Submission #600799

#	Time	Username	Problem	Language	Result	Execution time	Memory
600799		jasmin	Star Trek (CEOI20_startrek)	C++14	30 / 100	1087 ms	16208 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>& cnt_red_children, vector<int>& redchild){
    for(auto u: adi[v]){
        if(u==p) continue;
 
        if(!dfs_win(u, v, adi, cnt_red_children, redchild)){
            redchild[v]=u;
            cnt_red_children[v]++;
        }
    }
    return cnt_red_children[v]>0;
}
 
int dfs_redforce(int v, int p, vector<vector<int> >& adi, vector<int>& cnt_red_children, vector<int>& redchild){
    int redforce=0;
 
    if(cnt_red_children[v]==0){ //red
        redforce++;
        for(auto u: adi[v]){
            if(u!=p) redforce+=dfs_redforce(u, v, adi, cnt_red_children, redchild);
        }
    }
    else if(cnt_red_children[v]==1){ //green with one red child
        redforce+=dfs_redforce(redchild[v], v, adi, cnt_red_children, redchild);
    }
    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;
    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, cnt_red_children, redchild);
        int redforce=dfs_redforce(i, -1, adi, cnt_red_children, redchild);
 
        if(we_win){
            c++;
            g1=n;
            r1=n-redforce;
        }
        else{
            g1=0;
            r1=redforce;
        }
        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, (n*n)-R};
    matrix p=power(m2, d-1);
    vector<int> ans=mul(m1, mul(p, {c, n-c}));
    cout << ans[0] << "\n";
}

• Subtask 1: 0 / 0
• Subtask 2: 7 / 7
• Subtask 3: 8 / 8
• Subtask 4: 15 / 15
• Subtask 5: 0 / 15
• Subtask 6: 0 / 20
• Subtask 7: 0 / 20
• Subtask 8: 0 / 15