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답안 #585643

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
585643 2022-06-29T07:12:03 Z 박상훈(#8384) Star Trek (CEOI20_startrek) C++17
45 / 100
 87 ms 21404 KB 
#include <bits/stdc++.h>

typedef long long ll;
using namespace std;
const int MOD = 1e9+7;
vector<int> adj[100100];
bool _win[100100], _win_pa[100100], _win_root[100100], ok[100100];
ll S[100100];

void dfs1(int s, int pa = -1){
    int wcnt = 0, lcnt = 0;
    for (auto &v:adj[s]) if (v!=pa){
        dfs1(v, s);
        if (_win[v]) wcnt++;
        else lcnt++;
    }

    if (!lcnt) _win[s] = 0;
    else _win[s] = 1;

    if (lcnt<=1) ok[s] = 1;
}

void dfs2(int s, int pa = -1){
    int wcnt = 0, lcnt = 0;
    for (auto &v:adj[s]) if (v!=pa){
        if (_win[v]) wcnt++;
        else lcnt++;
    }
    if (pa!=-1){
        if (_win_pa[s]) wcnt++;
        else lcnt++;
    }

    for (auto &v:adj[s]) if (v!=pa){
        if (_win[v]) wcnt--;
        else lcnt--;

        if (!lcnt) _win_pa[v] = 0;
        else _win_pa[v] = 1;

        if (_win[v]) wcnt++;
        else lcnt++;
    }

    if (!lcnt) _win_root[s] = 0;
    else _win_root[s] = 1;

    for (auto &v:adj[s]) if (v!=pa) dfs2(v, s);
}

int lscnt[100100], lscnt_pa[100100], lscnt_root[100100];
void dfs3(int s, int pa = -1){
    if (!_win[s]) lscnt[s]++;

    int lcnt = 0, wcnt = 0;
    for (auto &v:adj[s]) if (v!=pa){
        dfs3(v, s);
        if (!_win[v]) lcnt++;
        else wcnt++;
    }

    for (auto &v:adj[s]) if (v!=pa){
        if (lcnt==1 && !_win[v]) lscnt[s] += lscnt[v];
        else if (lcnt==0) lscnt[s] += lscnt[v];
    }
}

void dfs4(int s, int pa = -1){
    ///count
    int wcnt = 0, lcnt = 0, sum = 0;
    vector<int> L;
    for (auto &v:adj[s]) if (v!=pa){
        if (_win[v]) wcnt++;
        else lcnt++;
        sum += lscnt[v];

        if (!_win[v]) L.push_back(v);
    }
    if (pa!=-1){
        if (_win_pa[s]) wcnt++;
        else lcnt++;
        sum += lscnt_pa[s];
    }

    ///calc pa
    for (auto &v:adj[s]) if (v!=pa){
        if (_win[v]) wcnt--;
        else lcnt--;
        sum -= lscnt[v];

        if (!lcnt) lscnt_pa[v] = sum+1;
        else if (lcnt==1){
            if (pa!=-1 && !_win_pa[s]) lscnt_pa[v] = lscnt_pa[s];
            else{
                if (L[0]!=v) lscnt_pa[v] = lscnt[L[0]];
                else lscnt_pa[v] = lscnt[L[1]];
            }
        }

        if (_win[v]) wcnt++;
        else lcnt++;
        sum += lscnt[v];
    }

    ///calc root
    if (!lcnt) lscnt_root[s] = sum+1;
    else if (lcnt==1){
        if (pa!=-1 && !_win_pa[s]) lscnt_root[s] = lscnt_pa[s];
        else lscnt_root[s] = lscnt[L[0]];
    }

    for (auto &v:adj[s]) if (v!=pa) dfs4(v, s);
}

ll pw(ll a, ll e){
    if (!e) return 1;
    ll ret = pw(a, e/2);
    if (e&1) return ret*ret%MOD*a%MOD;
    return ret*ret%MOD;
}

ll INV(ll x){return pw(x, MOD-2);}

int lscnt_naive[100100];
void naive(int n){
    for (int i=1;i<=n;i++){
        fill(_win, _win+n+1, 0);
        fill(lscnt, lscnt+n+1, 0);
        dfs1(i);
        dfs3(i);
        lscnt_naive[i] = lscnt[i];
        //lscnt_root[i] = lscnt_naive[i];
        assert(lscnt_root[i]==lscnt_naive[i]);
    }
    fill(_win, _win+n+1, 0);
    fill(lscnt, lscnt+n+1, 0);
    dfs1(1);
    dfs3(1);
}

int main(){
    int n;
    ll d;
    scanf("%d %lld", &n, &d);
    //if (n==2) {printf("%lld\n", pw(4, d)); return 0;}

    for (int i=1;i<=n-1;i++){
        int x, y;
        scanf("%d %d", &x, &y);
        adj[x].push_back(y);
        adj[y].push_back(x);
    }

    dfs1(1);
    dfs2(1);
    dfs3(1);
    dfs4(1);

    if (n<=1000) naive(n);

/*
    for (int i=1;i<=n;i++) printf("%d ", _win[i]); printf("\n");
    for (int i=1;i<=n;i++) printf("%d ", _win_pa[i]); printf("\n");
    for (int i=1;i<=n;i++) printf("%d ", _win_root[i]); printf("\n");
    for (int i=1;i<=n;i++) printf("%d ", lscnt[i]); printf("\n");
    for (int i=1;i<=n;i++) printf("%d ", lscnt_pa[i]); printf("\n");
    for (int i=1;i<=n;i++) printf("%d ", lscnt_root[i]); printf("\n");
*/

    ll ans = 0, T = 0, L = 0;
    for (int i=1;i<=n;i++){
        if (_win_root[i]) T += lscnt_root[i];
        else T -= lscnt_root[i], L++;

        if (T>=MOD) T -= MOD;
        if (T<0) T += MOD;
    }
    T = T * pw(INV(n), 2) % MOD;

    ll B = 0; ///B = S[d-1];
    if (T==1){
        B = (d%MOD) * L % MOD;
    }
    else if (T==0) B = L;
    else{
        ll X = L * INV(-T+1+MOD) % MOD;
        ll S0 = (L-X+MOD)%MOD;
        B = S0 * pw(T, d-1) % MOD;
        B = (B+X)%MOD;
    }

    /*S[0] = L;
    for (int i=1;i<=d;i++){
        //S[i] = (pw(n, i*2) * L % MOD + T * S[i-1] % MOD) % MOD;
        S[i] = (T * S[i-1] % MOD + L) % MOD;
    }

    S[d-1] = S[d-1] * pw(n, (d-1)*2) % MOD;*/

    if (_win[1]) ans = (pw(n, d*2) + MOD) - (lscnt_root[1] * B % MOD);
    else ans = lscnt_root[1] * B % MOD;
    ans %= MOD;

    printf("%lld\n", ans);

    return 0;
}

/*
int lcnt = 0;
    for (int i=1;i<=n;i++) if (!_win_root[i]) lcnt++;

    ll ans = 0;
    if (_win[1]) ans = (ll)n*n - (ll)lscnt[1] * lcnt;
    else ans = (ll)lscnt[1] * lcnt;
    ans %= MOD;

    printf("%lld\n", ans);
*/

Compilation message

startrek.cpp: In function 'int main()':
startrek.cpp:145:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  145 |     scanf("%d %lld", &n, &d);
      |     ~~~~~^~~~~~~~~~~~~~~~~~~
startrek.cpp:150:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  150 |         scanf("%d %d", &x, &y);
      |         ~~~~~^~~~~~~~~~~~~~~~~

Subtask #1
0.0 / 0.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Incorrect 36 ms 2644 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #2
7.0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 1 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct

Subtask #3
8.0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 3 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct

Subtask #4
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 3 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 38 ms 2800 KB Output is correct
8 Correct 43 ms 2880 KB Output is correct
9 Correct 24 ms 2644 KB Output is correct
10 Correct 34 ms 2644 KB Output is correct
11 Correct 36 ms 2732 KB Output is correct

Subtask #5
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 3 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 38 ms 2800 KB Output is correct
8 Correct 43 ms 2880 KB Output is correct
9 Correct 24 ms 2644 KB Output is correct
10 Correct 34 ms 2644 KB Output is correct
11 Correct 36 ms 2732 KB Output is correct
12 Correct 79 ms 13796 KB Output is correct
13 Correct 87 ms 21404 KB Output is correct
14 Correct 57 ms 7496 KB Output is correct
15 Correct 85 ms 7296 KB Output is correct
16 Correct 63 ms 7388 KB Output is correct

Subtask #6
0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 3 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 38 ms 2800 KB Output is correct
8 Correct 43 ms 2880 KB Output is correct
9 Correct 24 ms 2644 KB Output is correct
10 Correct 34 ms 2644 KB Output is correct
11 Correct 36 ms 2732 KB Output is correct
12 Correct 2 ms 2644 KB Output is correct
13 Incorrect 36 ms 2736 KB Output isn't correct
14 Halted 0 ms 0 KB -

Subtask #7
0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 3 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 38 ms 2800 KB Output is correct
8 Correct 43 ms 2880 KB Output is correct
9 Correct 24 ms 2644 KB Output is correct
10 Correct 34 ms 2644 KB Output is correct
11 Correct 36 ms 2732 KB Output is correct
12 Correct 79 ms 13796 KB Output is correct
13 Correct 87 ms 21404 KB Output is correct
14 Correct 57 ms 7496 KB Output is correct
15 Correct 85 ms 7296 KB Output is correct
16 Correct 63 ms 7388 KB Output is correct
17 Correct 2 ms 2644 KB Output is correct
18 Incorrect 36 ms 2736 KB Output isn't correct
19 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Incorrect 36 ms 2644 KB Output isn't correct
3 Halted 0 ms 0 KB -