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Submission #601232

# Submission time Handle Problem Language Result Execution time Memory
601232 2022-07-21T13:30:11 Z Petr Star Trek (CEOI20_startrek) C++17
85 / 100
 203 ms 54500 KB 
#include<bits/stdc++.h>
//#include<iostream>
//#include<vector>
using namespace std;
#define int long long
 
const int mod=1e9+7;
struct matrix{
    int a=1;
    int b=0;
    int c=0;
    int d=1;
};
matrix zero={1, 0, 0, 1};
vector<int> mul(matrix a, vector<int> b){
    vector<int> ans(2, -1);
    ans[0]=(a.a*b[0])%mod +(a.b*b[1])%mod;
    ans[0]%=mod;
    ans[1]=(a.c*b[0])%mod +(a.d*b[1])%mod;
    ans[1]%=mod;
    return ans;
}
matrix multiply(matrix a, matrix b){
    matrix ans;
    ans.a=(a.a*b.a)%mod + (a.b*b.c)%mod;
    ans.a%=mod;
    ans.b=(a.a*b.b)%mod + (a.b*b.d)%mod;
    ans.b%=mod;
    ans.c=(a.c*b.a)%mod + (a.d*b.c)%mod;
    ans.c%=mod;
    ans.d=(a.c*b.b)%mod + (a.d*b.d)%mod;
    ans.d%=mod;
    return ans;
}
matrix power(matrix a, int e){
    if(e==0){
        return zero;
    }
 
    matrix res=power(a, e/2);
    res=multiply(res, res);
    if(e%2==1){
        res=multiply(res, a);
    }
    return res;
}
 
 
// vertex_status ist: 
bool dfs_win(int v, int p, vector<vector<int> >& adi, vector<int>& vertex_status, vector<vector<int>>& red_neighbors){
    if (vertex_status[v] == -2) {
      vertex_status[v] = p;
      for(auto u: adi[v]){
          if(u==p) continue;
   
          if(!dfs_win(u, v, adi, vertex_status, red_neighbors)){
              red_neighbors[v].push_back(u);
          }
      }
    } else {
      if (vertex_status[v] >= 0 && vertex_status[v] != p) {
        auto u = vertex_status[v];
        if(!dfs_win(u, v, adi, vertex_status, red_neighbors)){
            red_neighbors[v].push_back(u);
        }
        vertex_status[v] = -1;
      }
    }
 
    if (vertex_status[v] == p) {
      return red_neighbors[v].size() > 0;
    } else {
      if (red_neighbors[v].size() >= 2) return true;
      if (red_neighbors[v].size() == 0) return false;
      return red_neighbors[v][0] != p;
    }
}
 
int dfs_redforce(int v, int p, vector<vector<int> >& adi, vector<vector<int>>& red_neighbors, vector<int>& vertex_status, vector<unordered_map<int, int> >& redf, vector<int>& summe){
    bool is_green;
    if (red_neighbors[v].size() >= 2) is_green = true;
    else if (red_neighbors[v].size() == 0) is_green = false;
    else  is_green = red_neighbors[v][0] != p;
 
    if(vertex_status[v]==-2){
        for(auto u: adi[v]){
            if(u==p) continue;
            redf[v][u]=dfs_redforce(u, v, adi, red_neighbors, vertex_status, redf, summe);
            summe[v]+=redf[v][u];
        }
 
        vertex_status[v]=p;
    }
    else{
        if(vertex_status[v]>=0 && vertex_status[v]!=p){
            auto u = vertex_status[v];
            redf[v][u]=dfs_redforce(u, v, adi, red_neighbors, vertex_status, redf, summe);
            summe[v]+=redf[v][u];
            vertex_status[v]=-1;
        }
    }
 
    int redforce = 0;
    if(!is_green){ //red
        redforce++;
        redforce+=summe[v];
        if (vertex_status[v] == -1 && p != -1) {
          redforce-=redf[v][p];
        }
    }
    else { //green with one red child
        bool needed=red_neighbors[v].size()<3;
        int u=red_neighbors[v][0];
        if(red_neighbors[v].size()==2){
            if(red_neighbors[v][0]==p) u=red_neighbors[v][1];
            else if(red_neighbors[v][1]!=p) needed=false;
        }
        if (needed) {
            redforce+=redf[v][u];
        }
    }
 
    return redforce;
 
}
 
signed main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
 
    //freopen("input1.txt", "r", stdin);
    //freopen("out.txt", "w", stdout);
 
    int n, d;
    cin >> n >> d;
    vector<vector<int> > adi(n);
    for(int i=0; i<n-1; i++){
        int a,b;
        cin >> a >> b;
        adi[a-1].push_back(b-1);
        adi[b-1].push_back(a-1);
    }
 
    int G=0; int R=0;
    int g1=0; int r1=0;
    int c=0;
    vector<int> vertex_status(n, -2);
    vector<int> vertex_status2(n, -2);
    vector<vector<int>> red_neighbors(n);
    vector<unordered_map<int,int> > redf(n);
    vector<int> summe(n, 0);
    for(int i=n-1; i>=0; i--){
 
        bool we_win=dfs_win(i, -1, adi, vertex_status, red_neighbors);
        int redforce=dfs_redforce(i, -1, adi, red_neighbors, vertex_status2, redf, summe);
 
        if(we_win){
            c++;
            g1=n;
            r1=n-redforce;
        }
        else{
            g1=0;
            r1=redforce;
        }
        G+=g1;
        R+=r1;
    }
 
    matrix m1={g1, r1, 0, 0};
    matrix m2={G, R, ((n*n)-G)%mod, ((n*n)-R)%mod};
    matrix p=power(m2, d-1);
    vector<int> v=mul(p, {c, n-c});
    vector<int> ans=mul(m1, v);
    cout << ans[0] << "\n";
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 2 ms 596 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 316 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 5 ms 700 KB Output is correct
8 Correct 1 ms 724 KB Output is correct
9 Correct 1 ms 580 KB Output is correct
10 Correct 2 ms 580 KB Output is correct
11 Correct 1 ms 596 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 5 ms 700 KB Output is correct
8 Correct 1 ms 724 KB Output is correct
9 Correct 1 ms 580 KB Output is correct
10 Correct 2 ms 580 KB Output is correct
11 Correct 1 ms 596 KB Output is correct
12 Correct 175 ms 48152 KB Output is correct
13 Correct 168 ms 54500 KB Output is correct
14 Correct 157 ms 36740 KB Output is correct
15 Correct 198 ms 37544 KB Output is correct
16 Correct 163 ms 36620 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 5 ms 700 KB Output is correct
8 Correct 1 ms 724 KB Output is correct
9 Correct 1 ms 580 KB Output is correct
10 Correct 2 ms 580 KB Output is correct
11 Correct 1 ms 596 KB Output is correct
12 Correct 1 ms 320 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 320 KB Output is correct
21 Correct 1 ms 712 KB Output is correct
22 Correct 1 ms 724 KB Output is correct
23 Correct 1 ms 596 KB Output is correct
24 Correct 1 ms 576 KB Output is correct
25 Correct 1 ms 596 KB Output is correct
26 Correct 1 ms 724 KB Output is correct
27 Correct 1 ms 836 KB Output is correct
28 Correct 1 ms 580 KB Output is correct
29 Correct 1 ms 596 KB Output is correct
30 Correct 2 ms 596 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 5 ms 700 KB Output is correct
8 Correct 1 ms 724 KB Output is correct
9 Correct 1 ms 580 KB Output is correct
10 Correct 2 ms 580 KB Output is correct
11 Correct 1 ms 596 KB Output is correct
12 Correct 175 ms 48152 KB Output is correct
13 Correct 168 ms 54500 KB Output is correct
14 Correct 157 ms 36740 KB Output is correct
15 Correct 198 ms 37544 KB Output is correct
16 Correct 163 ms 36620 KB Output is correct
17 Correct 1 ms 320 KB Output is correct
18 Correct 1 ms 596 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 1 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 1 ms 320 KB Output is correct
26 Correct 1 ms 712 KB Output is correct
27 Correct 1 ms 724 KB Output is correct
28 Correct 1 ms 596 KB Output is correct
29 Correct 1 ms 576 KB Output is correct
30 Correct 1 ms 596 KB Output is correct
31 Correct 1 ms 724 KB Output is correct
32 Correct 1 ms 836 KB Output is correct
33 Correct 1 ms 580 KB Output is correct
34 Correct 1 ms 596 KB Output is correct
35 Correct 2 ms 596 KB Output is correct
36 Correct 185 ms 48092 KB Output is correct
37 Correct 171 ms 54452 KB Output is correct
38 Correct 162 ms 36760 KB Output is correct
39 Correct 193 ms 37580 KB Output is correct
40 Correct 164 ms 36456 KB Output is correct
41 Correct 176 ms 44868 KB Output is correct
42 Correct 188 ms 47612 KB Output is correct
43 Correct 140 ms 32664 KB Output is correct
44 Correct 176 ms 37328 KB Output is correct
45 Correct 191 ms 36216 KB Output is correct

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 2 ms 596 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 316 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 5 ms 700 KB Output is correct
15 Correct 1 ms 724 KB Output is correct
16 Correct 1 ms 580 KB Output is correct
17 Correct 2 ms 580 KB Output is correct
18 Correct 1 ms 596 KB Output is correct
19 Correct 175 ms 48152 KB Output is correct
20 Correct 168 ms 54500 KB Output is correct
21 Correct 157 ms 36740 KB Output is correct
22 Correct 198 ms 37544 KB Output is correct
23 Correct 163 ms 36620 KB Output is correct
24 Correct 1 ms 320 KB Output is correct
25 Correct 1 ms 596 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 1 ms 212 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 1 ms 340 KB Output is correct
31 Correct 1 ms 340 KB Output is correct
32 Correct 1 ms 320 KB Output is correct
33 Correct 1 ms 712 KB Output is correct
34 Correct 1 ms 724 KB Output is correct
35 Correct 1 ms 596 KB Output is correct
36 Correct 1 ms 576 KB Output is correct
37 Correct 1 ms 596 KB Output is correct
38 Correct 1 ms 724 KB Output is correct
39 Correct 1 ms 836 KB Output is correct
40 Correct 1 ms 580 KB Output is correct
41 Correct 1 ms 596 KB Output is correct
42 Correct 2 ms 596 KB Output is correct
43 Correct 185 ms 48092 KB Output is correct
44 Correct 171 ms 54452 KB Output is correct
45 Correct 162 ms 36760 KB Output is correct
46 Correct 193 ms 37580 KB Output is correct
47 Correct 164 ms 36456 KB Output is correct
48 Correct 176 ms 44868 KB Output is correct
49 Correct 188 ms 47612 KB Output is correct
50 Correct 140 ms 32664 KB Output is correct
51 Correct 176 ms 37328 KB Output is correct
52 Correct 191 ms 36216 KB Output is correct
53 Incorrect 203 ms 50580 KB Output isn't correct
54 Halted 0 ms 0 KB -