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답안 #556297

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
556297 2022-05-02T19:25:05 Z FatihSolak Star Trek (CEOI20_startrek) C++17
100 / 100
 131 ms 41624 KB 
#include <bits/stdc++.h>
#define N 100005
using namespace std;
const int mod = 1e9 + 7;
long long binpow(long long a,long long b){
    long long ret = 1;
    while(b){
        if(b & 1)
            ret = ret * a %mod;
        a = a * a %mod;
        b >>=1;
    }
    return ret;
}
struct node{
    long long a,b,sz,sz2;
    node(){
        a = b = sz = sz2 = 0;
    }
};
struct matrix{
    long long a[3][3];
    matrix(){
        for(int i = 0;i<3;i++){
            for(int j = 0;j<3;j++){
                a[i][j] = 0;
            }
        }
    }
    matrix operator*(matrix other){
        matrix ret;
        for(int i = 0;i<3;i++){
            for(int j =0;j<3;j++){
                for(int k = 0;k<3;k++){
                    ret.a[i][k] = (ret.a[i][k] + a[i][j]*other.a[j][k])%mod;
                }
            }
        }
        return ret;
    }
};
matrix binexpo(matrix a,long long b){
    matrix ret;
    for(int i = 0;i<3;i++)
        ret.a[i][i] = 1;
    while(b){
        if(b&1)
            ret = ret * a;
        a = a * a;
        b>>=1;
    }
    return ret;
}
vector<int> adj[N];
long long ans = 0;
long long n,d;
int win[N];
int sub[N];
int top[N];
int len[N];
int sum = 0;
int timer = 1;
int tin[N],tout[N];
bool dfs(int v,int par){
    tin[v] = timer++;
    sub[v] = 0;
    for(auto u:adj[v]){
        if(u == par)continue;
        if(dfs(u,v) == 0){
            win[v] = 1;
            sub[v] = 1;
        }
    }
    tout[v] = timer - 1;
    len[v] = tout[v] - tin[v] + 1;
    return sub[v];
}
void dfs2(int v,int par){
    int cnt = !top[v];
    for(auto u:adj[v]){
        if(u == par)continue;
        cnt += !sub[u];
    }
    for(auto u:adj[v]){
        if(u == par)continue;
        cnt -= !sub[u];
        if(!cnt){
            win[u] = 1;
            top[u] = 0;
        }
        cnt += !sub[u];
        dfs2(u,v);
    }
}
node subval[N];
node val[N];
node topval[N];
void merge(node &a,node b){
    a.a += b.b;
    a.b += b.a;
    a.sz += b.sz2;
    a.sz2 += b.sz;
    a.sz %= mod;
    a.sz2 %= mod;
}
void antimerge(node &a,node b){
    a.a -= b.b;
    a.b -= b.a;
    a.sz -= b.sz2;
    a.sz2 -= b.sz;
    a.sz = (a.sz + mod)%mod;
    a.sz2 = (a.sz2 + mod)%mod;
}
void dfs3(int v,int par){
    vector<int> places;
    subval[v] = node();
    for(auto u:adj[v]){
        if(u == par)continue;
        if(!sub[u]){
            places.push_back(u);
        }
        dfs3(u,v);
    }
    if(places.empty()){
        subval[v].b++;
        for(auto u:adj[v]){
            if(u == par)continue;
            merge(subval[v],subval[u]);
        }
    }
    if(places.size() == 1){        
        subval[v].sz += n * (len[v] - len[places[0]]);
        subval[v].sz %= mod;
        merge(subval[v],subval[places[0]]);
    }
    if(places.size() > 1){
        subval[v].sz += n * len[v];
        subval[v].sz %= mod;
    }
}
void dfs4(int v,int par){
    vector<int> places;
    if(!top[v])
        places.push_back(par);
    val[v] = node();
    for(auto u:adj[v]){
        if(u == par)continue;
        if(!sub[u]){
            places.push_back(u);
        }
    }
    if(places.empty()){
        val[v].b++;
        merge(val[v],topval[v]);
        for(auto u:adj[v]){
            if(u == par)continue;
            merge(val[v],subval[u]);
        }
    }
    if(places.size() == 1){        
        if(places[0] == par){
            val[v].sz += n * len[v];
            val[v].sz %= mod;
            merge(val[v],topval[v]);
        }
        else{
            val[v].sz += n * (n - len[places[0]]);
            val[v].sz %= mod;
            merge(val[v],subval[places[0]]);
        }
    }
    if(places.size() > 1){
        val[v].sz += n * n;
        val[v].sz %= mod;
    }
    node sum;
    merge(sum,topval[v]);
    for(auto u:adj[v]){
        if(u == par)continue;
        merge(sum,subval[u]);
    }
    for(auto u:adj[v]){
        if(u == par)continue;
        antimerge(sum,subval[u]);
        node tmp = sum;
        int x = places.size() - !sub[u];
        if(x == 0){
            tmp.b++;
        }
        if(x == 1){
            tmp = node();
            int pos = places[0];
            if(pos == u)
                pos = places[1];
            if(pos == par){
                tmp.sz += n * ( len[v] - len[u]);
                tmp.sz %= mod;
                merge(tmp,topval[v]);
            }
            else{
                tmp.sz += n * (n - len[pos] - len[u]);
                tmp.sz %= mod;
                merge(tmp,subval[pos]);
            }
        }
        if(x > 1){
            tmp = node();
            tmp.sz += n * (n - len[u]);
            tmp.sz %= mod;
        }
        topval[u] = tmp;
        merge(sum,subval[u]);
        dfs4(u,v);
    }
}
void solve(){
    cin >> n >> d;
    for(int i = 1;i<n;i++){
        int u,v;
        cin >> u >> v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
    vector<node> v;
    long long winstate = 0;
    for(int i = 1;i<=n;i++){
        win[i] = 0;
        sub[i] = 0;
        top[i] = 1;
    }
    dfs(1,0);
    dfs2(1,0);
    dfs3(1,0);
    dfs4(1,0);
    for(int x = 1;x<=n;x++){
        v.push_back(val[x]);
    }
    long long suma = 0,sumb = 0,sumsz = 0;
    for(auto u:v){
        suma += u.a;
        sumb += u.b;
        sumsz += u.sz;
        suma %= mod;
        sumb %= mod;
        sumsz %= mod;
    }
    for(int i = 1;i<=n;i++){
        winstate += win[i];
    }
    matrix single;
    single.a[0][0] = (suma - sumb +mod)%mod;
    single.a[1][0] = (sumb)%mod;
    single.a[2][0] = (sumsz)%mod;
    single.a[1][1] = n*n%mod;
    single.a[2][2] = n*n%mod;
    matrix total = binexpo(single,d-1);
    long long val = 0;
    val = (val + total.a[0][0] * winstate)%mod;
    val = (val + total.a[1][0] * n)%mod;
    val = (val + total.a[2][0] * 1)%mod;
    winstate = val;
    /*
    for(int i = 0;i<d-1;i++){
        winstate = (winstate * (suma - sumb + mod) + binpow(n,2*i+1)*sumb + binpow(n,2*i)*sumsz)%mod;
    }*/
    winstate = (winstate * (v[0].a - v[0].b + mod) + binpow(n,2*d-1)*v[0].b + binpow(n,2*d-2)*v[0].sz)%mod;
    cout << winstate;

}
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    #ifdef Local
        freopen("in.txt","r",stdin);
        freopen("out.txt","w",stdout);
    #endif
    int t = 1;
    //cin >> t;
    while(t--){
        solve();
    }
    #ifdef Local
        cout << endl << fixed << setprecision(2) << 1000.0 * clock() / CLOCKS_PER_SEC << " milliseconds.";
    #endif
}

Subtask #1
0.0 / 0.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 12076 KB Output is correct
2 Correct 6 ms 12184 KB Output is correct

Subtask #2
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 11988 KB Output is correct
2 Correct 6 ms 11988 KB Output is correct
3 Correct 6 ms 12072 KB Output is correct
4 Correct 6 ms 11988 KB Output is correct
5 Correct 6 ms 12076 KB Output is correct

Subtask #3
8.0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 11988 KB Output is correct
2 Correct 6 ms 11988 KB Output is correct
3 Correct 6 ms 12116 KB Output is correct
4 Correct 6 ms 11988 KB Output is correct
5 Correct 6 ms 11988 KB Output is correct
6 Correct 6 ms 11988 KB Output is correct

Subtask #4
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 11988 KB Output is correct
2 Correct 6 ms 11988 KB Output is correct
3 Correct 6 ms 12116 KB Output is correct
4 Correct 6 ms 11988 KB Output is correct
5 Correct 6 ms 11988 KB Output is correct
6 Correct 6 ms 11988 KB Output is correct
7 Correct 6 ms 12244 KB Output is correct
8 Correct 6 ms 12372 KB Output is correct
9 Correct 7 ms 12116 KB Output is correct
10 Correct 7 ms 12148 KB Output is correct
11 Correct 6 ms 12200 KB Output is correct

Subtask #5
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 11988 KB Output is correct
2 Correct 6 ms 11988 KB Output is correct
3 Correct 6 ms 12116 KB Output is correct
4 Correct 6 ms 11988 KB Output is correct
5 Correct 6 ms 11988 KB Output is correct
6 Correct 6 ms 11988 KB Output is correct
7 Correct 6 ms 12244 KB Output is correct
8 Correct 6 ms 12372 KB Output is correct
9 Correct 7 ms 12116 KB Output is correct
10 Correct 7 ms 12148 KB Output is correct
11 Correct 6 ms 12200 KB Output is correct
12 Correct 124 ms 31380 KB Output is correct
13 Correct 131 ms 41624 KB Output is correct
14 Correct 120 ms 22912 KB Output is correct
15 Correct 99 ms 22952 KB Output is correct
16 Correct 102 ms 22956 KB Output is correct

Subtask #6
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 11988 KB Output is correct
2 Correct 6 ms 11988 KB Output is correct
3 Correct 6 ms 12116 KB Output is correct
4 Correct 6 ms 11988 KB Output is correct
5 Correct 6 ms 11988 KB Output is correct
6 Correct 6 ms 11988 KB Output is correct
7 Correct 6 ms 12244 KB Output is correct
8 Correct 6 ms 12372 KB Output is correct
9 Correct 7 ms 12116 KB Output is correct
10 Correct 7 ms 12148 KB Output is correct
11 Correct 6 ms 12200 KB Output is correct
12 Correct 6 ms 11988 KB Output is correct
13 Correct 6 ms 12204 KB Output is correct
14 Correct 6 ms 11988 KB Output is correct
15 Correct 6 ms 12076 KB Output is correct
16 Correct 6 ms 12076 KB Output is correct
17 Correct 6 ms 12116 KB Output is correct
18 Correct 6 ms 11988 KB Output is correct
19 Correct 6 ms 11988 KB Output is correct
20 Correct 7 ms 12080 KB Output is correct
21 Correct 7 ms 12204 KB Output is correct
22 Correct 6 ms 12372 KB Output is correct
23 Correct 6 ms 12200 KB Output is correct
24 Correct 6 ms 12204 KB Output is correct
25 Correct 7 ms 12204 KB Output is correct
26 Correct 6 ms 12244 KB Output is correct
27 Correct 9 ms 12344 KB Output is correct
28 Correct 9 ms 12196 KB Output is correct
29 Correct 6 ms 12116 KB Output is correct
30 Correct 7 ms 12116 KB Output is correct

Subtask #7
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 11988 KB Output is correct
2 Correct 6 ms 11988 KB Output is correct
3 Correct 6 ms 12116 KB Output is correct
4 Correct 6 ms 11988 KB Output is correct
5 Correct 6 ms 11988 KB Output is correct
6 Correct 6 ms 11988 KB Output is correct
7 Correct 6 ms 12244 KB Output is correct
8 Correct 6 ms 12372 KB Output is correct
9 Correct 7 ms 12116 KB Output is correct
10 Correct 7 ms 12148 KB Output is correct
11 Correct 6 ms 12200 KB Output is correct
12 Correct 124 ms 31380 KB Output is correct
13 Correct 131 ms 41624 KB Output is correct
14 Correct 120 ms 22912 KB Output is correct
15 Correct 99 ms 22952 KB Output is correct
16 Correct 102 ms 22956 KB Output is correct
17 Correct 6 ms 11988 KB Output is correct
18 Correct 6 ms 12204 KB Output is correct
19 Correct 6 ms 11988 KB Output is correct
20 Correct 6 ms 12076 KB Output is correct
21 Correct 6 ms 12076 KB Output is correct
22 Correct 6 ms 12116 KB Output is correct
23 Correct 6 ms 11988 KB Output is correct
24 Correct 6 ms 11988 KB Output is correct
25 Correct 7 ms 12080 KB Output is correct
26 Correct 7 ms 12204 KB Output is correct
27 Correct 6 ms 12372 KB Output is correct
28 Correct 6 ms 12200 KB Output is correct
29 Correct 6 ms 12204 KB Output is correct
30 Correct 7 ms 12204 KB Output is correct
31 Correct 6 ms 12244 KB Output is correct
32 Correct 9 ms 12344 KB Output is correct
33 Correct 9 ms 12196 KB Output is correct
34 Correct 6 ms 12116 KB Output is correct
35 Correct 7 ms 12116 KB Output is correct
36 Correct 131 ms 31504 KB Output is correct
37 Correct 131 ms 41484 KB Output is correct
38 Correct 82 ms 22912 KB Output is correct
39 Correct 108 ms 22996 KB Output is correct
40 Correct 102 ms 22972 KB Output is correct
41 Correct 115 ms 36640 KB Output is correct
42 Correct 120 ms 39336 KB Output is correct
43 Correct 72 ms 22092 KB Output is correct
44 Correct 110 ms 22952 KB Output is correct
45 Correct 119 ms 22972 KB Output is correct

Subtask #8
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 6 ms 12076 KB Output is correct
2 Correct 6 ms 12184 KB Output is correct
3 Correct 6 ms 11988 KB Output is correct
4 Correct 6 ms 11988 KB Output is correct
5 Correct 6 ms 12072 KB Output is correct
6 Correct 6 ms 11988 KB Output is correct
7 Correct 6 ms 12076 KB Output is correct
8 Correct 6 ms 11988 KB Output is correct
9 Correct 6 ms 11988 KB Output is correct
10 Correct 6 ms 12116 KB Output is correct
11 Correct 6 ms 11988 KB Output is correct
12 Correct 6 ms 11988 KB Output is correct
13 Correct 6 ms 11988 KB Output is correct
14 Correct 6 ms 12244 KB Output is correct
15 Correct 6 ms 12372 KB Output is correct
16 Correct 7 ms 12116 KB Output is correct
17 Correct 7 ms 12148 KB Output is correct
18 Correct 6 ms 12200 KB Output is correct
19 Correct 124 ms 31380 KB Output is correct
20 Correct 131 ms 41624 KB Output is correct
21 Correct 120 ms 22912 KB Output is correct
22 Correct 99 ms 22952 KB Output is correct
23 Correct 102 ms 22956 KB Output is correct
24 Correct 6 ms 11988 KB Output is correct
25 Correct 6 ms 12204 KB Output is correct
26 Correct 6 ms 11988 KB Output is correct
27 Correct 6 ms 12076 KB Output is correct
28 Correct 6 ms 12076 KB Output is correct
29 Correct 6 ms 12116 KB Output is correct
30 Correct 6 ms 11988 KB Output is correct
31 Correct 6 ms 11988 KB Output is correct
32 Correct 7 ms 12080 KB Output is correct
33 Correct 7 ms 12204 KB Output is correct
34 Correct 6 ms 12372 KB Output is correct
35 Correct 6 ms 12200 KB Output is correct
36 Correct 6 ms 12204 KB Output is correct
37 Correct 7 ms 12204 KB Output is correct
38 Correct 6 ms 12244 KB Output is correct
39 Correct 9 ms 12344 KB Output is correct
40 Correct 9 ms 12196 KB Output is correct
41 Correct 6 ms 12116 KB Output is correct
42 Correct 7 ms 12116 KB Output is correct
43 Correct 131 ms 31504 KB Output is correct
44 Correct 131 ms 41484 KB Output is correct
45 Correct 82 ms 22912 KB Output is correct
46 Correct 108 ms 22996 KB Output is correct
47 Correct 102 ms 22972 KB Output is correct
48 Correct 115 ms 36640 KB Output is correct
49 Correct 120 ms 39336 KB Output is correct
50 Correct 72 ms 22092 KB Output is correct
51 Correct 110 ms 22952 KB Output is correct
52 Correct 119 ms 22972 KB Output is correct
53 Correct 126 ms 41496 KB Output is correct
54 Correct 119 ms 37680 KB Output is correct
55 Correct 68 ms 21624 KB Output is correct
56 Correct 121 ms 30660 KB Output is correct
57 Correct 97 ms 23000 KB Output is correct
58 Correct 96 ms 22972 KB Output is correct
59 Correct 100 ms 22976 KB Output is correct
60 Correct 94 ms 22976 KB Output is correct