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Submission #601057

# Submission time Handle Problem Language Result Execution time Memory
601057 2022-07-21T10:42:50 Z jasmin Star Trek (CEOI20_startrek) C++14
65 / 100
 221 ms 57568 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){
    if(vertex_status[v]==-2){
        int redforce=0;

        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;

        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];
        }

        if(!is_green){ //red
            redforce++;
            redforce+=summe[v];
        }
        else { //green with one red child
            vector<int> red_children;
            for (int x : red_neighbors[v]) if (x != p) red_children.push_back(x);
            if (red_children.size() == 1) {
                redforce+=redf[v][red_children[0]];
            }
        }
        vertex_status[v]=p;
        return redforce;
    }
    else{

        int redforce=0;
        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(!is_green){ //red
            redforce++;

            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;
            }
            redforce+=summe[v];
            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) {
                
                if(vertex_status[v]==u){
                    redf[v][u]=dfs_redforce(u, v, adi, red_neighbors, vertex_status, redf, summe);
                    summe[v]+=redf[v][u];
                    vertex_status[v]=-1;
                }
                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; G%=mod;
        R+=r1; R%=mod;
    }
 
    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 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 0 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 1 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 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 0 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 1 ms 724 KB Output is correct
8 Correct 2 ms 724 KB Output is correct
9 Correct 2 ms 596 KB Output is correct
10 Correct 1 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 1 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 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 724 KB Output is correct
8 Correct 2 ms 724 KB Output is correct
9 Correct 2 ms 596 KB Output is correct
10 Correct 1 ms 596 KB Output is correct
11 Correct 1 ms 596 KB Output is correct
12 Correct 205 ms 49032 KB Output is correct
13 Correct 195 ms 57568 KB Output is correct
14 Correct 151 ms 38352 KB Output is correct
15 Correct 208 ms 37716 KB Output is correct
16 Correct 166 ms 37784 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 0 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 1 ms 724 KB Output is correct
8 Correct 2 ms 724 KB Output is correct
9 Correct 2 ms 596 KB Output is correct
10 Correct 1 ms 596 KB Output is correct
11 Correct 1 ms 596 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 1 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 1 ms 340 KB Output is correct
21 Correct 1 ms 724 KB Output is correct
22 Correct 1 ms 724 KB Output is correct
23 Correct 2 ms 596 KB Output is correct
24 Correct 1 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 852 KB Output is correct
28 Correct 1 ms 596 KB Output is correct
29 Correct 1 ms 596 KB Output is correct
30 Correct 1 ms 596 KB Output is correct

Subtask #7
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 0 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 1 ms 724 KB Output is correct
8 Correct 2 ms 724 KB Output is correct
9 Correct 2 ms 596 KB Output is correct
10 Correct 1 ms 596 KB Output is correct
11 Correct 1 ms 596 KB Output is correct
12 Correct 205 ms 49032 KB Output is correct
13 Correct 195 ms 57568 KB Output is correct
14 Correct 151 ms 38352 KB Output is correct
15 Correct 208 ms 37716 KB Output is correct
16 Correct 166 ms 37784 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 1 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 1 ms 340 KB Output is correct
26 Correct 1 ms 724 KB Output is correct
27 Correct 1 ms 724 KB Output is correct
28 Correct 2 ms 596 KB Output is correct
29 Correct 1 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 852 KB Output is correct
33 Correct 1 ms 596 KB Output is correct
34 Correct 1 ms 596 KB Output is correct
35 Correct 1 ms 596 KB Output is correct
36 Correct 166 ms 50232 KB Output is correct
37 Correct 221 ms 57552 KB Output is correct
38 Correct 167 ms 38300 KB Output is correct
39 Correct 189 ms 37724 KB Output is correct
40 Correct 158 ms 37708 KB Output is correct
41 Correct 184 ms 46432 KB Output is correct
42 Correct 161 ms 49996 KB Output is correct
43 Correct 144 ms 34108 KB Output is correct
44 Incorrect 173 ms 37696 KB Output isn't correct
45 Halted 0 ms 0 KB -

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 0 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 1 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 1 ms 340 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 1 ms 724 KB Output is correct
15 Correct 2 ms 724 KB Output is correct
16 Correct 2 ms 596 KB Output is correct
17 Correct 1 ms 596 KB Output is correct
18 Correct 1 ms 596 KB Output is correct
19 Correct 205 ms 49032 KB Output is correct
20 Correct 195 ms 57568 KB Output is correct
21 Correct 151 ms 38352 KB Output is correct
22 Correct 208 ms 37716 KB Output is correct
23 Correct 166 ms 37784 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 1 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 1 ms 340 KB Output is correct
33 Correct 1 ms 724 KB Output is correct
34 Correct 1 ms 724 KB Output is correct
35 Correct 2 ms 596 KB Output is correct
36 Correct 1 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 852 KB Output is correct
40 Correct 1 ms 596 KB Output is correct
41 Correct 1 ms 596 KB Output is correct
42 Correct 1 ms 596 KB Output is correct
43 Correct 166 ms 50232 KB Output is correct
44 Correct 221 ms 57552 KB Output is correct
45 Correct 167 ms 38300 KB Output is correct
46 Correct 189 ms 37724 KB Output is correct
47 Correct 158 ms 37708 KB Output is correct
48 Correct 184 ms 46432 KB Output is correct
49 Correct 161 ms 49996 KB Output is correct
50 Correct 144 ms 34108 KB Output is correct
51 Incorrect 173 ms 37696 KB Output isn't correct
52 Halted 0 ms 0 KB -