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Submission #701564

# Submission time Handle Problem Language Result Execution time Memory
701564 2023-02-21T13:18:16 Z PCTprobability Star Trek (CEOI20_startrek) C++17
50 / 100
 34 ms 5204 KB 
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll mod = 1000000007;
#define fi first
#define se second
#define pb push_back
ll modPow(ll a,ll b,ll c){
  ll r=1;
  while(b){
    if(b&1) (r*=a)%=mod;
    (a*=a)%=mod;
    b/=2;
  }
  return r;
}
vector<ll> g[100000];
int v[100000];
bool win[100000];
void dfs(ll a,ll b){
  v[a]=1;
  for(auto e:g[a]){
    if(e==b) continue;
    dfs(e,a);
    if(!win[e]) win[a]=true;
    v[a]+=v[e];
  }
}
ll cnt=0;
void dfs2(ll a,ll b,ll x){
  if(x==0) cnt++;
  if(x==1){
    ll k=0;
    for(auto e:g[a]){
      if(e==b) continue;
      if(!win[e]) k++;
    }
    if(k>=2) return;
  }
  for(auto e:g[a]){
    if(e==b) continue;
    if(x==1&&win[e]) continue;
    dfs2(e,a,x^1);
  }
}
ll cnt2=0;
void dfs3(ll a,ll b,ll x){
  if(x) cnt2++;
  if(x==0){
    ll k=0;
    for(auto e:g[a]){
      if(e==b) continue;
      if(!win[e]) k++;
    }
    if(k>=2) return;
  }
  for(auto e:g[a]){
    if(e==b) continue;
    if(x==0&&win[e]) continue;
    dfs3(e,a,x^1);
  }
}
int main(){
  ll n,d;
  cin>>n>>d;
  if(n==2){
    cout<<modPow(4,d,mod)<<endl;
    return 0;
  }
  assert(n<=1000&&d<=100000);
  for(int i=0;i<n-1;i++){
    ll a,b;
    cin>>a>>b;
    a--;
    b--;
    g[a].pb(b);
    g[b].pb(a);
  }
  ll x=0,y=0;
  ll z=0;
  ll type=0,x1=0,y1=0;
  for(int i=0;i<n;i++){
    cnt=0,cnt2=0;
    for(int j=0;j<n;j++) win[j]=false;
    dfs(i,-1);
    ll cn=0,V=0;
    for(auto e:g[i]){
      if(!win[e]){
        cn++;
        V=e;
      }
    }
    if(cn) z++;
    if(cn>=2){
      x++;
    }
    if(cn==1){
      dfs3(V,i,1);
      x+=modPow(n,mod-2,mod)*(n-cnt2);
      x%=mod;
      y+=cnt2;
      y%=mod;
      if(i==0){
        type=1;
        x1+=modPow(n,mod-2,mod)*(n-cnt2);
        y1+=cnt2;
      }
    }
    if(cn==0){
      dfs2(i,-1,0);
      y-=cnt;
      y+=mod;
      y%=mod;
      x+=modPow(n%mod,mod-2,mod)*cnt;
      x%=mod;
      if(i==0){
        type=1;
        x1+=modPow(n%mod,mod-2,mod)*cnt;
        y1-=cnt;
        y1+=mod;
      }
    }
  }
  x1%=mod;
  y1%=mod;
  for(int i=1;i<d;i++){
    z=(z*y + x*modPow(n,2*i,mod));
    z%=mod;
  }
  if(type==0){
    cout<<modPow(n,2*d,mod)<<endl;
  }
  else{
    cout<<(x1*modPow(n,2*d,mod)+y1*z)%mod<<endl;
  }
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 14 ms 2696 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2656 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2644 KB Output is correct
5 Correct 1 ms 2644 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2660 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2660 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 20 ms 2732 KB Output is correct
8 Correct 28 ms 2744 KB Output is correct
9 Correct 16 ms 2644 KB Output is correct
10 Correct 15 ms 2696 KB Output is correct
11 Correct 21 ms 2732 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2660 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 20 ms 2732 KB Output is correct
8 Correct 28 ms 2744 KB Output is correct
9 Correct 16 ms 2644 KB Output is correct
10 Correct 15 ms 2696 KB Output is correct
11 Correct 21 ms 2732 KB Output is correct
12 Runtime error 3 ms 5204 KB Execution killed with signal 6
13 Halted 0 ms 0 KB -

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2660 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 20 ms 2732 KB Output is correct
8 Correct 28 ms 2744 KB Output is correct
9 Correct 16 ms 2644 KB Output is correct
10 Correct 15 ms 2696 KB Output is correct
11 Correct 21 ms 2732 KB Output is correct
12 Correct 1 ms 2644 KB Output is correct
13 Correct 14 ms 2696 KB Output is correct
14 Correct 1 ms 2644 KB Output is correct
15 Correct 1 ms 2644 KB Output is correct
16 Correct 2 ms 2624 KB Output is correct
17 Correct 2 ms 2644 KB Output is correct
18 Correct 1 ms 2644 KB Output is correct
19 Correct 1 ms 2644 KB Output is correct
20 Correct 3 ms 2660 KB Output is correct
21 Correct 20 ms 2732 KB Output is correct
22 Correct 28 ms 2768 KB Output is correct
23 Correct 16 ms 2696 KB Output is correct
24 Correct 15 ms 2696 KB Output is correct
25 Correct 22 ms 2644 KB Output is correct
26 Correct 22 ms 2720 KB Output is correct
27 Correct 34 ms 2748 KB Output is correct
28 Correct 19 ms 2696 KB Output is correct
29 Correct 22 ms 2772 KB Output is correct
30 Correct 25 ms 2676 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2660 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 20 ms 2732 KB Output is correct
8 Correct 28 ms 2744 KB Output is correct
9 Correct 16 ms 2644 KB Output is correct
10 Correct 15 ms 2696 KB Output is correct
11 Correct 21 ms 2732 KB Output is correct
12 Runtime error 3 ms 5204 KB Execution killed with signal 6
13 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 14 ms 2696 KB Output is correct
3 Correct 1 ms 2656 KB Output is correct
4 Correct 2 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 1 ms 2644 KB Output is correct
8 Correct 2 ms 2644 KB Output is correct
9 Correct 2 ms 2644 KB Output is correct
10 Correct 2 ms 2644 KB Output is correct
11 Correct 2 ms 2660 KB Output is correct
12 Correct 2 ms 2644 KB Output is correct
13 Correct 2 ms 2644 KB Output is correct
14 Correct 20 ms 2732 KB Output is correct
15 Correct 28 ms 2744 KB Output is correct
16 Correct 16 ms 2644 KB Output is correct
17 Correct 15 ms 2696 KB Output is correct
18 Correct 21 ms 2732 KB Output is correct
19 Runtime error 3 ms 5204 KB Execution killed with signal 6
20 Halted 0 ms 0 KB -