 4 ms 4180 KB Output is correct
9 Correct 4 ms 4052 KB Output is correct
10 Correct 5 ms 4052 KB Output is correct
11 Correct 5 ms 4052 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 3028 KB Output is correct
2 Correct 2 ms 3156 KB Output is correct
3 Correct 2 ms 3156 KB Output is correct
4 Correct 2 ms 3156 KB Output is correct
5 Correct 2 ms 3156 KB Output is correct
6 Correct 2 ms 3156 KB Output is correct
7 Correct 4 ms 4052 KB Output is correct
8 Correct 4 ms 4180 KB Output is correct
9 Correct 4 ms 4052 KB Output is correct
10 Correct 5 ms 4052 KB Output is correct
11 Correct 5 ms 4052 KB Output is correct
12 Correct 386 ms 107236 KB Output is correct
13 Correct 240 ms 113420 KB Output is correct
14 Correct 236 ms 104000 KB Output is correct
15 Correct 324 ms 104068 KB Output is correct
16 Correct 283 ms 104008 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 3028 KB Output is correct
2 Correct 2 ms 3156 KB Output is correct
3 Correct 2 ms 3156 KB Output is correct
4 Correct 2 ms 3156 KB Output is correct
5 Correct 2 ms 3156 KB Output is correct
6 Correct 2 ms 3156 KB Output is correct
7 Correct 4 ms 4052 KB Output is correct
8 Correct 4 ms 4180 KB Output is correct
9 Correct 4 ms 4052 KB Output is correct
10 Correct 5 ms 4052 KB Output is correct
11 Correct 5 ms 4052 KB Output is correct
12 Correct 2 ms 3028 KB Output is correct
13 Correct 5 ms 4052 KB Output is correct
14 Correct 1 ms 3028 KB Output is correct
15 Correct 2 ms 3028 KB Output is correct
16 Correct 2 ms 3156 KB Output is correct
17 Correct 2 ms 3156 KB Output is correct
18 Correct 2 ms 3156 KB Output is correct
19 Correct 2 ms 3156 KB Output is correct
20 Correct 2 ms 3156 KB Output is correct
21 Correct 4 ms 4052 KB Output is correct
22 Correct 4 ms 4180 KB Output is correct
23 Correct 5 ms 4032 KB Output is correct
24 Correct 5 ms 4052 KB Output is correct
25 Correct 4 ms 4052 KB Output is correct
26 Correct 5 ms 4052 KB Output is correct
27 Correct 4 ms 4180 KB Output is correct
28 Correct 3 ms 3924 KB Output is correct
29 Correct 5 ms 4052 KB Output is correct
30 Correct 4 ms 4052 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 3028 KB Output is correct
2 Correct 2 ms 3156 KB Output is correct
3 Correct 2 ms 3156 KB Output is correct
4 Correct 2 ms 3156 KB Output is correct
5 Correct 2 ms 3156 KB Output is correct
6 Correct 2 ms 3156 KB Output is correct
7 Correct 4 ms 4052 KB Output is correct
8 Correct 4 ms 4180 KB Output is correct
9 Correct 4 ms 4052 KB Output is correct
10 Correct 5 ms 4052 KB Output is correct
11 Correct 5 ms 4052 KB Output is correct
12 Correct 386 ms 107236 KB Output is correct
13 Correct 240 ms 113420 KB Output is correct
14 Correct 236 ms 104000 KB Output is correct
15 Correct 324 ms 104068 KB Output is correct
16 Correct 283 ms 104008 KB Output is correct
17 Correct 2 ms 3028 KB Output is correct
18 Correct 5 ms 4052 KB Output is correct
19 Correct 1 ms 3028 KB Output is correct
20 Correct 2 ms 3028 KB Output is correct
21 Correct 2 ms 3156 KB Output is correct
22 Correct 2 ms 3156 KB Output is correct
23 Correct 2 ms 3156 KB Output is correct
24 Correct 2 ms 3156 KB Output is correct
25 Correct 2 ms 3156 KB Output is correct
26 Correct 4 ms 4052 KB Output is correct
27 Correct 4 ms 4180 KB Output is correct
28 Correct 5 ms 4032 KB Output is correct
29 Correct 5 ms 4052 KB Output is correct
30 Correct 4 ms 4052 KB Output is correct
31 Correct 5 ms 4052 KB Output is correct
32 Correct 4 ms 4180 KB Output is correct
33 Correct 3 ms 3924 KB Output is correct
34 Correct 5 ms 4052 KB Output is correct
35 Correct 4 ms 4052 KB Output is correct
36 Correct 384 ms 108452 KB Output is correct
37 Correct 244 ms 113340 KB Output is correct
38 Correct 233 ms 103976 KB Output is correct
39 Correct 329 ms 104012 KB Output is correct
40 Correct 284 ms 103996 KB Output is correct
41 Correct 427 ms 112568 KB Output is correct
42 Correct 234 ms 105288 KB Output is correct
43 Correct 220 ms 94008 KB Output is correct
44 Correct 344 ms 105720 KB Output is correct
45 Correct 286 ms 105556 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 3028 KB Output is correct
2 Correct 5 ms 4052 KB Output is correct
3 Correct 1 ms 3028 KB Output is correct
4 Correct 2 ms 3028 KB Output is correct
5 Correct 2 ms 3028 KB Output is correct
6 Correct 1 ms 3028 KB Output is correct
7 Correct 2 ms 3028 KB Output is correct
8 Correct 2 ms 3028 KB Output is correct
9 Correct 2 ms 3156 KB Output is correct
10 Correct 2 ms 3156 KB Output is correct
11 Correct 2 ms 3156 KB Output is correct
12 Correct 2 ms 3156 KB Output is correct
13 Correct 2 ms 3156 KB Output is correct
14 Correct 4 ms 4052 KB Output is correct
15 Correct 4 ms 4180 KB Output is correct
16 Correct 4 ms 4052 KB Output is correct
17 Correct 5 ms 4052 KB Output is correct
18 Correct 5 ms 4052 KB Output is correct
19 Correct 386 ms 107236 KB Output is correct
20 Correct 240 ms 113420 KB Output is correct
21 Correct 236 ms 104000 KB Output is correct
22 Correct 324 ms 104068 KB Output is correct
23 Correct 283 ms 104008 KB Output is correct
24 Correct 2 ms 3028 KB Output is correct
25 Correct 5 ms 4052 KB Output is correct
26 Correct 1 ms 3028 KB Output is correct
27 Correct 2 ms 3028 KB Output is correct
28 Correct 2 ms 3156 KB Output is correct
29 Correct 2 ms 3156 KB Output is correct
30 Correct 2 ms 3156 KB Output is correct
31 Correct 2 ms 3156 KB Output is correct
32 Correct 2 ms 3156 KB Output is correct
33 Correct 4 ms 4052 KB Output is correct
34 Correct 4 ms 4180 KB Output is correct
35 Correct 5 ms 4032 KB Output is correct
36 Correct 5 ms 4052 KB Output is correct
37 Correct 4 ms 4052 KB Output is correct
38 Correct 5 ms 4052 KB Output is correct
39 Correct 4 ms 4180 KB Output is correct
40 Correct 3 ms 3924 KB Output is correct
41 Correct 5 ms 4052 KB Output is correct
42 Correct 4 ms 4052 KB Output is correct
43 Correct 384 ms 108452 KB Output is correct
44 Correct 244 ms 113340 KB Output is correct
45 Correct 233 ms 103976 KB Output is correct
46 Correct 329 ms 104012 KB Output is correct
47 Correct 284 ms 103996 KB Output is correct
48 Correct 427 ms 112568 KB Output is correct
49 Correct 234 ms 105288 KB Output is correct
50 Correct 220 ms 94008 KB Output is correct
51 Correct 344 ms 105720 KB Output is correct
52 Correct 286 ms 105556 KB Output is correct
53 Correct 244 ms 114972 KB Output is correct
54 Correct 532 ms 113172 KB Output is correct
55 Correct 235 ms 85192 KB Output is correct
56 Correct 375 ms 109948 KB Output is correct
57 Correct 390 ms 105644 KB Output is correct
58 Correct 364 ms 105936 KB Output is correct
59 Correct 409 ms 105720 KB Output is correct
60 Correct 351 ms 105676 KB Output is correct