oj.uz

Submission #630074

# Submission time Handle Problem Language Result Execution time Memory
630074 2022-08-15T15:49:39 Z Vladth11 Star Trek (CEOI20_startrek) C++14
45 / 100
 106 ms 22136 KB 
#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;
    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

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 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Incorrect 2 ms 2772 KB Output isn't correct
3 Halted 0 ms 0 KB -

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Correct 1 ms 2644 KB Output is correct
3 Correct 1 ms 2644 KB Output is correct
4 Correct 2 ms 2644 KB Output is correct
5 Correct 1 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 2644 KB Output is correct
4 Correct 1 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 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 1 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 3 ms 2772 KB Output is correct
8 Correct 2 ms 2772 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 2772 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 1 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 3 ms 2772 KB Output is correct
8 Correct 2 ms 2772 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 2772 KB Output is correct
12 Correct 80 ms 22136 KB Output is correct
13 Correct 86 ms 20832 KB Output is correct
14 Correct 64 ms 12360 KB Output is correct
15 Correct 106 ms 12380 KB Output is correct
16 Correct 84 ms 12492 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 1 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 3 ms 2772 KB Output is correct
8 Correct 2 ms 2772 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 2772 KB Output is correct
12 Correct 1 ms 2644 KB Output is correct
13 Incorrect 2 ms 2772 KB Output isn't correct
14 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 1 ms 2644 KB Output is correct
5 Correct 2 ms 2644 KB Output is correct
6 Correct 2 ms 2644 KB Output is correct
7 Correct 3 ms 2772 KB Output is correct
8 Correct 2 ms 2772 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 2772 KB Output is correct
12 Correct 80 ms 22136 KB Output is correct
13 Correct 86 ms 20832 KB Output is correct
14 Correct 64 ms 12360 KB Output is correct
15 Correct 106 ms 12380 KB Output is correct
16 Correct 84 ms 12492 KB Output is correct
17 Correct 1 ms 2644 KB Output is correct
18 Incorrect 2 ms 2772 KB Output isn't correct
19 Halted 0 ms 0 KB -

Subtask #8
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2644 KB Output is correct
2 Incorrect 2 ms 2772 KB Output isn't correct
3 Halted 0 ms 0 KB -