Submission #719886

#	Time	Username	Problem	Language	Result	Execution time	Memory
719886		phoebe	Star Trek (CEOI20_startrek)	C++17	100 / 100	83 ms	17984 KiB

startrek

#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
• Subtask 2: 7 / 7
• Subtask 3: 8 / 8
• Subtask 4: 15 / 15
• Subtask 5: 15 / 15
• Subtask 6: 20 / 20
• Subtask 7: 20 / 20
• Subtask 8: 15 / 15