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Submission #600437

# Submission time Handle Problem Language Result Execution time Memory
600437 2022-07-20T21:01:01 Z jasmin Star Trek (CEOI20_startrek) C++14
7 / 100
 31 ms 400 KB 
#include<bits/stdc++.h>
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;
}

vector<int> cnt_red_children;
vector<int> redchild;
bool dfs_win(int v, int p, vector<vector<int> >& adi){
    for(auto u: adi[v]){
        if(u==p) continue;

        if(!dfs_win(u, v, adi)){
            redchild[v]=u;
            cnt_red_children[v]++;
        }
    }
    return cnt_red_children[v]>0;
}

bool go_up(int v, int child, vector<int>& p, vector<int>& redf){
    if(v==-1 || redf[v]) return true;

    bool parent=go_up(p[v], v, p, redf);
    redf[v]=(cnt_red_children[v]==0 && parent);

    if(cnt_red_children[v]>1) return false;
    if(cnt_red_children[v]==1 && child!=redchild[v]) return false;
    return parent;
}

int redforce=0;
void dfs_redforce(int v, vector<int>& p, vector<int>& redf, vector<vector<int> >& adi){

    if(cnt_red_children[v]==0 && go_up(v, redchild[v], p, redf)){
        redforce++;
    }

    for(auto u: adi[v]){
        if(u!=p[v]){
            p[u]=v;
            dfs_redforce(u, p, redf, adi);
        }
    }
}

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--){
        redforce=0;
        redchild.assign(n, -1);
        cnt_red_children.assign(n, 0);

        bool we_win=dfs_win(i, -1, adi);
        vector<int> p(n, -1);
        vector<int> change(n, -1);
        change[i]=true;
        dfs_redforce(i, p, change, adi);

        if(we_win){
            c++;
            g1=n;
            r1=n-redforce;
        }
        else{
            g1=0;
            r1=redforce;
        }
        G+=g1;
        R+=r1;
    }

    //cout << "redforce: " << redforce << "\n";
    //cout << g1 << " " << r1 << " " << c << "\n";

    matrix m1={g1, r1, 0, 0};
    matrix m2={G, R, n*n-G, n*n-R};
    //matrix m2={G, n*n-G, R, 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 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Incorrect 31 ms 400 KB Output isn't correct
3 Halted 0 ms 0 KB -

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 316 KB Output is correct
5 Correct 1 ms 212 KB Output is correct

Subtask #3
0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 320 KB Output is correct
2 Incorrect 1 ms 212 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #4
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 320 KB Output is correct
2 Incorrect 1 ms 212 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 320 KB Output is correct
2 Incorrect 1 ms 212 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 320 KB Output is correct
2 Incorrect 1 ms 212 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 320 KB Output is correct
2 Incorrect 1 ms 212 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Incorrect 31 ms 400 KB Output isn't correct
3 Halted 0 ms 0 KB -