oj.uz

Submission #302366

# Submission time Handle Problem Language Result Execution time Memory
302366 2020-09-18T16:01:38 Z errorgorn Star Trek (CEOI20_startrek) C++14
50 / 100
 1000 ms 82064 KB 
//雪花飄飄北風嘯嘯
//天地一片蒼茫

#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,fma")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
#define ll long long
#define ii pair<ll,ll>
#define iii pair<ii,ll>
#define fi first
#define se second
#define endl '\n'
#define debug(x) cout << #x << " is " << x << endl

#define rep(x,start,end) for(auto x=(start)-((start)>(end));x!=(end)-((start)>(end));((start)<(end)?x++:x--))
#define all(x) (x).begin(),(x).end()
#define sz(x) (int)(x).size()

#define indexed_set tree<ll,null_type,less<ll>,rb_tree_tag,tree_order_statistics_node_update>
//change less to less_equal for non distinct pbds, but erase will bug

mt19937 rng(chrono::system_clock::now().time_since_epoch().count());

struct custom_hash {
    typedef unsigned long long ull;
    const ull FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
    static ull splitmix64(ull x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(ll x) const {
        return splitmix64(x + FIXED_RANDOM);
    }
    size_t operator()(const pair<int,int> &i)const{
        return splitmix64((((ll)i.first)^(((ll)i.second)<<32))+FIXED_RANDOM);
    }
};


const int MOD=1000000007;

vector<vector<ll> > mul(vector<vector<ll> > i, vector<vector<ll> > j,int m){
    vector<vector<ll> > res;
    for (int x=0;x<i.size();x++){
        res.push_back(vector<ll>());
        for (int y=0;y<i.size();y++){
            res[x].push_back(0);
            for (int z=0;z<i.size();z++){
                res[x][y]=(res[x][y]+i[x][z]*j[z][y])%m;
            }
        }
    }
    return res;
}

vector<vector<ll> > mexp(vector<vector<ll> > mat,long long p,int m){
    if (p==1) return mat;
    vector<vector<ll> > res=mexp(mat,p>>1,m);
    res=mul(res,res,m);
    if (p&1) res=mul(res,mat,m);
    return res;
}


ll qexp(ll b,ll p,int m){
	ll res=1;
	while (p){
		if (p&1) res=res*b%m;
		b=b*b%m;
		p>>=1;
	}
	return res;
}

ll fix(ll i){
	i%=MOD;
	if (i<0) i+=MOD;
	return i;
}

ll n,k;
vector<int> al[100005];

struct pi{
	ll a=0,b=0;
};

pi add(pi i,pi j){
	pi res;
	res.a=(i.a+j.a)%MOD;
	res.b=(i.b+j.b)%MOD;
	return res;
}

pi mul(pi i,pi j){
	pi res;
	res.a=(i.a*j.b)%MOD;
	res.b=fix((i.a+i.b)*(j.a+j.b)-res.a);
	return res;
}

struct dat{
	pi norm;
	pi extra;
};

struct mat{ //operation of tree
	int v[4][4];
	
	mat(int i){
		memset(v,0,sizeof(v));
		rep(x,0,4) v[x][x]=i;
	}
	mat(int a,int b,int c,int d){
		memset(v,0,sizeof(v));
		v[0][0]=b;
		v[1][0]=a;
		v[1][1]=(a+b)%MOD;
		
		v[2][2]=b;
		v[3][2]=a;
		v[3][3]=(a+b)%MOD;
		
		v[2][0]=d;
		v[3][0]=c;
		v[3][1]=(c+d)%MOD;
	}
};

mat mul(mat &i, mat &j){
	mat res=mat(0);
	rep(x,0,4) rep(y,0,4) rep(z,0,4)
		res.v[x][y]=(res.v[x][y]+i.v[x][z]*j.v[z][y])%MOD;
		
	return res;
}



pi pp;
unordered_map<ii,dat,custom_hash> memo;
int pa[100005];
vector<int> adj[100005];
vector<mat> fw[100005],bw[100005];

dat dfs(int i,int p){
	if (memo.count(ii(i,p))) return memo[ii(i,p)];
	
	mat matt=mat(1);
	if (pa[i]==0){
		pa[i]=p;
		vector<mat> v;
		for (auto &it:al[i]){
			if (it==p) continue;
			adj[i].push_back(it);
			auto res=dfs(it,i);
			v.push_back(mat(res.norm.a,res.norm.b,res.extra.a,res.extra.b));
		}
		
		if (sz(v)==1) fw[i].push_back(v[0]),bw[i].push_back(v[0]);
		else if (sz(v)>1){
			fw[i].push_back(v[0]);
			rep(x,1,sz(v)) fw[i].push_back(mul(fw[i].back(),v[x]));
			
			reverse(all(v));
			
			bw[i].push_back(v[0]);
			rep(x,1,sz(v)) bw[i].push_back(mul(bw[i].back(),v[x]));
			reverse(all(bw[i]));
		}
		if (!v.empty()) matt=fw[i].back();
	}
	else{
		if (pa[i]!=-1){
			auto res=dfs(pa[i],i);
			auto temp=mat(res.norm.a,res.norm.b,res.extra.a,res.extra.b);
			matt=mul(matt,temp);
		}
		if (!adj[i].empty()){
			if (p==-1){
				matt=mul(matt,fw[i].back());
			}
			else{
				int idx=distance(adj[i].begin(),lower_bound(all(adj[i]),p));
				if (idx!=0) matt=mul(matt,fw[i][idx-1]);
				if (idx!=sz(adj[i])-1) matt=mul(matt,bw[i][idx+1]);
			}
		}
	}
	
	dat res;
	res.norm.a=matt.v[0][0],res.norm.b=matt.v[1][0];
	res.extra.a=matt.v[2][0],res.extra.b=matt.v[3][0];
	res.extra=add(res.extra,mul(res.norm,pp));
	
	return memo[ii(i,p)]=res;
}

dat get(int i,int j){
	pp.a=i,pp.b=j;
	memo.clear();
	rep(x,0,100005){
		pa[x]=0;
		adj[x].clear();
		fw[x].clear();
		bw[x].clear();
	}
	dat temp;
	rep(x,1,n+1){
		auto res=dfs(x,-1);
		temp.norm=add(temp.norm,res.norm);
		temp.extra=add(temp.extra,res.extra);
	}
	return temp;
}

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin.exceptions(ios::badbit | ios::failbit);
	
	memo.reserve(4096);
	memo.max_load_factor(0.25);

	
	cin>>n>>k;
	
	ll a,b;
	rep(x,1,n){
		cin>>a>>b;
		al[a].push_back(b);
		al[b].push_back(a);
	}
	rep(x,1,n+1) sort(all(al[x]));
	
	vector<vector<ll> > mat={{0,0},{0,0}};
	
	dat temp;
	temp=get(1,0);
	mat[0][0]=temp.extra.a%MOD,mat[1][0]=temp.extra.b%MOD;
	
	temp=get(0,1);
	mat[0][1]=temp.extra.a%MOD,mat[1][1]=temp.extra.b%MOD;
	
	//cout<<mat[0][0]<<" "<<mat[0][1]<<endl;
	//cout<<mat[1][0]<<" "<<mat[1][1]<<endl;
	
	if (k==1) mat={{1,0},{0,1}};
	else mat=mexp(mat,k-1,MOD);
	
	temp=get(0,0);
	a=temp.norm.a%MOD,b=temp.norm.b%MOD;
	
	//cout<<a<<" "<<b<<endl;
	
	get((mat[0][0]*a+mat[0][1]*b)%MOD,(mat[1][0]*a+mat[1][1]*b)%MOD);
	cout<<dfs(1,-1).extra.b<<endl;
}

Compilation message

startrek.cpp: In function 'std::vector<std::vector<long long int> > mul(std::vector<std::vector<long long int> >, std::vector<std::vector<long long int> >, int)':
startrek.cpp:56:19: 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]
   56 |     for (int x=0;x<i.size();x++){
      |                  ~^~~~~~~~~
startrek.cpp:58:23: 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]
   58 |         for (int y=0;y<i.size();y++){
      |                      ~^~~~~~~~~
startrek.cpp:60:27: 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]
   60 |             for (int z=0;z<i.size();z++){
      |                          ~^~~~~~~~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 10112 KB Output is correct
2 Correct 15 ms 10752 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 10112 KB Output is correct
2 Correct 9 ms 10112 KB Output is correct
3 Correct 11 ms 10112 KB Output is correct
4 Correct 9 ms 10112 KB Output is correct
5 Correct 9 ms 10112 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 10112 KB Output is correct
2 Correct 10 ms 10240 KB Output is correct
3 Correct 9 ms 10240 KB Output is correct
4 Correct 10 ms 10240 KB Output is correct
5 Correct 10 ms 10144 KB Output is correct
6 Correct 10 ms 10240 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 10112 KB Output is correct
2 Correct 10 ms 10240 KB Output is correct
3 Correct 9 ms 10240 KB Output is correct
4 Correct 10 ms 10240 KB Output is correct
5 Correct 10 ms 10144 KB Output is correct
6 Correct 10 ms 10240 KB Output is correct
7 Correct 14 ms 10880 KB Output is correct
8 Correct 14 ms 11136 KB Output is correct
9 Correct 14 ms 10752 KB Output is correct
10 Correct 15 ms 10752 KB Output is correct
11 Correct 15 ms 10752 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 10112 KB Output is correct
2 Correct 10 ms 10240 KB Output is correct
3 Correct 9 ms 10240 KB Output is correct
4 Correct 10 ms 10240 KB Output is correct
5 Correct 10 ms 10144 KB Output is correct
6 Correct 10 ms 10240 KB Output is correct
7 Correct 14 ms 10880 KB Output is correct
8 Correct 14 ms 11136 KB Output is correct
9 Correct 14 ms 10752 KB Output is correct
10 Correct 15 ms 10752 KB Output is correct
11 Correct 15 ms 10752 KB Output is correct
12 Execution timed out 1070 ms 82064 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 10112 KB Output is correct
2 Correct 10 ms 10240 KB Output is correct
3 Correct 9 ms 10240 KB Output is correct
4 Correct 10 ms 10240 KB Output is correct
5 Correct 10 ms 10144 KB Output is correct
6 Correct 10 ms 10240 KB Output is correct
7 Correct 14 ms 10880 KB Output is correct
8 Correct 14 ms 11136 KB Output is correct
9 Correct 14 ms 10752 KB Output is correct
10 Correct 15 ms 10752 KB Output is correct
11 Correct 15 ms 10752 KB Output is correct
12 Correct 10 ms 10112 KB Output is correct
13 Correct 16 ms 10656 KB Output is correct
14 Correct 9 ms 10112 KB Output is correct
15 Correct 9 ms 10112 KB Output is correct
16 Correct 10 ms 10240 KB Output is correct
17 Correct 10 ms 10240 KB Output is correct
18 Correct 10 ms 10240 KB Output is correct
19 Correct 9 ms 10240 KB Output is correct
20 Correct 10 ms 10240 KB Output is correct
21 Correct 14 ms 11008 KB Output is correct
22 Correct 14 ms 11136 KB Output is correct
23 Correct 16 ms 10752 KB Output is correct
24 Correct 15 ms 10752 KB Output is correct
25 Correct 14 ms 10752 KB Output is correct
26 Correct 14 ms 10880 KB Output is correct
27 Correct 14 ms 11136 KB Output is correct
28 Correct 13 ms 10624 KB Output is correct
29 Correct 19 ms 10752 KB Output is correct
30 Correct 14 ms 10752 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 10112 KB Output is correct
2 Correct 10 ms 10240 KB Output is correct
3 Correct 9 ms 10240 KB Output is correct
4 Correct 10 ms 10240 KB Output is correct
5 Correct 10 ms 10144 KB Output is correct
6 Correct 10 ms 10240 KB Output is correct
7 Correct 14 ms 10880 KB Output is correct
8 Correct 14 ms 11136 KB Output is correct
9 Correct 14 ms 10752 KB Output is correct
10 Correct 15 ms 10752 KB Output is correct
11 Correct 15 ms 10752 KB Output is correct
12 Execution timed out 1070 ms 82064 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 10112 KB Output is correct
2 Correct 15 ms 10752 KB Output is correct
3 Correct 8 ms 10112 KB Output is correct
4 Correct 9 ms 10112 KB Output is correct
5 Correct 11 ms 10112 KB Output is correct
6 Correct 9 ms 10112 KB Output is correct
7 Correct 9 ms 10112 KB Output is correct
8 Correct 9 ms 10112 KB Output is correct
9 Correct 10 ms 10240 KB Output is correct
10 Correct 9 ms 10240 KB Output is correct
11 Correct 10 ms 10240 KB Output is correct
12 Correct 10 ms 10144 KB Output is correct
13 Correct 10 ms 10240 KB Output is correct
14 Correct 14 ms 10880 KB Output is correct
15 Correct 14 ms 11136 KB Output is correct
16 Correct 14 ms 10752 KB Output is correct
17 Correct 15 ms 10752 KB Output is correct
18 Correct 15 ms 10752 KB Output is correct
19 Execution timed out 1070 ms 82064 KB Time limit exceeded
20 Halted 0 ms 0 KB -