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Submission #601081

# Submission time Handle Problem Language Result Execution time Memory
601081 2022-07-21T10:58:02 Z jasmin Star Trek (CEOI20_startrek) C++14
85 / 100
 227 ms 53364 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){
        int redforce=0;
 
        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){
            redf[v][vertex_status[v]]=dfs_redforce(vertex_status[v], v, adi, red_neighbors, vertex_status, redf, summe);
            summe[v]+=redf[v][vertex_status[v]];
            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";
}

Compilation message

startrek.cpp: In function 'long long int dfs_redforce(long long int, long long int, std::vector<std::vector<long long int> >&, std::vector<std::vector<long long int> >&, std::vector<long long int>&, std::vector<std::unordered_map<long long int, long long int> >&, std::vector<long long int>&)':
startrek.cpp:86:13: warning: unused variable 'redforce' [-Wunused-variable]
   86 |         int redforce=0;
      |             ^~~~~~~~

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 0 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 0 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 1 ms 596 KB Output is correct
11 Correct 1 ms 616 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 1 ms 596 KB Output is correct
11 Correct 1 ms 616 KB Output is correct
12 Correct 182 ms 46932 KB Output is correct
13 Correct 178 ms 53268 KB Output is correct
14 Correct 155 ms 35728 KB Output is correct
15 Correct 178 ms 36428 KB Output is correct
16 Correct 181 ms 35384 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 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 1 ms 596 KB Output is correct
11 Correct 1 ms 616 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 1 ms 596 KB Output is correct
14 Correct 0 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 0 ms 340 KB Output is correct
18 Correct 0 ms 340 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 0 ms 340 KB Output is correct
21 Correct 1 ms 724 KB Output is correct
22 Correct 2 ms 724 KB Output is correct
23 Correct 1 ms 584 KB Output is correct
24 Correct 2 ms 596 KB Output is correct
25 Correct 2 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 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 0 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 1 ms 596 KB Output is correct
11 Correct 1 ms 616 KB Output is correct
12 Correct 182 ms 46932 KB Output is correct
13 Correct 178 ms 53268 KB Output is correct
14 Correct 155 ms 35728 KB Output is correct
15 Correct 178 ms 36428 KB Output is correct
16 Correct 181 ms 35384 KB Output is correct
17 Correct 0 ms 212 KB Output is correct
18 Correct 1 ms 596 KB Output is correct
19 Correct 0 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 0 ms 340 KB Output is correct
23 Correct 0 ms 340 KB Output is correct
24 Correct 1 ms 340 KB Output is correct
25 Correct 0 ms 340 KB Output is correct
26 Correct 1 ms 724 KB Output is correct
27 Correct 2 ms 724 KB Output is correct
28 Correct 1 ms 584 KB Output is correct
29 Correct 2 ms 596 KB Output is correct
30 Correct 2 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 596 KB Output is correct
35 Correct 2 ms 596 KB Output is correct
36 Correct 180 ms 46880 KB Output is correct
37 Correct 189 ms 53364 KB Output is correct
38 Correct 155 ms 35820 KB Output is correct
39 Correct 227 ms 36452 KB Output is correct
40 Correct 176 ms 35276 KB Output is correct
41 Correct 182 ms 43752 KB Output is correct
42 Correct 154 ms 46540 KB Output is correct
43 Correct 157 ms 31724 KB Output is correct
44 Correct 177 ms 36064 KB Output is correct
45 Correct 221 ms 35256 KB Output is correct

Subtask #8
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 0 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 1 ms 596 KB Output is correct
18 Correct 1 ms 616 KB Output is correct
19 Correct 182 ms 46932 KB Output is correct
20 Correct 178 ms 53268 KB Output is correct
21 Correct 155 ms 35728 KB Output is correct
22 Correct 178 ms 36428 KB Output is correct
23 Correct 181 ms 35384 KB Output is correct
24 Correct 0 ms 212 KB Output is correct
25 Correct 1 ms 596 KB Output is correct
26 Correct 0 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 0 ms 340 KB Output is correct
30 Correct 0 ms 340 KB Output is correct
31 Correct 1 ms 340 KB Output is correct
32 Correct 0 ms 340 KB Output is correct
33 Correct 1 ms 724 KB Output is correct
34 Correct 2 ms 724 KB Output is correct
35 Correct 1 ms 584 KB Output is correct
36 Correct 2 ms 596 KB Output is correct
37 Correct 2 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 596 KB Output is correct
42 Correct 2 ms 596 KB Output is correct
43 Correct 180 ms 46880 KB Output is correct
44 Correct 189 ms 53364 KB Output is correct
45 Correct 155 ms 35820 KB Output is correct
46 Correct 227 ms 36452 KB Output is correct
47 Correct 176 ms 35276 KB Output is correct
48 Correct 182 ms 43752 KB Output is correct
49 Correct 154 ms 46540 KB Output is correct
50 Correct 157 ms 31724 KB Output is correct
51 Correct 177 ms 36064 KB Output is correct
52 Correct 221 ms 35256 KB Output is correct
53 Incorrect 206 ms 49372 KB Output isn't correct
54 Halted 0 ms 0 KB -