oj.uz

Submission #601251

# Submission time Handle Problem Language Result Execution time Memory
601251 2022-07-21T14:05:42 Z Petr Star Trek (CEOI20_startrek) C++17
100 / 100
 155 ms 30708 KB 
#include<bits/stdc++.h>
//#include<iostream>
//#include<vector>
using namespace std;
#define int long long

const int mod=1e9+7;

// Using a modint type instead of inserting "% mod" in appropriate
// places makes it easier to avoid both negative numbers and overflows.
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;
}

// Fixed-size arrays are nicer than vectors in that you don't
// need to resize(), and they also work much faster, so if we can
// use them, it's typically a good idea.
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 peid, const vector<vector<int> >& adi, const vector<int>& dest, vector<int>& vertex_status, vector<vector<int>>& red_neighbors){
    if (vertex_status[v] == -2) {
      vertex_status[v] = peid;
      for(auto eid: adi[v]){
          if (eid == peid) continue;
          auto u = dest[eid];
          if(!dfs_win(u, eid ^ 1, adi, dest, vertex_status, red_neighbors)){
              red_neighbors[v].push_back(eid);
          }
      }
    } else {
      if (vertex_status[v] >= 0 && vertex_status[v] != peid) {
        auto eid = vertex_status[v];
        auto u = dest[eid];
        if(!dfs_win(u, eid ^ 1, adi, dest, vertex_status, red_neighbors)){
            red_neighbors[v].push_back(eid);
        }
        vertex_status[v] = -1;
      }
    }
 
    if (vertex_status[v] == peid) {
      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] != peid;
    }
}
 
int dfs_redforce(int v, int peid, const vector<vector<int> >& adi, const vector<int>& dest, const vector<vector<int>>& red_neighbors, vector<int>& vertex_status, vector<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] != peid;
 
    if(vertex_status[v]==-2){
        for(auto eid: adi[v]){
            if(eid==peid) {
              continue;
            }
            auto u = dest[eid];
            redf[eid]=dfs_redforce(u, eid ^ 1, adi, dest, red_neighbors, vertex_status, redf, summe);
            summe[v]+=redf[eid];
        }
 
        vertex_status[v]=peid;
    }
    else{
        if(vertex_status[v]>=0 && vertex_status[v]!=peid){
            auto eid = vertex_status[v];
            auto u = dest[eid];
            redf[eid]=dfs_redforce(u, eid ^ 1, adi, dest, red_neighbors, vertex_status, redf, summe);
            summe[v]+=redf[eid];
            vertex_status[v]=-1;
        }
    }
 
    int redforce = 0;
    if(!is_green){ //red
        redforce++;
        redforce+=summe[v];
        if (vertex_status[v] == -1 && peid != -1) {
          redforce-=redf[peid];
        }
    }
    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]==peid) u=red_neighbors[v][1];
            else if(red_neighbors[v][1]!=peid) needed=false;
        }
        if (needed) {
            redforce+=redf[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;
    // Now we store edge numbers here, and the target of the edge in "dest" array.
    // This allows us to avoid unordered_map. We also maintain the property
    // that the reverse to the edge x is the edge x^1.
    vector<vector<int> > adi(n);
    vector<int> dest(2 * (n - 1));
    for(int i=0; i<n-1; i++){
        int a,b;
        cin >> a >> b;
        adi[a-1].push_back(2 * i);
        dest[2 * i] = b - 1;
        adi[b-1].push_back(2 * i + 1);
        dest[2 * i + 1] = 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<int> redf(2 * (n - 1), 0);
    vector<int> summe(n, 0);
    for(int i=n-1; i>=0; i--){
 
        bool we_win=dfs_win(i, -1, adi, dest, vertex_status, red_neighbors);
        int redforce=dfs_redforce(i, -1, adi, dest, 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:42:21: 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]
   42 |   for (int i = 0; i < res.size(); ++i) res[i][i] = 1;
      |                   ~~^~~~~~~~~~~~
startrek.cpp: In function 'vect mul(matrix, vect)':
startrek.cpp:48:21: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::array<modint, 2>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   48 |   for (int i = 0; i < res.size(); ++i) {
      |                   ~~^~~~~~~~~~~~
startrek.cpp:49:23: warning: comparison of integer expressions of different signedness: 'long long int' and 'std::array<modint, 2>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   49 |     for (int j = 0; j < res.size(); ++j) {
      |                     ~~^~~~~~~~~~~~
startrek.cpp: In function 'matrix multiply(matrix, matrix)':
startrek.cpp:58:21: 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]
   58 |   for (int i = 0; i < res.size(); ++i) {
      |                   ~~^~~~~~~~~~~~
startrek.cpp:59:23: 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]
   59 |     for (int j = 0; j < res.size(); ++j) {
      |                     ~~^~~~~~~~~~~~
startrek.cpp:60:25: 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]
   60 |       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 468 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 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 0 ms 212 KB Output is correct
2 Correct 0 ms 340 KB Output is correct
3 Correct 0 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

# 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 0 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 1 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 468 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 0 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 1 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 155 ms 25420 KB Output is correct
13 Correct 126 ms 30700 KB Output is correct
14 Correct 94 ms 15552 KB Output is correct
15 Correct 138 ms 16784 KB Output is correct
16 Correct 106 ms 15824 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 0 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 1 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 2 ms 468 KB Output is correct
14 Correct 0 ms 212 KB Output is correct
15 Correct 0 ms 212 KB Output is correct
16 Correct 0 ms 212 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 1 ms 232 KB Output is correct
20 Correct 0 ms 212 KB Output is correct
21 Correct 1 ms 468 KB Output is correct
22 Correct 1 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 1 ms 468 KB Output is correct
25 Correct 1 ms 468 KB Output is correct
26 Correct 1 ms 468 KB Output is correct
27 Correct 1 ms 496 KB Output is correct
28 Correct 1 ms 340 KB Output is correct
29 Correct 1 ms 468 KB Output is correct
30 Correct 1 ms 468 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 0 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 1 ms 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 155 ms 25420 KB Output is correct
13 Correct 126 ms 30700 KB Output is correct
14 Correct 94 ms 15552 KB Output is correct
15 Correct 138 ms 16784 KB Output is correct
16 Correct 106 ms 15824 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 2 ms 468 KB Output is correct
19 Correct 0 ms 212 KB Output is correct
20 Correct 0 ms 212 KB Output is correct
21 Correct 0 ms 212 KB Output is correct
22 Correct 1 ms 340 KB Output is correct
23 Correct 1 ms 212 KB Output is correct
24 Correct 1 ms 232 KB Output is correct
25 Correct 0 ms 212 KB Output is correct
26 Correct 1 ms 468 KB Output is correct
27 Correct 1 ms 468 KB Output is correct
28 Correct 1 ms 468 KB Output is correct
29 Correct 1 ms 468 KB Output is correct
30 Correct 1 ms 468 KB Output is correct
31 Correct 1 ms 468 KB Output is correct
32 Correct 1 ms 496 KB Output is correct
33 Correct 1 ms 340 KB Output is correct
34 Correct 1 ms 468 KB Output is correct
35 Correct 1 ms 468 KB Output is correct
36 Correct 127 ms 25364 KB Output is correct
37 Correct 121 ms 30708 KB Output is correct
38 Correct 81 ms 15580 KB Output is correct
39 Correct 139 ms 16844 KB Output is correct
40 Correct 124 ms 15788 KB Output is correct
41 Correct 108 ms 22780 KB Output is correct
42 Correct 107 ms 26240 KB Output is correct
43 Correct 65 ms 13724 KB Output is correct
44 Correct 150 ms 16568 KB Output is correct
45 Correct 101 ms 15560 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 468 KB Output is correct
3 Correct 1 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 0 ms 212 KB Output is correct
9 Correct 0 ms 340 KB Output is correct
10 Correct 0 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 1 ms 468 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 1 ms 468 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 155 ms 25420 KB Output is correct
20 Correct 126 ms 30700 KB Output is correct
21 Correct 94 ms 15552 KB Output is correct
22 Correct 138 ms 16784 KB Output is correct
23 Correct 106 ms 15824 KB Output is correct
24 Correct 1 ms 212 KB Output is correct
25 Correct 2 ms 468 KB Output is correct
26 Correct 0 ms 212 KB Output is correct
27 Correct 0 ms 212 KB Output is correct
28 Correct 0 ms 212 KB Output is correct
29 Correct 1 ms 340 KB Output is correct
30 Correct 1 ms 212 KB Output is correct
31 Correct 1 ms 232 KB Output is correct
32 Correct 0 ms 212 KB Output is correct
33 Correct 1 ms 468 KB Output is correct
34 Correct 1 ms 468 KB Output is correct
35 Correct 1 ms 468 KB Output is correct
36 Correct 1 ms 468 KB Output is correct
37 Correct 1 ms 468 KB Output is correct
38 Correct 1 ms 468 KB Output is correct
39 Correct 1 ms 496 KB Output is correct
40 Correct 1 ms 340 KB Output is correct
41 Correct 1 ms 468 KB Output is correct
42 Correct 1 ms 468 KB Output is correct
43 Correct 127 ms 25364 KB Output is correct
44 Correct 121 ms 30708 KB Output is correct
45 Correct 81 ms 15580 KB Output is correct
46 Correct 139 ms 16844 KB Output is correct
47 Correct 124 ms 15788 KB Output is correct
48 Correct 108 ms 22780 KB Output is correct
49 Correct 107 ms 26240 KB Output is correct
50 Correct 65 ms 13724 KB Output is correct
51 Correct 150 ms 16568 KB Output is correct
52 Correct 101 ms 15560 KB Output is correct
53 Correct 115 ms 27352 KB Output is correct
54 Correct 116 ms 25820 KB Output is correct
55 Correct 57 ms 12460 KB Output is correct
56 Correct 115 ms 21356 KB Output is correct
57 Correct 106 ms 16192 KB Output is correct
58 Correct 120 ms 15988 KB Output is correct
59 Correct 105 ms 16928 KB Output is correct
60 Correct 106 ms 15468 KB Output is correct