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Submission #601234

# Submission time Handle Problem Language Result Execution time Memory
601234 2022-07-21T13:32:20 Z Petr Star Trek (CEOI20_startrek) C++17
100 / 100
 221 ms 53368 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;
}
 
 
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%mod, R%mod, ((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 0 ms 212 KB Output is correct
2 Correct 1 ms 596 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 212 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 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 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 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 1 ms 724 KB Output is correct
8 Correct 1 ms 724 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 2 ms 596 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 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 1 ms 724 KB Output is correct
8 Correct 1 ms 724 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 2 ms 596 KB Output is correct
11 Correct 1 ms 596 KB Output is correct
12 Correct 221 ms 46952 KB Output is correct
13 Correct 173 ms 53368 KB Output is correct
14 Correct 172 ms 35728 KB Output is correct
15 Correct 194 ms 36428 KB Output is correct
16 Correct 176 ms 35356 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 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 1 ms 724 KB Output is correct
8 Correct 1 ms 724 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 2 ms 596 KB Output is correct
11 Correct 1 ms 596 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 0 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 0 ms 340 KB Output is correct
19 Correct 1 ms 252 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 2 ms 724 KB Output is correct
22 Correct 2 ms 724 KB Output is correct
23 Correct 1 ms 596 KB Output is correct
24 Correct 2 ms 596 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 724 KB Output is correct
28 Correct 1 ms 596 KB Output is correct
29 Correct 1 ms 624 KB Output is correct
30 Correct 1 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 0 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 0 ms 340 KB Output is correct
7 Correct 1 ms 724 KB Output is correct
8 Correct 1 ms 724 KB Output is correct
9 Correct 1 ms 596 KB Output is correct
10 Correct 2 ms 596 KB Output is correct
11 Correct 1 ms 596 KB Output is correct
12 Correct 221 ms 46952 KB Output is correct
13 Correct 173 ms 53368 KB Output is correct
14 Correct 172 ms 35728 KB Output is correct
15 Correct 194 ms 36428 KB Output is correct
16 Correct 176 ms 35356 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 596 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 0 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 0 ms 340 KB Output is correct
24 Correct 1 ms 252 KB Output is correct
25 Correct 1 ms 340 KB Output is correct
26 Correct 2 ms 724 KB Output is correct
27 Correct 2 ms 724 KB Output is correct
28 Correct 1 ms 596 KB Output is correct
29 Correct 2 ms 596 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 724 KB Output is correct
33 Correct 1 ms 596 KB Output is correct
34 Correct 1 ms 624 KB Output is correct
35 Correct 1 ms 596 KB Output is correct
36 Correct 217 ms 46956 KB Output is correct
37 Correct 206 ms 53360 KB Output is correct
38 Correct 160 ms 35788 KB Output is correct
39 Correct 208 ms 36448 KB Output is correct
40 Correct 166 ms 35272 KB Output is correct
41 Correct 176 ms 43656 KB Output is correct
42 Correct 166 ms 46540 KB Output is correct
43 Correct 150 ms 31728 KB Output is correct
44 Correct 191 ms 36116 KB Output is correct
45 Correct 170 ms 35160 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 596 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 0 ms 340 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 0 ms 340 KB Output is correct
13 Correct 0 ms 340 KB Output is correct
14 Correct 1 ms 724 KB Output is correct
15 Correct 1 ms 724 KB Output is correct
16 Correct 1 ms 596 KB Output is correct
17 Correct 2 ms 596 KB Output is correct
18 Correct 1 ms 596 KB Output is correct
19 Correct 221 ms 46952 KB Output is correct
20 Correct 173 ms 53368 KB Output is correct
21 Correct 172 ms 35728 KB Output is correct
22 Correct 194 ms 36428 KB Output is correct
23 Correct 176 ms 35356 KB Output is correct
24 Correct 1 ms 212 KB Output is correct
25 Correct 1 ms 596 KB Output is correct
26 Correct 1 ms 212 KB Output is correct
27 Correct 0 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 0 ms 340 KB Output is correct
31 Correct 1 ms 252 KB Output is correct
32 Correct 1 ms 340 KB Output is correct
33 Correct 2 ms 724 KB Output is correct
34 Correct 2 ms 724 KB Output is correct
35 Correct 1 ms 596 KB Output is correct
36 Correct 2 ms 596 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 724 KB Output is correct
40 Correct 1 ms 596 KB Output is correct
41 Correct 1 ms 624 KB Output is correct
42 Correct 1 ms 596 KB Output is correct
43 Correct 217 ms 46956 KB Output is correct
44 Correct 206 ms 53360 KB Output is correct
45 Correct 160 ms 35788 KB Output is correct
46 Correct 208 ms 36448 KB Output is correct
47 Correct 166 ms 35272 KB Output is correct
48 Correct 176 ms 43656 KB Output is correct
49 Correct 166 ms 46540 KB Output is correct
50 Correct 150 ms 31728 KB Output is correct
51 Correct 191 ms 36116 KB Output is correct
52 Correct 170 ms 35160 KB Output is correct
53 Correct 182 ms 49220 KB Output is correct
54 Correct 180 ms 48476 KB Output is correct
55 Correct 121 ms 29248 KB Output is correct
56 Correct 179 ms 43308 KB Output is correct
57 Correct 212 ms 37008 KB Output is correct
58 Correct 163 ms 36760 KB Output is correct
59 Correct 179 ms 37680 KB Output is correct
60 Correct 191 ms 36196 KB Output is correct