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Submission #630075

# Submission time Handle Problem Language Result Execution time Memory
630075 2022-08-15T15:52:49 Z Vladth11 Star Trek (CEOI20_startrek) C++14
100 / 100
 112 ms 23116 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 * 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

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 Correct 2 ms 2772 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 1 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 1 ms 2644 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2708 KB Output is correct
2 Correct 1 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 1 ms 2644 KB Output is correct
6 Correct 2 ms 2696 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2708 KB Output is correct
2 Correct 1 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 1 ms 2644 KB Output is correct
6 Correct 2 ms 2696 KB Output is correct
7 Correct 2 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 3 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 1 ms 2708 KB Output is correct
2 Correct 1 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 1 ms 2644 KB Output is correct
6 Correct 2 ms 2696 KB Output is correct
7 Correct 2 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 3 ms 2772 KB Output is correct
11 Correct 2 ms 2772 KB Output is correct
12 Correct 112 ms 22196 KB Output is correct
13 Correct 103 ms 20940 KB Output is correct
14 Correct 56 ms 12444 KB Output is correct
15 Correct 74 ms 12396 KB Output is correct
16 Correct 70 ms 12544 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2708 KB Output is correct
2 Correct 1 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 1 ms 2644 KB Output is correct
6 Correct 2 ms 2696 KB Output is correct
7 Correct 2 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 3 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 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 3 ms 2644 KB Output is correct
18 Correct 2 ms 2644 KB Output is correct
19 Correct 1 ms 2644 KB Output is correct
20 Correct 1 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 2772 KB Output is correct
24 Correct 2 ms 2772 KB Output is correct
25 Correct 2 ms 2772 KB Output is correct
26 Correct 2 ms 2772 KB Output is correct
27 Correct 2 ms 2868 KB Output is correct
28 Correct 2 ms 2772 KB Output is correct
29 Correct 3 ms 2772 KB Output is correct
30 Correct 2 ms 2772 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2708 KB Output is correct
2 Correct 1 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 1 ms 2644 KB Output is correct
6 Correct 2 ms 2696 KB Output is correct
7 Correct 2 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 3 ms 2772 KB Output is correct
11 Correct 2 ms 2772 KB Output is correct
12 Correct 112 ms 22196 KB Output is correct
13 Correct 103 ms 20940 KB Output is correct
14 Correct 56 ms 12444 KB Output is correct
15 Correct 74 ms 12396 KB Output is correct
16 Correct 70 ms 12544 KB Output is correct
17 Correct 1 ms 2644 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 3 ms 2644 KB Output is correct
23 Correct 2 ms 2644 KB Output is correct
24 Correct 1 ms 2644 KB Output is correct
25 Correct 1 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 2772 KB Output is correct
29 Correct 2 ms 2772 KB Output is correct
30 Correct 2 ms 2772 KB Output is correct
31 Correct 2 ms 2772 KB Output is correct
32 Correct 2 ms 2868 KB Output is correct
33 Correct 2 ms 2772 KB Output is correct
34 Correct 3 ms 2772 KB Output is correct
35 Correct 2 ms 2772 KB Output is correct
36 Correct 112 ms 22216 KB Output is correct
37 Correct 100 ms 20840 KB Output is correct
38 Correct 67 ms 12344 KB Output is correct
39 Correct 68 ms 12420 KB Output is correct
40 Correct 69 ms 12496 KB Output is correct
41 Correct 90 ms 16748 KB Output is correct
42 Correct 106 ms 22012 KB Output is correct
43 Correct 53 ms 11256 KB Output is correct
44 Correct 67 ms 12492 KB Output is correct
45 Correct 68 ms 12340 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 2772 KB Output is correct
3 Correct 1 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 1 ms 2644 KB Output is correct
7 Correct 1 ms 2644 KB Output is correct
8 Correct 1 ms 2708 KB Output is correct
9 Correct 1 ms 2644 KB Output is correct
10 Correct 2 ms 2644 KB Output is correct
11 Correct 2 ms 2644 KB Output is correct
12 Correct 1 ms 2644 KB Output is correct
13 Correct 2 ms 2696 KB Output is correct
14 Correct 2 ms 2772 KB Output is correct
15 Correct 2 ms 2772 KB Output is correct
16 Correct 2 ms 2772 KB Output is correct
17 Correct 3 ms 2772 KB Output is correct
18 Correct 2 ms 2772 KB Output is correct
19 Correct 112 ms 22196 KB Output is correct
20 Correct 103 ms 20940 KB Output is correct
21 Correct 56 ms 12444 KB Output is correct
22 Correct 74 ms 12396 KB Output is correct
23 Correct 70 ms 12544 KB Output is correct
24 Correct 1 ms 2644 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 3 ms 2644 KB Output is correct
30 Correct 2 ms 2644 KB Output is correct
31 Correct 1 ms 2644 KB Output is correct
32 Correct 1 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 2772 KB Output is correct
36 Correct 2 ms 2772 KB Output is correct
37 Correct 2 ms 2772 KB Output is correct
38 Correct 2 ms 2772 KB Output is correct
39 Correct 2 ms 2868 KB Output is correct
40 Correct 2 ms 2772 KB Output is correct
41 Correct 3 ms 2772 KB Output is correct
42 Correct 2 ms 2772 KB Output is correct
43 Correct 112 ms 22216 KB Output is correct
44 Correct 100 ms 20840 KB Output is correct
45 Correct 67 ms 12344 KB Output is correct
46 Correct 68 ms 12420 KB Output is correct
47 Correct 69 ms 12496 KB Output is correct
48 Correct 90 ms 16748 KB Output is correct
49 Correct 106 ms 22012 KB Output is correct
50 Correct 53 ms 11256 KB Output is correct
51 Correct 67 ms 12492 KB Output is correct
52 Correct 68 ms 12340 KB Output is correct
53 Correct 76 ms 19680 KB Output is correct
54 Correct 78 ms 23116 KB Output is correct
55 Correct 41 ms 11240 KB Output is correct
56 Correct 80 ms 19204 KB Output is correct
57 Correct 84 ms 13772 KB Output is correct
58 Correct 76 ms 13812 KB Output is correct
59 Correct 67 ms 13444 KB Output is correct
60 Correct 71 ms 13520 KB Output is correct