oj.uz

Submission #719886

# Submission time Handle Problem Language Result Execution time Memory
719886 2023-04-07T02:02:32 Z phoebe Star Trek (CEOI20_startrek) C++17
100 / 100
 83 ms 17984 KB 
#include <bits/stdc++.h>
using namespace std;

#define int long long
#define ll long long
#define pii pair<int, int>
#define F first
#define S second
#define PB push_back
#define ALL(x) x.begin(), x.end()
#define FOR(i, n) for (int i = 0; i < n; i++)
#define NYOOM ios::sync_with_stdio(0); cin.tie(0);
#define endl '\n'
const int INF = 1e9 + 7;
const ll LLINF = 1ll<<60;

const int maxn = 1e5 + 10;
int n, D, toggle[maxn] = {0}, cnt[maxn] = {0}, win_sum[maxn] = {0}, lose_sum[maxn] = {0}, 
a = 0, b = 0, c = 0, d = 0, cnt_win = 0, cnt_lose = 0;
bool lose[maxn] = {0};
vector<int> adj[maxn];

// u = #win, v = #lose
// u' = a * u + b * v
// v' = c * u + d * v

void dfs(int v, int p){
    for (auto u : adj[v]){
        if (u == p) continue;
        dfs(u, v);
        if (lose[u]) cnt[v]++, lose_sum[v] = (lose_sum[v] + toggle[u]) % INF;
        else win_sum[v] = (win_sum[v] + toggle[u]) % INF;
    }
    if (cnt[v] == 0) lose[v] = true, toggle[v] = 1 + win_sum[v];
    else if (cnt[v] == 1) lose[v] = false, toggle[v] = lose_sum[v];
    else lose[v] = false, toggle[v] = 0;
}

void add(int v, int u){
    if (lose[u]) lose_sum[v] = (lose_sum[v] + toggle[u]) % INF, cnt[v]++;
    else win_sum[v] = (win_sum[v] + toggle[u]) % INF;
    if (cnt[v] == 0) lose[v] = true, toggle[v] = 1 + win_sum[v];
    else if (cnt[v] == 1) lose[v] = false, toggle[v] = lose_sum[v];
    else lose[v] = false, toggle[v] = 0;
}

void remove(int v, int u){
    if (lose[u]) lose_sum[v] = (lose_sum[v] - toggle[u] + INF) % INF, cnt[v]--;
    else win_sum[v] = (win_sum[v] - toggle[u] + INF) % INF;
    if (cnt[v] == 0) lose[v] = true, toggle[v] = 1 + win_sum[v];
    else if (cnt[v] == 1) lose[v] = false, toggle[v] = lose_sum[v];
    else lose[v] = false, toggle[v] = 0;
}

void reroot(int v, int p){
    if (lose[v]){
        cnt_lose++;
        c = (c + n) % INF; // can connect any node to win state and keep node v at lose
        d = (d + (n - toggle[v])) % INF; 
        b = (b + toggle[v]) % INF; // toggling will turn to win
    }
    else{
        cnt_win++;
        a = (a + n) % INF;
        b = (b + (n - toggle[v])) % INF;
        d = (d + toggle[v]) % INF;
    }
    for (auto u : adj[v]){
        if (u == p) continue;
        remove(v, u); add(u, v);
        reroot(u, v);
        remove(u, v); add(v, u);
    }
}

vector<int> combine(vector<int> s1, vector<int> s2){
    int a1 = s1[0], b1 = s1[1], c1 = s1[2], d1 = s1[3];
    int a2 = s2[0], b2 = s2[1], c2 = s2[2], d2 = s2[3];
    vector<int> re(4);
    re[0] = (a1 * a2 + c1 * b2) % INF;
    re[1] = (b1 * a2 + d1 * b2) % INF;
    re[2] = (a1 * c2 + c1 * d2) % INF;
    re[3] = (b1 * c2 + d1 * d2) % INF;
    return re;
}

vector<int> mpow(vector<int> s, int e){
    vector<int> re = {1, 0, 0, 1};
    while (e){
        if (e % 2) re = combine(re, s);
        s = combine(s, s);
        e /= 2;
    }
    return re;
}

signed main(){
    NYOOM;
    cin >> n >> D;
    FOR(i, n - 1){
        int u, v; cin >> u >> v;
        adj[u].PB(v); adj[v].PB(u);
    }
    dfs(1, 1); 
    // FOR(i, n) cout << toggle[i + 1] << ' '; cout << endl;
    // cout << endl << toggle[1] << endl << endl;
    bool start_lose = lose[1]; int start_toggle = toggle[1];
    // cout << endl << start_toggle << endl << endl;
    reroot(1, 1);
    vector<int> s = mpow({a, b, c, d}, D - 1);
    int temp = cnt_win;
    cnt_win = (s[0] * cnt_win + s[1] * cnt_lose) % INF;
    cnt_lose = (s[2] * temp + s[3] * cnt_lose) % INF;
    // cout << cnt_win << ' ' << cnt_lose << endl;
    if (start_lose){
        // cout << start_toggle << ' ' << cnt_lose << endl;
        cout << (start_toggle * cnt_lose) % INF;
    }
    else{
        int total = (n * cnt_win) % INF;
        total = (total + ((n - start_toggle) * cnt_lose) % INF) % INF; 
        cout << total << endl;
    }
}

Subtask #1
0.0 / 0.0

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

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2668 KB Output is correct
3 Correct 2 ms 2676 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

# 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 2676 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 2676 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 2676 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 2676 KB Output is correct
7 Correct 2 ms 2772 KB Output is correct
8 Correct 2 ms 2812 KB Output is correct
9 Correct 2 ms 2772 KB Output is correct
10 Correct 2 ms 2772 KB Output is correct
11 Correct 2 ms 2644 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 2676 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 2676 KB Output is correct
7 Correct 2 ms 2772 KB Output is correct
8 Correct 2 ms 2812 KB Output is correct
9 Correct 2 ms 2772 KB Output is correct
10 Correct 2 ms 2772 KB Output is correct
11 Correct 2 ms 2644 KB Output is correct
12 Correct 74 ms 13784 KB Output is correct
13 Correct 64 ms 17984 KB Output is correct
14 Correct 63 ms 10364 KB Output is correct
15 Correct 78 ms 10524 KB Output is correct
16 Correct 72 ms 10644 KB Output is correct

Subtask #6
20.0 / 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 2676 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 2676 KB Output is correct
7 Correct 2 ms 2772 KB Output is correct
8 Correct 2 ms 2812 KB Output is correct
9 Correct 2 ms 2772 KB Output is correct
10 Correct 2 ms 2772 KB Output is correct
11 Correct 2 ms 2644 KB Output is correct
12 Correct 2 ms 2676 KB Output is correct
13 Correct 2 ms 2772 KB Output is correct
14 Correct 2 ms 2644 KB Output is correct
15 Correct 2 ms 2644 KB Output is correct
16 Correct 2 ms 2644 KB Output is correct
17 Correct 2 ms 2644 KB Output is correct
18 Correct 2 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 2 ms 2772 KB Output is correct
22 Correct 2 ms 2772 KB Output is correct
23 Correct 2 ms 2684 KB Output is correct
24 Correct 2 ms 2800 KB Output is correct
25 Correct 2 ms 2644 KB Output is correct
26 Correct 2 ms 2772 KB Output is correct
27 Correct 2 ms 2772 KB Output is correct
28 Correct 2 ms 2644 KB Output is correct
29 Correct 3 ms 2644 KB Output is correct
30 Correct 3 ms 2680 KB Output is correct

Subtask #7
20.0 / 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 2676 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 2676 KB Output is correct
7 Correct 2 ms 2772 KB Output is correct
8 Correct 2 ms 2812 KB Output is correct
9 Correct 2 ms 2772 KB Output is correct
10 Correct 2 ms 2772 KB Output is correct
11 Correct 2 ms 2644 KB Output is correct
12 Correct 74 ms 13784 KB Output is correct
13 Correct 64 ms 17984 KB Output is correct
14 Correct 63 ms 10364 KB Output is correct
15 Correct 78 ms 10524 KB Output is correct
16 Correct 72 ms 10644 KB Output is correct
17 Correct 2 ms 2676 KB Output is correct
18 Correct 2 ms 2772 KB Output is correct
19 Correct 2 ms 2644 KB Output is correct
20 Correct 2 ms 2644 KB Output is correct
21 Correct 2 ms 2644 KB Output is correct
22 Correct 2 ms 2644 KB Output is correct
23 Correct 2 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 2 ms 2772 KB Output is correct
27 Correct 2 ms 2772 KB Output is correct
28 Correct 2 ms 2684 KB Output is correct
29 Correct 2 ms 2800 KB Output is correct
30 Correct 2 ms 2644 KB Output is correct
31 Correct 2 ms 2772 KB Output is correct
32 Correct 2 ms 2772 KB Output is correct
33 Correct 2 ms 2644 KB Output is correct
34 Correct 3 ms 2644 KB Output is correct
35 Correct 3 ms 2680 KB Output is correct
36 Correct 70 ms 13880 KB Output is correct
37 Correct 72 ms 17960 KB Output is correct
38 Correct 68 ms 10312 KB Output is correct
39 Correct 83 ms 10524 KB Output is correct
40 Correct 72 ms 10540 KB Output is correct
41 Correct 81 ms 16096 KB Output is correct
42 Correct 63 ms 16616 KB Output is correct
43 Correct 40 ms 9412 KB Output is correct
44 Correct 76 ms 10700 KB Output is correct
45 Correct 64 ms 10512 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 2 ms 2644 KB Output is correct
3 Correct 1 ms 2644 KB Output is correct
4 Correct 2 ms 2668 KB Output is correct
5 Correct 2 ms 2676 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 2 ms 2644 KB Output is correct
8 Correct 2 ms 2644 KB Output is correct
9 Correct 2 ms 2644 KB Output is correct
10 Correct 2 ms 2676 KB Output is correct
11 Correct 2 ms 2644 KB Output is correct
12 Correct 2 ms 2644 KB Output is correct
13 Correct 2 ms 2676 KB Output is correct
14 Correct 2 ms 2772 KB Output is correct
15 Correct 2 ms 2812 KB Output is correct
16 Correct 2 ms 2772 KB Output is correct
17 Correct 2 ms 2772 KB Output is correct
18 Correct 2 ms 2644 KB Output is correct
19 Correct 74 ms 13784 KB Output is correct
20 Correct 64 ms 17984 KB Output is correct
21 Correct 63 ms 10364 KB Output is correct
22 Correct 78 ms 10524 KB Output is correct
23 Correct 72 ms 10644 KB Output is correct
24 Correct 2 ms 2676 KB Output is correct
25 Correct 2 ms 2772 KB Output is correct
26 Correct 2 ms 2644 KB Output is correct
27 Correct 2 ms 2644 KB Output is correct
28 Correct 2 ms 2644 KB Output is correct
29 Correct 2 ms 2644 KB Output is correct
30 Correct 2 ms 2644 KB Output is correct
31 Correct 2 ms 2644 KB Output is correct
32 Correct 2 ms 2644 KB Output is correct
33 Correct 2 ms 2772 KB Output is correct
34 Correct 2 ms 2772 KB Output is correct
35 Correct 2 ms 2684 KB Output is correct
36 Correct 2 ms 2800 KB Output is correct
37 Correct 2 ms 2644 KB Output is correct
38 Correct 2 ms 2772 KB Output is correct
39 Correct 2 ms 2772 KB Output is correct
40 Correct 2 ms 2644 KB Output is correct
41 Correct 3 ms 2644 KB Output is correct
42 Correct 3 ms 2680 KB Output is correct
43 Correct 70 ms 13880 KB Output is correct
44 Correct 72 ms 17960 KB Output is correct
45 Correct 68 ms 10312 KB Output is correct
46 Correct 83 ms 10524 KB Output is correct
47 Correct 72 ms 10540 KB Output is correct
48 Correct 81 ms 16096 KB Output is correct
49 Correct 63 ms 16616 KB Output is correct
50 Correct 40 ms 9412 KB Output is correct
51 Correct 76 ms 10700 KB Output is correct
52 Correct 64 ms 10512 KB Output is correct
53 Correct 79 ms 17952 KB Output is correct
54 Correct 69 ms 16444 KB Output is correct
55 Correct 44 ms 8812 KB Output is correct
56 Correct 67 ms 14064 KB Output is correct
57 Correct 72 ms 10764 KB Output is correct
58 Correct 74 ms 10764 KB Output is correct
59 Correct 67 ms 10572 KB Output is correct
60 Correct 63 ms 10404 KB Output is correct