oj.uz

Submission #601241

# Submission time Handle Problem Language Result Execution time Memory
601241 2022-07-21T13:47:31 Z Petr Star Trek (CEOI20_startrek) C++17
100 / 100
 200 ms 53304 KB 
#include<bits/stdc++.h>
//#include<iostream>
//#include<vector>
using namespace std;
#define int long long

const int mod=1e9+7;

struct modint {
  int val;

  modint() : val(0) {}

  modint(int val_) : val(val_ % mod) {
    if (val < 0) val += mod;
  }
}; 

modint operator+(modint a, modint b) {
  return a.val + b.val;
}

modint operator-(modint a, modint b) {
  return a.val - b.val;
}

modint operator*(modint a, modint b) {
  return a.val * b.val;
}

using vect = array<modint, 2>;
using matrix = array<vect, 2>;

matrix unit() {
  // Note that " = {};" is important to zero-initialize std::array.
  matrix res = {};
  for (int i = 0; i < res.size(); ++i) res[i][i] = 1;
  return res;
}

vect mul(matrix a, vect b) {
  vect res = {};
  for (int i = 0; i < res.size(); ++i) {
    for (int j = 0; j < res.size(); ++j) {
      res[i] = res[i] + a[i][j] * b[j];
    }
  }
  return res;
}

matrix multiply(matrix a, matrix b) {
  matrix res = {};
  for (int i = 0; i < res.size(); ++i) {
    for (int j = 0; j < res.size(); ++j) {
      for (int k = 0; k < res.size(); ++k) {
        res[i][j] = res[i][j] + a[i][k] * b[k][j];
      }
    }
  }
  return res;
}

matrix power(matrix a, int e){
    if(e==0){
        return unit();
    }
 
    matrix res=power(a, e/2);
    res=multiply(res, res);
    if(e%2==1){
        res=multiply(res, a);
    }
    return res;
}
 
 
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){
        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){
            auto u = vertex_status[v];
            redf[v][u]=dfs_redforce(u, v, adi, red_neighbors, vertex_status, redf, summe);
            summe[v]+=redf[v][u];
            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 = {};
    m1[0][0] = g1;
    m1[0][1] = r1;
    m1[1][0] = n - g1; // This value is not important since we only print ans[0], but in case we also wanted ans[1] this would be correct.
    m1[1][1] = n - r1; // This value is not important since we only print ans[0], but in case we also wanted ans[1] this would be correct.
    matrix m2 = {};
    m2[0][0] = G;
    m2[0][1] = R;
    m2[1][0] = n * n - G;
    m2[1][1] = n * n - R;
    matrix p=power(m2, d-1);
    vect v=mul(p, {c, n-c});
    vect ans=mul(m1, v);
    cout << ans[0].val << "\n";
}

Compilation message

startrek.cpp: In function 'matrix unit()':
startrek.cpp:37:21: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::array<std::array<modint, 2>, 2>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   37 |   for (int i = 0; i < res.size(); ++i) res[i][i] = 1;
      |                   ~~^~~~~~~~~~~~
startrek.cpp: In function 'vect mul(matrix, vect)':
startrek.cpp:43:21: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::array<modint, 2>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   43 |   for (int i = 0; i < res.size(); ++i) {
      |                   ~~^~~~~~~~~~~~
startrek.cpp:44:23: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::array<modint, 2>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   44 |     for (int j = 0; j < res.size(); ++j) {
      |                     ~~^~~~~~~~~~~~
startrek.cpp: In function 'matrix multiply(matrix, matrix)':
startrek.cpp:53:21: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::array<std::array<modint, 2>, 2>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   53 |   for (int i = 0; i < res.size(); ++i) {
      |                   ~~^~~~~~~~~~~~
startrek.cpp:54:23: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::array<std::array<modint, 2>, 2>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   54 |     for (int j = 0; j < res.size(); ++j) {
      |                     ~~^~~~~~~~~~~~
startrek.cpp:55:25: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::array<std::array<modint, 2>, 2>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   55 |       for (int k = 0; k < res.size(); ++k) {
      |                       ~~^~~~~~~~~~~~

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 1 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 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 1 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 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 1 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 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 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 176 ms 46924 KB Output is correct
13 Correct 163 ms 53304 KB Output is correct
14 Correct 152 ms 35708 KB Output is correct
15 Correct 175 ms 36456 KB Output is correct
16 Correct 167 ms 35352 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 1 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 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 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 2 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 668 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 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 1 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 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 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 176 ms 46924 KB Output is correct
13 Correct 163 ms 53304 KB Output is correct
14 Correct 152 ms 35708 KB Output is correct
15 Correct 175 ms 36456 KB Output is correct
16 Correct 167 ms 35352 KB Output is correct
17 Correct 1 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 2 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 668 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 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 175 ms 46952 KB Output is correct
37 Correct 160 ms 53240 KB Output is correct
38 Correct 156 ms 35744 KB Output is correct
39 Correct 173 ms 36448 KB Output is correct
40 Correct 156 ms 35272 KB Output is correct
41 Correct 164 ms 43688 KB Output is correct
42 Correct 167 ms 46508 KB Output is correct
43 Correct 122 ms 31716 KB Output is correct
44 Correct 163 ms 36180 KB Output is correct
45 Correct 184 ms 35104 KB Output is correct

Subtask #8
15.0 / 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 1 ms 212 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 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 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 176 ms 46924 KB Output is correct
20 Correct 163 ms 53304 KB Output is correct
21 Correct 152 ms 35708 KB Output is correct
22 Correct 175 ms 36456 KB Output is correct
23 Correct 167 ms 35352 KB Output is correct
24 Correct 1 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 2 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 668 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 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 175 ms 46952 KB Output is correct
44 Correct 160 ms 53240 KB Output is correct
45 Correct 156 ms 35744 KB Output is correct
46 Correct 173 ms 36448 KB Output is correct
47 Correct 156 ms 35272 KB Output is correct
48 Correct 164 ms 43688 KB Output is correct
49 Correct 167 ms 46508 KB Output is correct
50 Correct 122 ms 31716 KB Output is correct
51 Correct 163 ms 36180 KB Output is correct
52 Correct 184 ms 35104 KB Output is correct
53 Correct 168 ms 49284 KB Output is correct
54 Correct 165 ms 47336 KB Output is correct
55 Correct 109 ms 28420 KB Output is correct
56 Correct 170 ms 42148 KB Output is correct
57 Correct 152 ms 35776 KB Output is correct
58 Correct 150 ms 35576 KB Output is correct
59 Correct 200 ms 36472 KB Output is correct
60 Correct 164 ms 35104 KB Output is correct