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Submission #291194

# Submission time Handle Problem Language Result Execution time Memory
291194 2020-09-04T21:04:10 Z TadijaSebez Star Trek (CEOI20_startrek) C++11
100 / 100
 285 ms 54368 KB 
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
const int mod=1e9+7;
int add(int x,int y){x+=y;return x>=mod?x-mod:x;}
int sub(int x,int y){x-=y;return x<0?x+mod:x;}
int mul(int x,int y){return (ll)x*y%mod;}
void ckadd(int&x,int y){x=add(x,y);}
void cksub(int&x,int y){x=sub(x,y);}
void ckmul(int&x,int y){x=mul(x,y);}
int powmod(int x,ll k){
	int ans=1;
	for(;k;k>>=1,ckmul(x,x))if(k&1)ckmul(ans,x);
	return ans;
}
const int N=100050;
int n;
ll d;
vector<int> E[N];
struct info{
	int x,y,z;
	info(int a=0,int b=0,int c=0):x(a),y(b),z(c){}
	info operator + (info b){return info(add(x,b.x),add(y,b.y),add(z,b.z));}
	info operator * (info b){return info(mul(x,b.x),add(mul(x,b.y),mul(b.x,y)),add(mul(x,b.z),mul(b.x,z)));}
	int get(int w,int l){return add(x,add(mul(w,y),mul(l,z)));}
	void p(){printf("%i %i %i\n",x,y,z);}
};
info operator += (info&a,info b){return a=a+b;}
info operator *= (info&a,info b){return a=a*b;}
struct DP{
	info a[2][2];
	void cl(){for(int i=0;i<2;++i)for(int j=0;j<2;++j)a[i][j]=info();}
	DP(){}
	void id(){a[0][0]=info(1);}
};
DP operator + (DP a,DP b){
	DP ans;
	for(int i=0;i<2;++i)
		for(int j=0;j<2;++j)
			for(int k=0;k<2;++k)
				for(int l=0;l<2;++l){
					if(i+k<2){
						ans.a[i|k][j|l]+=a.a[i][j]*b.a[k][l];
					}
				}
	return ans;
}
DP operator += (DP&a,DP b){return a=a+b;}
DP sw(DP a){
	DP b=a;
	for(int i=0;i<2;++i)swap(b.a[i][0],b.a[i][1]);
	return b;
}
DP dw[N],idx;
void DW(int u,int p){
	dw[u]=idx;
	for(int v:E[u])if(v!=p){
		DW(v,u);
		dw[u]+=sw(dw[v]);
	}
}
DP dp[N],up[N];
void UP(int u,int p){
	dp[u]=sw(up[u])+dw[u];
	DP tmp=idx;
	for(int v:E[u])if(v!=p){
		up[v]=tmp;
		tmp+=sw(dw[v]);
	}
	tmp=sw(up[u]);
	reverse(E[u].begin(),E[u].end());
	for(int v:E[u])if(v!=p){
		up[v]+=tmp;
		UP(v,u);
		tmp+=sw(dw[v]);
	}
}
#define matrix vector<vector<int>>
matrix mul(matrix a,matrix b){
	int n=a.size();
	matrix ans(n,vector<int>(n,0));
	for(int i=0;i<n;++i)
		for(int j=0;j<n;++j)
			for(int k=0;k<n;++k)
				ckadd(ans[i][j],mul(a[i][k],b[k][j]));
	return ans;
}
matrix pow(matrix x,ll k){
	int n=x.size();
	matrix ans(n,vector<int>(n,0));
	for(int i=0;i<n;i++)ans[i][i]=1;
	for(;k;k>>=1,x=mul(x,x))if(k&1)ans=mul(ans,x);
	return ans;
}
vector<int> mul(matrix a,vector<int> b){
	int n=a.size();
	vector<int> ans(n,0);
	for(int i=0;i<n;++i)
		for(int j=0;j<n;++j)
			ckadd(ans[i],mul(a[i][j],b[j]));
	return ans;
}
int main(){
	//freopen("input1.txt","r",stdin);
	scanf("%i %lld",&n,&d);
	for(int i=1,u,v;i<n;i++)scanf("%i %i",&u,&v),E[u].pb(v),E[v].pb(u);
	idx.id();
	idx.a[1][0]=info(0,1,0);
	idx.a[1][1]=info(0,0,1);
	DW(1,0);
	up[1].id();
	up[1]=sw(up[1]);
	UP(1,0);
	info sum_win=info(),sum_lose=info();
	for(int i=1;i<=n;i++){
		sum_win+=dp[i].a[1][1];
		sum_lose+=dp[i].a[1][0];
		//printf("%i\n",i);
		//dw[i].a[1][1].p();
		//dw[i].a[1][0].p();
	}
	//printf("sum\n");
	//sum_win.p();
	//sum_lose.p();
	int w=0,l=0;
	for(int i=1;i<=n;i++){
		ckadd(w,dp[i].a[0][1].x);
		ckadd(l,dp[i].a[0][0].x);
	}
	matrix base(3,vector<int>(3,0));
	base[0][0]=sum_lose.z;
	base[0][1]=sum_lose.y;
	base[0][2]=sum_lose.x;
	base[1][0]=sum_win.z;
	base[1][1]=sum_win.y;
	base[1][2]=sum_win.x;
	base[2][2]=1;
	vector<int> v={l,w,1};
	base=pow(base,d-1);
	/*for(int i=1;i<d;i++){
		tie(w,l)=make_pair(sum_win.get(w,l),sum_lose.get(w,l));
	}*/
	v=mul(base,v);
	l=v[0];
	w=v[1];
	int ans=dp[1].a[1][1].get(w,l);
	printf("%i\n",ans);
	return 0;
}

Compilation message

startrek.cpp: In function 'int main()':
startrek.cpp:106:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  106 |  scanf("%i %lld",&n,&d);
      |  ~~~~~^~~~~~~~~~~~~~~~~
startrek.cpp:107:31: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  107 |  for(int i=1,u,v;i<n;i++)scanf("%i %i",&u,&v),E[u].pb(v),E[v].pb(u);
      |                          ~~~~~^~~~~~~~~~~~~~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 16768 KB Output is correct
2 Correct 13 ms 16768 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 16768 KB Output is correct
2 Correct 11 ms 16768 KB Output is correct
3 Correct 11 ms 16768 KB Output is correct
4 Correct 12 ms 16768 KB Output is correct
5 Correct 11 ms 16768 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 16768 KB Output is correct
2 Correct 11 ms 16768 KB Output is correct
3 Correct 11 ms 16768 KB Output is correct
4 Correct 11 ms 16744 KB Output is correct
5 Correct 11 ms 16768 KB Output is correct
6 Correct 11 ms 16768 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 16768 KB Output is correct
2 Correct 11 ms 16768 KB Output is correct
3 Correct 11 ms 16768 KB Output is correct
4 Correct 11 ms 16744 KB Output is correct
5 Correct 11 ms 16768 KB Output is correct
6 Correct 11 ms 16768 KB Output is correct
7 Correct 13 ms 17024 KB Output is correct
8 Correct 13 ms 17152 KB Output is correct
9 Correct 14 ms 16768 KB Output is correct
10 Correct 13 ms 16768 KB Output is correct
11 Correct 13 ms 16768 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 16768 KB Output is correct
2 Correct 11 ms 16768 KB Output is correct
3 Correct 11 ms 16768 KB Output is correct
4 Correct 11 ms 16744 KB Output is correct
5 Correct 11 ms 16768 KB Output is correct
6 Correct 11 ms 16768 KB Output is correct
7 Correct 13 ms 17024 KB Output is correct
8 Correct 13 ms 17152 KB Output is correct
9 Correct 14 ms 16768 KB Output is correct
10 Correct 13 ms 16768 KB Output is correct
11 Correct 13 ms 16768 KB Output is correct
12 Correct 267 ms 35832 KB Output is correct
13 Correct 285 ms 54368 KB Output is correct
14 Correct 228 ms 20136 KB Output is correct
15 Correct 232 ms 19960 KB Output is correct
16 Correct 241 ms 19960 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 16768 KB Output is correct
2 Correct 11 ms 16768 KB Output is correct
3 Correct 11 ms 16768 KB Output is correct
4 Correct 11 ms 16744 KB Output is correct
5 Correct 11 ms 16768 KB Output is correct
6 Correct 11 ms 16768 KB Output is correct
7 Correct 13 ms 17024 KB Output is correct
8 Correct 13 ms 17152 KB Output is correct
9 Correct 14 ms 16768 KB Output is correct
10 Correct 13 ms 16768 KB Output is correct
11 Correct 13 ms 16768 KB Output is correct
12 Correct 11 ms 16768 KB Output is correct
13 Correct 13 ms 16768 KB Output is correct
14 Correct 11 ms 16768 KB Output is correct
15 Correct 11 ms 16768 KB Output is correct
16 Correct 11 ms 16772 KB Output is correct
17 Correct 11 ms 16768 KB Output is correct
18 Correct 11 ms 16768 KB Output is correct
19 Correct 11 ms 16768 KB Output is correct
20 Correct 11 ms 16768 KB Output is correct
21 Correct 13 ms 17024 KB Output is correct
22 Correct 14 ms 17152 KB Output is correct
23 Correct 13 ms 16768 KB Output is correct
24 Correct 13 ms 16896 KB Output is correct
25 Correct 13 ms 16768 KB Output is correct
26 Correct 13 ms 16896 KB Output is correct
27 Correct 13 ms 17280 KB Output is correct
28 Correct 12 ms 16768 KB Output is correct
29 Correct 13 ms 16768 KB Output is correct
30 Correct 13 ms 16768 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 16768 KB Output is correct
2 Correct 11 ms 16768 KB Output is correct
3 Correct 11 ms 16768 KB Output is correct
4 Correct 11 ms 16744 KB Output is correct
5 Correct 11 ms 16768 KB Output is correct
6 Correct 11 ms 16768 KB Output is correct
7 Correct 13 ms 17024 KB Output is correct
8 Correct 13 ms 17152 KB Output is correct
9 Correct 14 ms 16768 KB Output is correct
10 Correct 13 ms 16768 KB Output is correct
11 Correct 13 ms 16768 KB Output is correct
12 Correct 267 ms 35832 KB Output is correct
13 Correct 285 ms 54368 KB Output is correct
14 Correct 228 ms 20136 KB Output is correct
15 Correct 232 ms 19960 KB Output is correct
16 Correct 241 ms 19960 KB Output is correct
17 Correct 11 ms 16768 KB Output is correct
18 Correct 13 ms 16768 KB Output is correct
19 Correct 11 ms 16768 KB Output is correct
20 Correct 11 ms 16768 KB Output is correct
21 Correct 11 ms 16772 KB Output is correct
22 Correct 11 ms 16768 KB Output is correct
23 Correct 11 ms 16768 KB Output is correct
24 Correct 11 ms 16768 KB Output is correct
25 Correct 11 ms 16768 KB Output is correct
26 Correct 13 ms 17024 KB Output is correct
27 Correct 14 ms 17152 KB Output is correct
28 Correct 13 ms 16768 KB Output is correct
29 Correct 13 ms 16896 KB Output is correct
30 Correct 13 ms 16768 KB Output is correct
31 Correct 13 ms 16896 KB Output is correct
32 Correct 13 ms 17280 KB Output is correct
33 Correct 12 ms 16768 KB Output is correct
34 Correct 13 ms 16768 KB Output is correct
35 Correct 13 ms 16768 KB Output is correct
36 Correct 255 ms 35708 KB Output is correct
37 Correct 273 ms 54264 KB Output is correct
38 Correct 230 ms 20140 KB Output is correct
39 Correct 238 ms 19996 KB Output is correct
40 Correct 241 ms 20088 KB Output is correct
41 Correct 265 ms 45304 KB Output is correct
42 Correct 248 ms 51064 KB Output is correct
43 Correct 200 ms 19828 KB Output is correct
44 Correct 237 ms 20088 KB Output is correct
45 Correct 230 ms 19960 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 16768 KB Output is correct
2 Correct 13 ms 16768 KB Output is correct
3 Correct 11 ms 16768 KB Output is correct
4 Correct 11 ms 16768 KB Output is correct
5 Correct 11 ms 16768 KB Output is correct
6 Correct 12 ms 16768 KB Output is correct
7 Correct 11 ms 16768 KB Output is correct
8 Correct 11 ms 16768 KB Output is correct
9 Correct 11 ms 16768 KB Output is correct
10 Correct 11 ms 16768 KB Output is correct
11 Correct 11 ms 16744 KB Output is correct
12 Correct 11 ms 16768 KB Output is correct
13 Correct 11 ms 16768 KB Output is correct
14 Correct 13 ms 17024 KB Output is correct
15 Correct 13 ms 17152 KB Output is correct
16 Correct 14 ms 16768 KB Output is correct
17 Correct 13 ms 16768 KB Output is correct
18 Correct 13 ms 16768 KB Output is correct
19 Correct 267 ms 35832 KB Output is correct
20 Correct 285 ms 54368 KB Output is correct
21 Correct 228 ms 20136 KB Output is correct
22 Correct 232 ms 19960 KB Output is correct
23 Correct 241 ms 19960 KB Output is correct
24 Correct 11 ms 16768 KB Output is correct
25 Correct 13 ms 16768 KB Output is correct
26 Correct 11 ms 16768 KB Output is correct
27 Correct 11 ms 16768 KB Output is correct
28 Correct 11 ms 16772 KB Output is correct
29 Correct 11 ms 16768 KB Output is correct
30 Correct 11 ms 16768 KB Output is correct
31 Correct 11 ms 16768 KB Output is correct
32 Correct 11 ms 16768 KB Output is correct
33 Correct 13 ms 17024 KB Output is correct
34 Correct 14 ms 17152 KB Output is correct
35 Correct 13 ms 16768 KB Output is correct
36 Correct 13 ms 16896 KB Output is correct
37 Correct 13 ms 16768 KB Output is correct
38 Correct 13 ms 16896 KB Output is correct
39 Correct 13 ms 17280 KB Output is correct
40 Correct 12 ms 16768 KB Output is correct
41 Correct 13 ms 16768 KB Output is correct
42 Correct 13 ms 16768 KB Output is correct
43 Correct 255 ms 35708 KB Output is correct
44 Correct 273 ms 54264 KB Output is correct
45 Correct 230 ms 20140 KB Output is correct
46 Correct 238 ms 19996 KB Output is correct
47 Correct 241 ms 20088 KB Output is correct
48 Correct 265 ms 45304 KB Output is correct
49 Correct 248 ms 51064 KB Output is correct
50 Correct 200 ms 19828 KB Output is correct
51 Correct 237 ms 20088 KB Output is correct
52 Correct 230 ms 19960 KB Output is correct
53 Correct 267 ms 54332 KB Output is correct
54 Correct 265 ms 47224 KB Output is correct
55 Correct 180 ms 19516 KB Output is correct
56 Correct 254 ms 35704 KB Output is correct
57 Correct 238 ms 19960 KB Output is correct
58 Correct 234 ms 20088 KB Output is correct
59 Correct 237 ms 19960 KB Output is correct
60 Correct 231 ms 20088 KB Output is correct