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Submission #600988

# Submission time Handle Problem Language Result Execution time Memory
600988 2022-07-21T09:50:18 Z jasmin Star Trek (CEOI20_startrek) C++14
50 / 100
 1000 ms 46808 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){
    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;

        if(!is_green){ //red
            redforce++;
            for(auto u: adi[v]){
                if(u!=p){
                    redf[v][u]=dfs_redforce(u, v, adi, red_neighbors, vertex_status, redf);
                    redforce+=redf[v][u];
                } 
            }
        }
        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) {
            redf[v][red_children[0]]=dfs_redforce(red_children[0], v, adi, red_neighbors, vertex_status, redf);
            redforce+=redf[v][red_children[0]];
            }
        }
        return redforce;
    }
    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);
        }
        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++;
            for(auto u: adi[v]){
                if(u==p) continue;

                if(vertex_status[v]==u && u!=p){
                    redf[v][u]=dfs_redforce(u, v, adi, red_neighbors, vertex_status, redf);
                }
                redforce+=redf[v][u];
            }
        }
        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) {
                int u=red_children[0];
                if(vertex_status[v]==u){
                    redf[v][u]=dfs_redforce(u, v, adi, red_neighbors, vertex_status, redf);
                }
                redforce+=redf[v][u];
            }
        }

        vertex_status[v]=-1;
        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);
    for(int i=n-1; i>=0; i--){
        vector<int> redchild(n, -1);
        vector<int> cnt_red_children(n, 0);
 
        bool we_win=dfs_win(i, -1, adi, vertex_status, red_neighbors);
        int redforce=dfs_redforce(i, -1, adi, red_neighbors, vertex_status2, redf);
 
        if(we_win){
            c++;
            g1=n;
            r1=n-redforce;
        }
        else{
            g1=0;
            r1=redforce;
        }
        //cout << i+1 << ": " << g1 << " " << r1 << " " << redforce << "\n";
        G+=g1; G%=mod;
        R+=r1; R%=mod;
    }
 
    //cout << g1 << " " << r1 << " " << c << "\n";
    //cout << G << " " << R << "\n";
 
    matrix m1={g1, r1, 0, 0};
    matrix m2={G, R, ((n*n)-G)%mod, ((n*n)-R)%mod};
    //cout << m2.a << " " << m2.b << "\n" << m2.c << " " << m2.d << "\n";
    matrix p=power(m2, d-1);
    //cout << p.a << " " << p.b << "\n" << p.c << " " << p.d << "\n";
    vector<int> v=mul(p, {c, n-c});
    //cout << v[0] << " " << v[1] << "\n";
    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 4 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 316 KB Output is correct
3 Correct 0 ms 316 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 324 KB Output is correct
2 Correct 1 ms 316 KB Output is correct
3 Correct 1 ms 320 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 324 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 324 KB Output is correct
2 Correct 1 ms 316 KB Output is correct
3 Correct 1 ms 320 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 324 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 14 ms 704 KB Output is correct
8 Correct 42 ms 852 KB Output is correct
9 Correct 24 ms 596 KB Output is correct
10 Correct 2 ms 596 KB Output is correct
11 Correct 21 ms 664 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 324 KB Output is correct
2 Correct 1 ms 316 KB Output is correct
3 Correct 1 ms 320 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 324 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 14 ms 704 KB Output is correct
8 Correct 42 ms 852 KB Output is correct
9 Correct 24 ms 596 KB Output is correct
10 Correct 2 ms 596 KB Output is correct
11 Correct 21 ms 664 KB Output is correct
12 Execution timed out 1079 ms 46808 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 324 KB Output is correct
2 Correct 1 ms 316 KB Output is correct
3 Correct 1 ms 320 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 324 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 14 ms 704 KB Output is correct
8 Correct 42 ms 852 KB Output is correct
9 Correct 24 ms 596 KB Output is correct
10 Correct 2 ms 596 KB Output is correct
11 Correct 21 ms 664 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 4 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 1 ms 316 KB Output is correct
19 Correct 1 ms 340 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 13 ms 724 KB Output is correct
22 Correct 40 ms 860 KB Output is correct
23 Correct 28 ms 636 KB Output is correct
24 Correct 4 ms 596 KB Output is correct
25 Correct 34 ms 660 KB Output is correct
26 Correct 5 ms 724 KB Output is correct
27 Correct 33 ms 872 KB Output is correct
28 Correct 13 ms 572 KB Output is correct
29 Correct 2 ms 596 KB Output is correct
30 Correct 18 ms 644 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 324 KB Output is correct
2 Correct 1 ms 316 KB Output is correct
3 Correct 1 ms 320 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 324 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 14 ms 704 KB Output is correct
8 Correct 42 ms 852 KB Output is correct
9 Correct 24 ms 596 KB Output is correct
10 Correct 2 ms 596 KB Output is correct
11 Correct 21 ms 664 KB Output is correct
12 Execution timed out 1079 ms 46808 KB Time limit exceeded
13 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 4 ms 596 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 316 KB Output is correct
5 Correct 0 ms 316 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 324 KB Output is correct
9 Correct 1 ms 316 KB Output is correct
10 Correct 1 ms 320 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 1 ms 324 KB Output is correct
13 Correct 1 ms 340 KB Output is correct
14 Correct 14 ms 704 KB Output is correct
15 Correct 42 ms 852 KB Output is correct
16 Correct 24 ms 596 KB Output is correct
17 Correct 2 ms 596 KB Output is correct
18 Correct 21 ms 664 KB Output is correct
19 Execution timed out 1079 ms 46808 KB Time limit exceeded
20 Halted 0 ms 0 KB -