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Submission #585641

# Submission time Handle Problem Language Result Execution time Memory
585641 2022-06-29T07:03:43 Z 박상훈(#8384) Star Trek (CEOI20_startrek) C++17
38 / 100
 89 ms 21792 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);

    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

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 34 ms 2736 KB Output is correct

Subtask #2
0 / 7.0

# Verdict Execution time Memory 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 7520 KB Execution killed with signal 11
4 Halted 0 ms 0 KB -

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 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 2 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2656 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 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 2 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2656 KB Output is correct
7 Correct 36 ms 2828 KB Output is correct
8 Correct 38 ms 2868 KB Output is correct
9 Correct 24 ms 2664 KB Output is correct
10 Correct 33 ms 2672 KB Output is correct
11 Correct 33 ms 2744 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 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 2 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2656 KB Output is correct
7 Correct 36 ms 2828 KB Output is correct
8 Correct 38 ms 2868 KB Output is correct
9 Correct 24 ms 2664 KB Output is correct
10 Correct 33 ms 2672 KB Output is correct
11 Correct 33 ms 2744 KB Output is correct
12 Correct 81 ms 14024 KB Output is correct
13 Correct 89 ms 21792 KB Output is correct
14 Correct 48 ms 7904 KB Output is correct
15 Correct 66 ms 7772 KB Output is correct
16 Correct 78 ms 7760 KB Output is correct

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 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 2 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2656 KB Output is correct
7 Correct 36 ms 2828 KB Output is correct
8 Correct 38 ms 2868 KB Output is correct
9 Correct 24 ms 2664 KB Output is correct
10 Correct 33 ms 2672 KB Output is correct
11 Correct 33 ms 2744 KB Output is correct
12 Correct 2 ms 2644 KB Output is correct
13 Correct 32 ms 2740 KB Output is correct
14 Correct 2 ms 2644 KB Output is correct
15 Correct 2 ms 2792 KB Output is correct
16 Correct 2 ms 2644 KB Output is correct
17 Correct 2 ms 2660 KB Output is correct
18 Correct 2 ms 2644 KB Output is correct
19 Correct 2 ms 2664 KB Output is correct
20 Correct 2 ms 2644 KB Output is correct
21 Correct 36 ms 2772 KB Output is correct
22 Correct 40 ms 2864 KB Output is correct
23 Correct 24 ms 2664 KB Output is correct
24 Correct 34 ms 2752 KB Output is correct
25 Correct 33 ms 2740 KB Output is correct
26 Correct 39 ms 3404 KB Output is correct
27 Correct 46 ms 3540 KB Output is correct
28 Incorrect 16 ms 3508 KB Output isn't correct
29 Halted 0 ms 0 KB -

Subtask #7
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 2 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 2 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2656 KB Output is correct
7 Correct 36 ms 2828 KB Output is correct
8 Correct 38 ms 2868 KB Output is correct
9 Correct 24 ms 2664 KB Output is correct
10 Correct 33 ms 2672 KB Output is correct
11 Correct 33 ms 2744 KB Output is correct
12 Correct 81 ms 14024 KB Output is correct
13 Correct 89 ms 21792 KB Output is correct
14 Correct 48 ms 7904 KB Output is correct
15 Correct 66 ms 7772 KB Output is correct
16 Correct 78 ms 7760 KB Output is correct
17 Correct 2 ms 2644 KB Output is correct
18 Correct 32 ms 2740 KB Output is correct
19 Correct 2 ms 2644 KB Output is correct
20 Correct 2 ms 2792 KB Output is correct
21 Correct 2 ms 2644 KB Output is correct
22 Correct 2 ms 2660 KB Output is correct
23 Correct 2 ms 2644 KB Output is correct
24 Correct 2 ms 2664 KB Output is correct
25 Correct 2 ms 2644 KB Output is correct
26 Correct 36 ms 2772 KB Output is correct
27 Correct 40 ms 2864 KB Output is correct
28 Correct 24 ms 2664 KB Output is correct
29 Correct 34 ms 2752 KB Output is correct
30 Correct 33 ms 2740 KB Output is correct
31 Correct 39 ms 3404 KB Output is correct
32 Correct 46 ms 3540 KB Output is correct
33 Incorrect 16 ms 3508 KB Output isn't correct
34 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 2644 KB Output is correct
2 Correct 34 ms 2736 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 7520 KB Execution killed with signal 11
6 Halted 0 ms 0 KB -