Submission #630075

#	Time	Username	Problem	Language	Result	Execution time	Memory
630075		Vladth11	Star Trek (CEOI20_startrek)	C++14	100 / 100	112 ms	23116 KiB

startrek

#include <bits/stdc++.h>
#define C 1
#define P 0
#define debug(x) cerr << #x << " " << x << "\n"
#define debugs(x) cerr << #x << " " << x << " "

using namespace std;
typedef long long ll;
typedef pair <ll, ll> pii;
typedef pair <long double, pii> muchie;

const ll NMAX = 100001;
const ll VMAX = 101;
const ll INF = (1LL << 60);
const ll MOD = 1000000007;
const ll BLOCK = 447;
const ll base = 117;
const ll nr_of_bits = 18;
const ll inv2 = 500000004;

vector <ll> v[NMAX];
ll col[NMAX];
ll children[NMAX][2];
ll maximal[NMAX];
ll rosii[NMAX];
ll criticals[NMAX];
ll adv[NMAX];
ll sumR[NMAX][2];

void DFS(ll node, ll p) {
    col[node] = P;
    for(auto x : v[node]) {
        if(x == p) continue;
        DFS(x, node);
        children[node][col[x]]++;
    }
    if(children[node][C] == (ll)v[node].size() - (p != 0)) {
        col[node] = P;
    } else {
        col[node] = C;
    }
    if(col[node] == P)
        rosii[node] = 1;
    for(auto x : v[node]) {
        if(x == p) continue;
        if(col[node] != col[x] && children[node][C] >= (ll)v[node].size() - (p != 0) - 1) {
            rosii[node] += rosii[x];
        }
        sumR[node][col[x]] += rosii[x];
    }
}

ll perdanti = 0;

void bagaR(int node, int p) {
    rosii[node] = (col[node] == P);
    if(children[node][C] >= (ll)v[node].size() - (p != 0) - 1) { /// mereu facem bagaR pentru root
        rosii[node] += sumR[node][P + C - col[node]];
    }
}

void Rerooting(ll node, ll p) {
    adv[node] = col[node];
    criticals[node] = rosii[node];
    if(adv[node] == P)
        perdanti++;
    for(auto x : v[node]) {
        if(x == p) continue;
        ll cx = col[x], cnode = col[node];
        children[node][col[x]]--;
        sumR[node][col[x]] -= rosii[x];
        if(children[node][C] == v[node].size() - 1) {
            col[node] = P;
        } else {
            col[node] = C;
        }
        bagaR(node, x);
        children[x][col[node]]++;
        sumR[x][col[node]] += rosii[node];
        if(children[x][C] == v[x].size()) {
            col[x] = P;
        } else {
            col[x] = C;
        }
        bagaR(x, 0);
        Rerooting(x, node);
        children[x][col[node]]--;
        sumR[x][col[node]] -= rosii[node];
        col[x] = cx;
        bagaR(x, node);
        col[node] = cnode;
        children[node][col[x]]++;
        sumR[node][col[x]] += rosii[x];
        bagaR(node, 0);
    }
}

ll lgput(ll n, ll p) {
    ll r = 1;
    while(p) {
        if(p % 2) {
            r *= n;
            r %= MOD;
        }
        n *= n;
        n %= MOD;
        p /= 2;
    }
    return r;
}

void add(ll &x, ll val) {
    x += val;
    if(x >= MOD)
        x -= MOD;
    if(x < 0)
        x += MOD;
}

ll L[NMAX];

ll mat[2][2];

void inmulteste(ll p) {
    p--;
    ll cv[2][2];
    cv[0][0] = mat[0][0];
    cv[0][1] = mat[0][1];
    cv[1][0] = mat[1][0];
    cv[1][1] = mat[1][1];
    while(p) {
        if(p % 2) {
            ll rez[2][2];
            rez[0][0] = rez[0][1] = rez[1][0] = rez[1][1] = 0;
            for(int i = 0; i < 2; i++) {
                for(int j = 0; j < 2; j++) {
                    for(int k = 0; k < 2; k++) {
                        add(rez[i][j], (mat[i][k] * cv[k][j]) % MOD);
                    }
                }
            }
            cv[0][0] = rez[0][0];
            cv[0][1] = rez[0][1];
            cv[1][0] = rez[1][0];
            cv[1][1] = rez[1][1];
        }
        ll rez[2][2];
        rez[0][0] = rez[0][1] = rez[1][0] = rez[1][1] = 0;
        for(int i = 0; i < 2; i++) {
            for(int j = 0; j < 2; j++) {
                for(int k = 0; k < 2; k++) {
                    add(rez[i][j], (mat[i][k] * mat[k][j]) % MOD);
                }
            }
        }
        mat[0][0] = rez[0][0];
        mat[0][1] = rez[0][1];
        mat[1][0] = rez[1][0];
        mat[1][1] = rez[1][1];
        p /= 2;
    }

    mat[0][0] = cv[0][0];
    mat[0][1] = cv[0][1];
    mat[1][0] = cv[1][0];
    mat[1][1] = cv[1][1];
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    ll n, d, i, criticalDif = 0;
    cin >> n >> d;
    if(n == 2) {
        cout << lgput(4, d);
        return 0;
    }
    for(i = 1; i < n; i++) {
        ll a, b;
        cin >> a >> b;
        v[a].push_back(b);
        v[b].push_back(a);
    }
    DFS(2, 0);
    Rerooting(2, 0);
    for(i = 1; i <= n; i++) {
        if(adv[i] == P) {
            add(criticalDif, -criticals[i]);
        } else {
            add(criticalDif, criticals[i]);
        }
    }
    ll B = criticalDif;
    ll A = 1;
    /// L0 = perdanti
    /// L1 = A + L0 * B
    /// Li = A + Li-1 * B
    L[0] = perdanti;
    A = 1;
    mat[0][0] = B;
    mat[0][1] = (n * n) % MOD * perdanti % MOD;
    mat[1][0] = 0;
    mat[1][1] = (n * n) % MOD;
    ll LP = L[0];
    if(d > 1){
        inmulteste(d - 1);
        LP = (mat[0][0] * L[0] % MOD + mat[0][1] * A) % MOD; /// Asta e L[d - 1]
    }
    ll schimba = (LP * criticals[1]) % MOD;
    if(adv[1] == P) {
        cout << schimba;
    } else {
        cout << (lgput(n, 2 * d) - schimba + MOD) % MOD;
    }
    return 0;
}

Compilation message (stderr)

startrek.cpp: In function 'void Rerooting(ll, ll)':
startrek.cpp:72:30: warning: comparison of integer expressions of different signedness: 'll' {aka 'long long int'} and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   72 |         if(children[node][C] == v[node].size() - 1) {
      |            ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~
startrek.cpp:80:27: warning: comparison of integer expressions of different signedness: 'll' {aka 'long long int'} and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   80 |         if(children[x][C] == v[x].size()) {
      |            ~~~~~~~~~~~~~~~^~~~~~~~~~~~~~

• 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