답안 #600927

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
600927	2022-07-21T09:15:04 Z	jasmin	Star Trek (CEOI20_startrek)	C++14	50 / 100	1000 ms	23792 KB

startrek

#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){
    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) redforce+=dfs_redforce(u, v, adi, red_neighbors);
        }
    }
    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+=dfs_redforce(red_children[0], v, adi, red_neighbors);
        }
    }
    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<vector<int>> red_neighbors(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);
 
        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

#	결과	실행 시간	메모리	Grader output
1	Correct	0 ms	212 KB	Output is correct
2	Correct	3 ms	340 KB	Output is correct

Subtask #2
7.0 / 7.0

#	결과	메모리	Grader output
1	Correct	212 KB	Output is correct
2	Correct	212 KB	Output is correct
3	Correct	212 KB	Output is correct
4	Correct	212 KB	Output is correct
5	Correct	212 KB	Output is correct

Subtask #3
8.0 / 8.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	0 ms	212 KB	Output is correct
3	Correct	1 ms	340 KB	Output is correct
4	Correct	1 ms	212 KB	Output is correct
5	Correct	0 ms	212 KB	Output is correct
6	Correct	1 ms	212 KB	Output is correct

Subtask #4
15.0 / 15.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	0 ms	212 KB	Output is correct
3	Correct	1 ms	340 KB	Output is correct
4	Correct	1 ms	212 KB	Output is correct
5	Correct	0 ms	212 KB	Output is correct
6	Correct	1 ms	212 KB	Output is correct
7	Correct	9 ms	524 KB	Output is correct
8	Correct	27 ms	584 KB	Output is correct
9	Correct	10 ms	440 KB	Output is correct
10	Correct	1 ms	340 KB	Output is correct
11	Correct	13 ms	440 KB	Output is correct

Subtask #5
0 / 15.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	0 ms	212 KB	Output is correct
3	Correct	1 ms	340 KB	Output is correct
4	Correct	1 ms	212 KB	Output is correct
5	Correct	0 ms	212 KB	Output is correct
6	Correct	1 ms	212 KB	Output is correct
7	Correct	9 ms	524 KB	Output is correct
8	Correct	27 ms	584 KB	Output is correct
9	Correct	10 ms	440 KB	Output is correct
10	Correct	1 ms	340 KB	Output is correct
11	Correct	13 ms	440 KB	Output is correct
12	Execution timed out	1086 ms	23792 KB	Time limit exceeded
13	Halted	0 ms	0 KB	-

Subtask #6
20.0 / 20.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	0 ms	212 KB	Output is correct
3	Correct	1 ms	340 KB	Output is correct
4	Correct	1 ms	212 KB	Output is correct
5	Correct	0 ms	212 KB	Output is correct
6	Correct	1 ms	212 KB	Output is correct
7	Correct	9 ms	524 KB	Output is correct
8	Correct	27 ms	584 KB	Output is correct
9	Correct	10 ms	440 KB	Output is correct
10	Correct	1 ms	340 KB	Output is correct
11	Correct	13 ms	440 KB	Output is correct
12	Correct	0 ms	212 KB	Output is correct
13	Correct	3 ms	340 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	212 KB	Output is correct
17	Correct	0 ms	340 KB	Output is correct
18	Correct	1 ms	212 KB	Output is correct
19	Correct	0 ms	212 KB	Output is correct
20	Correct	0 ms	212 KB	Output is correct
21	Correct	11 ms	520 KB	Output is correct
22	Correct	24 ms	468 KB	Output is correct
23	Correct	11 ms	340 KB	Output is correct
24	Correct	2 ms	340 KB	Output is correct
25	Correct	14 ms	340 KB	Output is correct
26	Correct	4 ms	484 KB	Output is correct
27	Correct	28 ms	572 KB	Output is correct
28	Correct	7 ms	340 KB	Output is correct
29	Correct	2 ms	340 KB	Output is correct
30	Correct	11 ms	340 KB	Output is correct

Subtask #7
0 / 20.0

#	결과	실행 시간	메모리	Grader output
1	Correct	1 ms	212 KB	Output is correct
2	Correct	0 ms	212 KB	Output is correct
3	Correct	1 ms	340 KB	Output is correct
4	Correct	1 ms	212 KB	Output is correct
5	Correct	0 ms	212 KB	Output is correct
6	Correct	1 ms	212 KB	Output is correct
7	Correct	9 ms	524 KB	Output is correct
8	Correct	27 ms	584 KB	Output is correct
9	Correct	10 ms	440 KB	Output is correct
10	Correct	1 ms	340 KB	Output is correct
11	Correct	13 ms	440 KB	Output is correct
12	Execution timed out	1086 ms	23792 KB	Time limit exceeded
13	Halted	0 ms	0 KB	-

Subtask #8
0 / 15.0

#	결과	실행 시간	메모리	Grader output
1	Correct	0 ms	212 KB	Output is correct
2	Correct	3 ms	340 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	0 ms	212 KB	Output is correct
10	Correct	1 ms	340 KB	Output is correct
11	Correct	1 ms	212 KB	Output is correct
12	Correct	0 ms	212 KB	Output is correct
13	Correct	1 ms	212 KB	Output is correct
14	Correct	9 ms	524 KB	Output is correct
15	Correct	27 ms	584 KB	Output is correct
16	Correct	10 ms	440 KB	Output is correct
17	Correct	1 ms	340 KB	Output is correct
18	Correct	13 ms	440 KB	Output is correct
19	Execution timed out	1086 ms	23792 KB	Time limit exceeded
20	Halted	0 ms	0 KB	-

답안 #600927

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