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Submission #600884

# Submission time Handle Problem Language Result Execution time Memory
600884 2022-07-21T08:47:28 Z jasmin Star Trek (CEOI20_startrek) C++14
50 / 100
 1000 ms 16068 KB 
#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;
        }
        //cout << i+1 << ": " << g1 << " " << r1 << " " << redforce << "\n";
        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)%mod, ((n*n)-R)%mod};
    //cout << m2.a << " " << m2.b << "\n" << m2.c << " " << m2.d << "\n";
    matrix p=power(m2, d-1);
    //cout << p.a << " " << p.b << "\n" << p.c << " " << p.d << "\n";
    vector<int> v=mul(p, {c, n-c});
    //cout << v[0] << " " << v[1] << "\n";
    vector<int> ans=mul(m1, v);
    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 Correct 13 ms 408 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 320 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 320 KB Output is correct
5 Correct 1 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 328 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 340 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 1 ms 212 KB Output is correct
2 Correct 1 ms 328 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 20 ms 340 KB Output is correct
8 Correct 27 ms 488 KB Output is correct
9 Correct 14 ms 340 KB Output is correct
10 Correct 14 ms 404 KB Output is correct
11 Correct 20 ms 340 KB Output is correct

Subtask #5
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 328 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 20 ms 340 KB Output is correct
8 Correct 27 ms 488 KB Output is correct
9 Correct 14 ms 340 KB Output is correct
10 Correct 14 ms 404 KB Output is correct
11 Correct 20 ms 340 KB Output is correct
12 Execution timed out 1075 ms 16068 KB Time limit exceeded
13 Halted 0 ms 0 KB -

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 328 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 20 ms 340 KB Output is correct
8 Correct 27 ms 488 KB Output is correct
9 Correct 14 ms 340 KB Output is correct
10 Correct 14 ms 404 KB Output is correct
11 Correct 20 ms 340 KB Output is correct
12 Correct 1 ms 212 KB Output is correct
13 Correct 14 ms 384 KB Output is correct
14 Correct 0 ms 324 KB Output is correct
15 Correct 0 ms 320 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 212 KB Output is correct
18 Correct 1 ms 212 KB Output is correct
19 Correct 1 ms 320 KB Output is correct
20 Correct 1 ms 212 KB Output is correct
21 Correct 19 ms 340 KB Output is correct
22 Correct 24 ms 468 KB Output is correct
23 Correct 12 ms 412 KB Output is correct
24 Correct 13 ms 400 KB Output is correct
25 Correct 18 ms 340 KB Output is correct
26 Correct 15 ms 424 KB Output is correct
27 Correct 25 ms 448 KB Output is correct
28 Correct 8 ms 324 KB Output is correct
29 Correct 14 ms 340 KB Output is correct
30 Correct 17 ms 316 KB Output is correct

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 328 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 20 ms 340 KB Output is correct
8 Correct 27 ms 488 KB Output is correct
9 Correct 14 ms 340 KB Output is correct
10 Correct 14 ms 404 KB Output is correct
11 Correct 20 ms 340 KB Output is correct
12 Execution timed out 1075 ms 16068 KB Time limit exceeded
13 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 Correct 13 ms 408 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 320 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 0 ms 320 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 1 ms 328 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 1 ms 212 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 212 KB Output is correct
14 Correct 20 ms 340 KB Output is correct
15 Correct 27 ms 488 KB Output is correct
16 Correct 14 ms 340 KB Output is correct
17 Correct 14 ms 404 KB Output is correct
18 Correct 20 ms 340 KB Output is correct
19 Execution timed out 1075 ms 16068 KB Time limit exceeded
20 Halted 0 ms 0 KB -