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Submission #292927

# Submission time Handle Problem Language Result Execution time Memory
292927 2020-09-07T14:50:41 Z arnold518 Star Trek (CEOI20_startrek) C++14
100 / 100
 138 ms 16788 KB 
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int MAXN = 1e5;
const ll MOD = 1e9+7;

int N; ll D;
vector<int> adj[MAXN+10];

typedef vector<vector<ll>> Mat;

Mat operator * (const Mat &p, const Mat &q)
{
	Mat ret=vector<vector<ll>>(p.size(), vector<ll>(q[0].size()));
	assert(p[0].size()==q.size());
	for(int i=0; i<p.size(); i++) for(int j=0; j<q[0].size(); j++)
	{
		for(int k=0; k<p[0].size(); k++)
		{
			ret[i][j]+=p[i][k]*q[k][j]%MOD;
			ret[i][j]%=MOD;
		}
	}
	return ret;
}

Mat mypow(Mat x, ll y)
{
	if(y==0) return {{1, 0}, {0, 1}};
	if(y%2) return mypow(x, y-1)*x;
	Mat t=mypow(x, y/2);
	return t*t;
}

ll ans;

ll a, b, c, d, p, q, x, y;

int dp[MAXN+10], dp2[MAXN+10], zero;
int cnt0[MAXN+10], cnt1[MAXN+10];

void dfs(int now, int bef)
{
	for(int nxt : adj[now])
	{
		if(nxt==bef) continue;
		dfs(nxt, now);
		dp[now]+=!dp[nxt];
	}
	zero+=!dp[now];

	dp2[now]=!dp[now];
	for(int nxt : adj[now])
	{
		if(nxt==bef) continue;
		if(dp[nxt]==0) cnt0[now]+=dp2[nxt];
		else if(dp[nxt]==1) cnt1[now]+=dp2[nxt];
	}
	if(dp[now]==0) dp2[now]+=cnt1[now];
	else if(dp[now]==1) dp2[now]+=cnt0[now];
}

void dfs2(int now, int bef)
{
	//printf("%d : dp %d dp2 %d zero %d\n", now, dp[now], dp2[now], zero);
	//for(int i=1; i<=N; i++) printf("%d : %d / ", i, dp2[i]); printf("\n");
	if(dp[now]==0) c++;
	else a++;

	if(dp[now]==0) d+=N-zero;
	else b+=N-zero;

	if(dp[now]==0)
	{
		b+=dp2[now];
		d+=zero-dp2[now];
	}
	else
	{
		d+=dp2[now];
		b+=zero-dp2[now];
	}

	//printf("%lld %lld %lld %lld\n", a, b, c, d);
	if(now==1) { x=a; y=b; }

	for(int nxt : adj[now])
	{
		if(nxt==bef) continue;

		int m1=dp2[now], m2=dp2[nxt];
		int m3=cnt1[now], m4=cnt0[now], m5=cnt1[nxt], m6=cnt0[nxt];

		zero-=!dp[now];
		zero-=!dp[nxt];

		dp[now]-=!dp[nxt];
		if(dp[nxt]==0) cnt0[now]-=dp2[nxt];
		else if(dp[nxt]==1) cnt1[now]-=dp2[nxt];

		dp2[now]=!dp[now];
		if(dp[now]==0) dp2[now]+=cnt1[now];
		else if(dp[now]==1) dp2[now]+=cnt0[now];

		dp[nxt]+=!dp[now];
		if(dp[now]==0) cnt0[nxt]+=dp2[now];
		else if(dp[now]==1) cnt1[nxt]+=dp2[now];

		dp2[nxt]=!dp[nxt];
		if(dp[nxt]==0) dp2[nxt]+=cnt1[nxt];
		else if(dp[nxt]==1) dp2[nxt]+=cnt0[nxt];

		zero+=!dp[nxt];
		zero+=!dp[now];

		dfs2(nxt, now);

		zero-=!dp[now];
		zero-=!dp[nxt];

		dp[nxt]-=!dp[now];
		dp[now]+=!dp[nxt];
		zero+=!dp[nxt];
		zero+=!dp[now];

		dp2[now]=m1;
		dp2[nxt]=m2;

		cnt1[now]=m3; cnt0[now]=m4;
		cnt1[nxt]=m5; cnt0[nxt]=m6;
	}
}

int main()
{
	scanf("%d%lld", &N, &D);

	for(int i=1; i<N; i++)
	{
		int u, v;
		scanf("%d%d", &u, &v);
		adj[u].push_back(v);
		adj[v].push_back(u);
	}

	dfs(1, 1);
	dfs2(1, 1);

	p=a; q=c;
	a*=N; c*=N; x*=N;

	a%=MOD; b%=MOD; c%=MOD; d%=MOD; x%=MOD; y%=MOD; p%=MOD; q%=MOD;

	Mat M2={{a, b}, {c, d}};
	Mat M1={{x, y}, {0, 0}};
	Mat M3={{p}, {q}};

	Mat MM=M1*mypow(M2, D-1)*M3;

	//printf("!a %lld b %lld c %lld d %lld / x %lld y %lld\n", a, b, c, d, x, y);

	printf("%lld\n", MM[0][0]);
}

Compilation message

startrek.cpp: In function 'Mat operator*(const Mat&, const Mat&)':
startrek.cpp:20:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<std::vector<long long int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   20 |  for(int i=0; i<p.size(); i++) for(int j=0; j<q[0].size(); j++)
      |               ~^~~~~~~~~
startrek.cpp:20:46: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   20 |  for(int i=0; i<p.size(); i++) for(int j=0; j<q[0].size(); j++)
      |                                             ~^~~~~~~~~~~~
startrek.cpp:22:17: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   22 |   for(int k=0; k<p[0].size(); k++)
      |                ~^~~~~~~~~~~~
startrek.cpp: In function 'int main()':
startrek.cpp:140:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  140 |  scanf("%d%lld", &N, &D);
      |  ~~~~~^~~~~~~~~~~~~~~~~~
startrek.cpp:145:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  145 |   scanf("%d%d", &u, &v);
      |   ~~~~~^~~~~~~~~~~~~~~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2720 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct
7 Correct 3 ms 2816 KB Output is correct
8 Correct 3 ms 2816 KB Output is correct
9 Correct 2 ms 2688 KB Output is correct
10 Correct 2 ms 2688 KB Output is correct
11 Correct 3 ms 2688 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct
7 Correct 3 ms 2816 KB Output is correct
8 Correct 3 ms 2816 KB Output is correct
9 Correct 2 ms 2688 KB Output is correct
10 Correct 2 ms 2688 KB Output is correct
11 Correct 3 ms 2688 KB Output is correct
12 Correct 117 ms 11656 KB Output is correct
13 Correct 138 ms 16736 KB Output is correct
14 Correct 83 ms 7620 KB Output is correct
15 Correct 110 ms 7364 KB Output is correct
16 Correct 96 ms 7416 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct
7 Correct 3 ms 2816 KB Output is correct
8 Correct 3 ms 2816 KB Output is correct
9 Correct 2 ms 2688 KB Output is correct
10 Correct 2 ms 2688 KB Output is correct
11 Correct 3 ms 2688 KB Output is correct
12 Correct 2 ms 2688 KB Output is correct
13 Correct 3 ms 2688 KB Output is correct
14 Correct 2 ms 2688 KB Output is correct
15 Correct 2 ms 2688 KB Output is correct
16 Correct 2 ms 2688 KB Output is correct
17 Correct 3 ms 2688 KB Output is correct
18 Correct 2 ms 2688 KB Output is correct
19 Correct 2 ms 2688 KB Output is correct
20 Correct 2 ms 2688 KB Output is correct
21 Correct 3 ms 2816 KB Output is correct
22 Correct 3 ms 2816 KB Output is correct
23 Correct 2 ms 2688 KB Output is correct
24 Correct 2 ms 2688 KB Output is correct
25 Correct 2 ms 2688 KB Output is correct
26 Correct 2 ms 2688 KB Output is correct
27 Correct 3 ms 2816 KB Output is correct
28 Correct 2 ms 2688 KB Output is correct
29 Correct 3 ms 2688 KB Output is correct
30 Correct 3 ms 2688 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2688 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct
7 Correct 3 ms 2816 KB Output is correct
8 Correct 3 ms 2816 KB Output is correct
9 Correct 2 ms 2688 KB Output is correct
10 Correct 2 ms 2688 KB Output is correct
11 Correct 3 ms 2688 KB Output is correct
12 Correct 117 ms 11656 KB Output is correct
13 Correct 138 ms 16736 KB Output is correct
14 Correct 83 ms 7620 KB Output is correct
15 Correct 110 ms 7364 KB Output is correct
16 Correct 96 ms 7416 KB Output is correct
17 Correct 2 ms 2688 KB Output is correct
18 Correct 3 ms 2688 KB Output is correct
19 Correct 2 ms 2688 KB Output is correct
20 Correct 2 ms 2688 KB Output is correct
21 Correct 2 ms 2688 KB Output is correct
22 Correct 3 ms 2688 KB Output is correct
23 Correct 2 ms 2688 KB Output is correct
24 Correct 2 ms 2688 KB Output is correct
25 Correct 2 ms 2688 KB Output is correct
26 Correct 3 ms 2816 KB Output is correct
27 Correct 3 ms 2816 KB Output is correct
28 Correct 2 ms 2688 KB Output is correct
29 Correct 2 ms 2688 KB Output is correct
30 Correct 2 ms 2688 KB Output is correct
31 Correct 2 ms 2688 KB Output is correct
32 Correct 3 ms 2816 KB Output is correct
33 Correct 2 ms 2688 KB Output is correct
34 Correct 3 ms 2688 KB Output is correct
35 Correct 3 ms 2688 KB Output is correct
36 Correct 102 ms 11640 KB Output is correct
37 Correct 104 ms 16760 KB Output is correct
38 Correct 81 ms 7540 KB Output is correct
39 Correct 118 ms 7540 KB Output is correct
40 Correct 101 ms 7584 KB Output is correct
41 Correct 104 ms 14456 KB Output is correct
42 Correct 100 ms 15608 KB Output is correct
43 Correct 63 ms 7028 KB Output is correct
44 Correct 105 ms 7416 KB Output is correct
45 Correct 94 ms 7416 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2688 KB Output is correct
2 Correct 2 ms 2688 KB Output is correct
3 Correct 2 ms 2688 KB Output is correct
4 Correct 2 ms 2720 KB Output is correct
5 Correct 2 ms 2688 KB Output is correct
6 Correct 2 ms 2688 KB Output is correct
7 Correct 2 ms 2688 KB Output is correct
8 Correct 2 ms 2688 KB Output is correct
9 Correct 2 ms 2688 KB Output is correct
10 Correct 2 ms 2688 KB Output is correct
11 Correct 2 ms 2688 KB Output is correct
12 Correct 2 ms 2688 KB Output is correct
13 Correct 2 ms 2688 KB Output is correct
14 Correct 3 ms 2816 KB Output is correct
15 Correct 3 ms 2816 KB Output is correct
16 Correct 2 ms 2688 KB Output is correct
17 Correct 2 ms 2688 KB Output is correct
18 Correct 3 ms 2688 KB Output is correct
19 Correct 117 ms 11656 KB Output is correct
20 Correct 138 ms 16736 KB Output is correct
21 Correct 83 ms 7620 KB Output is correct
22 Correct 110 ms 7364 KB Output is correct
23 Correct 96 ms 7416 KB Output is correct
24 Correct 2 ms 2688 KB Output is correct
25 Correct 3 ms 2688 KB Output is correct
26 Correct 2 ms 2688 KB Output is correct
27 Correct 2 ms 2688 KB Output is correct
28 Correct 2 ms 2688 KB Output is correct
29 Correct 3 ms 2688 KB Output is correct
30 Correct 2 ms 2688 KB Output is correct
31 Correct 2 ms 2688 KB Output is correct
32 Correct 2 ms 2688 KB Output is correct
33 Correct 3 ms 2816 KB Output is correct
34 Correct 3 ms 2816 KB Output is correct
35 Correct 2 ms 2688 KB Output is correct
36 Correct 2 ms 2688 KB Output is correct
37 Correct 2 ms 2688 KB Output is correct
38 Correct 2 ms 2688 KB Output is correct
39 Correct 3 ms 2816 KB Output is correct
40 Correct 2 ms 2688 KB Output is correct
41 Correct 3 ms 2688 KB Output is correct
42 Correct 3 ms 2688 KB Output is correct
43 Correct 102 ms 11640 KB Output is correct
44 Correct 104 ms 16760 KB Output is correct
45 Correct 81 ms 7540 KB Output is correct
46 Correct 118 ms 7540 KB Output is correct
47 Correct 101 ms 7584 KB Output is correct
48 Correct 104 ms 14456 KB Output is correct
49 Correct 100 ms 15608 KB Output is correct
50 Correct 63 ms 7028 KB Output is correct
51 Correct 105 ms 7416 KB Output is correct
52 Correct 94 ms 7416 KB Output is correct
53 Correct 111 ms 16788 KB Output is correct
54 Correct 98 ms 14840 KB Output is correct
55 Correct 56 ms 6644 KB Output is correct
56 Correct 96 ms 11640 KB Output is correct
57 Correct 95 ms 7416 KB Output is correct
58 Correct 94 ms 7672 KB Output is correct
59 Correct 108 ms 7416 KB Output is correct
60 Correct 100 ms 7544 KB Output is correct