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답안 #585642

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
585642 2022-06-29T07:04:55 Z 박상훈(#8384) Star Trek (CEOI20_startrek) C++17
78 / 100
 125 ms 21704 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;

    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] * S[d-1] % MOD);
    else ans = lscnt_root[1] * S[d-1] % 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 Correct 32 ms 2740 KB Output is correct

Subtask #2
0 / 7.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2772 KB Output is correct
3 Runtime error 10 ms 7584 KB Execution killed with signal 11
4 Halted 0 ms 0 KB -

Subtask #3
8.0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2676 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 3 ms 2644 KB Output is correct

Subtask #4
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2676 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 3 ms 2644 KB Output is correct
7 Correct 39 ms 2824 KB Output is correct
8 Correct 41 ms 2772 KB Output is correct
9 Correct 25 ms 2644 KB Output is correct
10 Correct 36 ms 2724 KB Output is correct
11 Correct 33 ms 2732 KB Output is correct

Subtask #5
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2676 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 3 ms 2644 KB Output is correct
7 Correct 39 ms 2824 KB Output is correct
8 Correct 41 ms 2772 KB Output is correct
9 Correct 25 ms 2644 KB Output is correct
10 Correct 36 ms 2724 KB Output is correct
11 Correct 33 ms 2732 KB Output is correct
12 Correct 88 ms 13796 KB Output is correct
13 Correct 107 ms 21432 KB Output is correct
14 Correct 46 ms 7544 KB Output is correct
15 Correct 60 ms 7300 KB Output is correct
16 Correct 59 ms 7400 KB Output is correct

Subtask #6
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2676 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 3 ms 2644 KB Output is correct
7 Correct 39 ms 2824 KB Output is correct
8 Correct 41 ms 2772 KB Output is correct
9 Correct 25 ms 2644 KB Output is correct
10 Correct 36 ms 2724 KB Output is correct
11 Correct 33 ms 2732 KB Output is correct
12 Correct 1 ms 2644 KB Output is correct
13 Correct 31 ms 2744 KB Output is correct
14 Correct 1 ms 2644 KB Output is correct
15 Correct 2 ms 2772 KB Output is correct
16 Correct 2 ms 2644 KB Output is correct
17 Correct 2 ms 2644 KB Output is correct
18 Correct 1 ms 2644 KB Output is correct
19 Correct 2 ms 2644 KB Output is correct
20 Correct 2 ms 2644 KB Output is correct
21 Correct 36 ms 2824 KB Output is correct
22 Correct 43 ms 2772 KB Output is correct
23 Correct 30 ms 2644 KB Output is correct
24 Correct 37 ms 2744 KB Output is correct
25 Correct 36 ms 2764 KB Output is correct
26 Correct 35 ms 3416 KB Output is correct
27 Correct 41 ms 3532 KB Output is correct
28 Correct 16 ms 3496 KB Output is correct
29 Correct 35 ms 3380 KB Output is correct
30 Correct 35 ms 3148 KB Output is correct

Subtask #7
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 2 ms 2676 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 3 ms 2644 KB Output is correct
7 Correct 39 ms 2824 KB Output is correct
8 Correct 41 ms 2772 KB Output is correct
9 Correct 25 ms 2644 KB Output is correct
10 Correct 36 ms 2724 KB Output is correct
11 Correct 33 ms 2732 KB Output is correct
12 Correct 88 ms 13796 KB Output is correct
13 Correct 107 ms 21432 KB Output is correct
14 Correct 46 ms 7544 KB Output is correct
15 Correct 60 ms 7300 KB Output is correct
16 Correct 59 ms 7400 KB Output is correct
17 Correct 1 ms 2644 KB Output is correct
18 Correct 31 ms 2744 KB Output is correct
19 Correct 1 ms 2644 KB Output is correct
20 Correct 2 ms 2772 KB Output is correct
21 Correct 2 ms 2644 KB Output is correct
22 Correct 2 ms 2644 KB Output is correct
23 Correct 1 ms 2644 KB Output is correct
24 Correct 2 ms 2644 KB Output is correct
25 Correct 2 ms 2644 KB Output is correct
26 Correct 36 ms 2824 KB Output is correct
27 Correct 43 ms 2772 KB Output is correct
28 Correct 30 ms 2644 KB Output is correct
29 Correct 37 ms 2744 KB Output is correct
30 Correct 36 ms 2764 KB Output is correct
31 Correct 35 ms 3416 KB Output is correct
32 Correct 41 ms 3532 KB Output is correct
33 Correct 16 ms 3496 KB Output is correct
34 Correct 35 ms 3380 KB Output is correct
35 Correct 35 ms 3148 KB Output is correct
36 Correct 105 ms 14004 KB Output is correct
37 Correct 125 ms 21704 KB Output is correct
38 Correct 50 ms 7792 KB Output is correct
39 Correct 63 ms 7628 KB Output is correct
40 Correct 62 ms 7628 KB Output is correct
41 Correct 113 ms 18696 KB Output is correct
42 Correct 102 ms 20748 KB Output is correct
43 Correct 41 ms 7880 KB Output is correct
44 Correct 80 ms 7768 KB Output is correct
45 Correct 65 ms 8352 KB Output is correct

Subtask #8
0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 32 ms 2740 KB Output is correct
3 Correct 2 ms 2644 KB Output is correct
4 Correct 2 ms 2772 KB Output is correct
5 Runtime error 10 ms 7584 KB Execution killed with signal 11
6 Halted 0 ms 0 KB -