Submission #601234

#	Time	Username	Problem	Language	Result	Execution time	Memory
601234		Petr	Star Trek (CEOI20_startrek)	C++17	100 / 100	221 ms	53368 KiB

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;
}
 
 
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={g1, r1, 0, 0};
    matrix m2={G%mod, R%mod, ((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
• Subtask 2: 7 / 7
• Subtask 3: 8 / 8
• Subtask 4: 15 / 15
• Subtask 5: 15 / 15
• Subtask 6: 20 / 20
• Subtask 7: 20 / 20
• Subtask 8: 15 / 15