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Submission #601062

# Submission time Handle Problem Language Result Execution time Memory
601062 2022-07-21T10:49:32 Z jasmin Star Trek (CEOI20_startrek) C++14
85 / 100
 231 ms 56448 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;
        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";
}

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 1 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 1 ms 340 KB Output is correct
4 Correct 0 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 1 ms 340 KB Output is correct
4 Correct 0 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 596 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 1 ms 340 KB Output is correct
4 Correct 0 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 596 KB Output is correct
12 Correct 209 ms 49120 KB Output is correct
13 Correct 198 ms 56448 KB Output is correct
14 Correct 183 ms 37400 KB Output is correct
15 Correct 173 ms 36520 KB Output is correct
16 Correct 186 ms 36640 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 1 ms 340 KB Output is correct
4 Correct 0 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 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 1 ms 212 KB Output is correct
16 Correct 0 ms 340 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 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 1 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
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 1 ms 340 KB Output is correct
4 Correct 0 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 596 KB Output is correct
12 Correct 209 ms 49120 KB Output is correct
13 Correct 198 ms 56448 KB Output is correct
14 Correct 183 ms 37400 KB Output is correct
15 Correct 173 ms 36520 KB Output is correct
16 Correct 186 ms 36640 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 1 ms 212 KB Output is correct
21 Correct 0 ms 340 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 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 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
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 222 ms 49056 KB Output is correct
37 Correct 202 ms 56380 KB Output is correct
38 Correct 169 ms 37388 KB Output is correct
39 Correct 173 ms 36600 KB Output is correct
40 Correct 180 ms 36584 KB Output is correct
41 Correct 199 ms 45320 KB Output is correct
42 Correct 153 ms 48976 KB Output is correct
43 Correct 138 ms 33104 KB Output is correct
44 Correct 231 ms 36492 KB Output is correct
45 Correct 199 ms 37772 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 0 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 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 1 ms 340 KB Output is correct
11 Correct 0 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 596 KB Output is correct
19 Correct 209 ms 49120 KB Output is correct
20 Correct 198 ms 56448 KB Output is correct
21 Correct 183 ms 37400 KB Output is correct
22 Correct 173 ms 36520 KB Output is correct
23 Correct 186 ms 36640 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 1 ms 212 KB Output is correct
28 Correct 0 ms 340 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 1 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 1 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 222 ms 49056 KB Output is correct
44 Correct 202 ms 56380 KB Output is correct
45 Correct 169 ms 37388 KB Output is correct
46 Correct 173 ms 36600 KB Output is correct
47 Correct 180 ms 36584 KB Output is correct
48 Correct 199 ms 45320 KB Output is correct
49 Correct 153 ms 48976 KB Output is correct
50 Correct 138 ms 33104 KB Output is correct
51 Correct 231 ms 36492 KB Output is correct
52 Correct 199 ms 37772 KB Output is correct
53 Incorrect 180 ms 52808 KB Output isn't correct
54 Halted 0 ms 0 KB -