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Submission #658634

# Submission time Handle Problem Language Result Execution time Memory
658634 2022-11-13T22:25:32 Z lunchbox1 Star Trek (CEOI20_startrek) C++17
100 / 100
 200 ms 23304 KB 
/*
 Star Trek
 https://oj.uz/problem/view/CEOI20_startrek
*/
#include <bits/stdc++.h>
using namespace std;

const int N = 1e5, P = 1e9 + 7;

struct dat {
 int a, b, c;
 bool g;

 dat(bool d) {
  a = b = c = -1, g = d;
 }
 void add(int i) {
  if (a == -1)
   a = i;
  else if (b == -1)
   b = i;
  else if (c == -1)
   c = i;
 }
 bool good(int i) {
  return (a != -1 && a != i) || (b != -1 && b != i) || (c != -1 && c != i) || g;
 }
};

struct mat {
 array<array<int, 2>, 2> v;
 
 mat(bool i = 0) {
  v[0][0] = v[0][1] = v[1][0] = v[1][1] = 0;
  if (i)
   v[0][0] = v[1][1] = 1;
 }
 mat operator*(mat o) {
  mat r;
  for (int a = 0; a < 2; a++)
   for (int b = 0; b < 2; b++)
    r.v[a][b] = (1LL * v[a][0] * o.v[0][b] + 1LL * v[a][1] * o.v[1][b]) % P;
  return r;
 }
};

vector<int> g[N];
array<int, 2> c[N];
bool w0[N], w1[N];

void dfs1(int i) {
 for (int j : g[i]) {
  g[j].erase(find(g[j].begin(), g[j].end(), i));
  dfs1(j), w0[i] |= !w0[j];
 }
}

void dfs2(int i, bool u) {
 w1[i] = !u;
 dat t(!u);
 for (int j : g[i])
  if (!w0[j])
   w1[i] = 1, t.add(j);
 for (int j : g[i])
  dfs2(j, t.good(j));
}

bool tmp;

void dfs3(int i) {
 dat t(0);
 for (int j : g[i])
  if (!w0[j])
   t.add(j);
 c[i][0] = c[i][1] = 0;
 for (int j : g[i]) {
  dfs3(j);
  (c[i][t.good(j) | !0] += c[j][0]) %= P;
  (c[i][t.good(j) | !1] += c[j][1]) %= P;
 }
 if (!tmp)
  c[i][w0[i] | !0]++;
 else
  c[i][w0[i] | !1]++;
}

mat m;

void dfs4(int i, bool u, array<int, 2> d) {
 dat t(0);
 if (!u)
  t.add(i);
 for (int j : g[i])
  if (!w0[j])
   t.add(j);
 int s0 = 0, s1 = 0;
 array<int, 2> q = {0, 0};
 q[t.good(i) || !0] += d[0], s0 += d[0];
 q[t.good(i) || !1] += d[1], s1 += d[1];
 for (int j : g[i]) {
  q[t.good(j) || !0] += c[j][0], s0 += c[j][0];
  q[t.good(j) || !1] += c[j][1], s1 += c[j][1];
 }
 swap(d, c[i]);
 for (int j : g[i]) {
  s0 -= c[j][0], s1 -= c[j][1];
  array<int, 2> e = {0, 0};
  e[t.good(j) | !tmp]++;
  e[1] += s0;
  if (t.c != -1)
   e[1] += s1;
  else if (t.b != -1) {
   if (j != t.a && j != t.b)
    e[1] += s1;
   else
    e[1] += s1 - c[t.a ^ t.b ^ j][1], e[0] += c[t.a ^ t.b ^ j][1];
  } else if (t.a != -1) {
   if (t.a == j)
    e[0] += s1;
   else
    e[1] += s1 - c[t.a][1], e[0] += c[t.a][1];
  } else
   e[0] += s1;
  dfs4(j, t.good(j), e);
  s0 += c[j][0], s1 += c[j][1];
 }
 swap(d, c[i]);
 q[t.good(-1) | !tmp]++;
 m.v[tmp][0] = (m.v[tmp][0] + q[0]) % P, m.v[tmp][1] = (m.v[tmp][1] + q[1]) % P;
}

int x, y;

array<int, 2> dfs5(int i) {
 dat t(0);
 for (int j : g[i])
  if (!w0[j])
   t.add(j);
 array<int, 2> c = {0, 0};
 for (int j : g[i]) {
  auto [c0, c1] = dfs5(j);
  (c[t.good(j) || !0] += c0) %= P;
  (c[t.good(j) || !1] += c1) %= P;
 }
 (c[w0[i] | !0] += x) %= P;
 (c[w0[i] | !1] += y) %= P;
 return c;
}

int main() {
 ios::sync_with_stdio(0), cin.tie(0);
 int n;
 long long k;
 cin >> n >> k;
 for (int h = 0; h < n - 1; h++) {
  int i, j;
  cin >> i >> j, i--, j--;
  g[i].push_back(j), g[j].push_back(i);
 }
 dfs1(0);
 dfs2(0, 1);
 tmp = 0;
 dfs3(0);
 dfs4(0, 1, {0, 0});
 tmp = 1;
 dfs3(0);
 dfs4(0, 1, {0, 0});
 mat p(1);
 k--;
 while (k > 0) {
  if (k & 1)
   p = p * m;
  m = m * m, k >>= 1;
 }
 int c = 0;
 for (int i = 0; i < n; i++)
  c += w1[i];
 x = (1LL * (n - c) * p.v[0][0] + 1LL * c * p.v[1][0]) % P;
 y = (1LL * (n - c) * p.v[0][1] + 1LL * c * p.v[1][1]) % P;
 cout << dfs5(0)[1] << '\n';
 return 0;
}

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 3 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 2 ms 2644 KB Output is correct
2 Correct 4 ms 2676 KB Output is correct
3 Correct 2 ms 2676 KB Output is correct
4 Correct 3 ms 2676 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 3 ms 2644 KB Output is correct
4 Correct 2 ms 2680 KB Output is correct
5 Correct 2 ms 2676 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 3 ms 2644 KB Output is correct
4 Correct 2 ms 2680 KB Output is correct
5 Correct 2 ms 2676 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 2644 KB Output is correct
10 Correct 4 ms 2644 KB Output is correct
11 Correct 4 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 3 ms 2644 KB Output is correct
4 Correct 2 ms 2680 KB Output is correct
5 Correct 2 ms 2676 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 2644 KB Output is correct
10 Correct 4 ms 2644 KB Output is correct
11 Correct 4 ms 2644 KB Output is correct
12 Correct 200 ms 14352 KB Output is correct
13 Correct 154 ms 22900 KB Output is correct
14 Correct 73 ms 7240 KB Output is correct
15 Correct 100 ms 7204 KB Output is correct
16 Correct 79 ms 7176 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 3 ms 2644 KB Output is correct
4 Correct 2 ms 2680 KB Output is correct
5 Correct 2 ms 2676 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 2644 KB Output is correct
10 Correct 4 ms 2644 KB Output is correct
11 Correct 4 ms 2644 KB Output is correct
12 Correct 2 ms 2644 KB Output is correct
13 Correct 2 ms 2644 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 3 ms 2644 KB Output is correct
21 Correct 3 ms 2772 KB Output is correct
22 Correct 2 ms 2772 KB Output is correct
23 Correct 2 ms 2676 KB Output is correct
24 Correct 3 ms 2644 KB Output is correct
25 Correct 2 ms 2684 KB Output is correct
26 Correct 2 ms 2772 KB Output is correct
27 Correct 3 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 2656 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 3 ms 2644 KB Output is correct
4 Correct 2 ms 2680 KB Output is correct
5 Correct 2 ms 2676 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 2644 KB Output is correct
10 Correct 4 ms 2644 KB Output is correct
11 Correct 4 ms 2644 KB Output is correct
12 Correct 200 ms 14352 KB Output is correct
13 Correct 154 ms 22900 KB Output is correct
14 Correct 73 ms 7240 KB Output is correct
15 Correct 100 ms 7204 KB Output is correct
16 Correct 79 ms 7176 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 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 3 ms 2644 KB Output is correct
26 Correct 3 ms 2772 KB Output is correct
27 Correct 2 ms 2772 KB Output is correct
28 Correct 2 ms 2676 KB Output is correct
29 Correct 3 ms 2644 KB Output is correct
30 Correct 2 ms 2684 KB Output is correct
31 Correct 2 ms 2772 KB Output is correct
32 Correct 3 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 2656 KB Output is correct
36 Correct 127 ms 14344 KB Output is correct
37 Correct 142 ms 22704 KB Output is correct
38 Correct 84 ms 7392 KB Output is correct
39 Correct 74 ms 7272 KB Output is correct
40 Correct 89 ms 7356 KB Output is correct
41 Correct 123 ms 18972 KB Output is correct
42 Correct 119 ms 21324 KB Output is correct
43 Correct 52 ms 7044 KB Output is correct
44 Correct 72 ms 7380 KB Output is correct
45 Correct 94 ms 7580 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 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 4 ms 2676 KB Output is correct
5 Correct 2 ms 2676 KB Output is correct
6 Correct 3 ms 2676 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 3 ms 2644 KB Output is correct
11 Correct 2 ms 2680 KB Output is correct
12 Correct 2 ms 2676 KB Output is correct
13 Correct 2 ms 2644 KB Output is correct
14 Correct 3 ms 2772 KB Output is correct
15 Correct 2 ms 2772 KB Output is correct
16 Correct 2 ms 2644 KB Output is correct
17 Correct 4 ms 2644 KB Output is correct
18 Correct 4 ms 2644 KB Output is correct
19 Correct 200 ms 14352 KB Output is correct
20 Correct 154 ms 22900 KB Output is correct
21 Correct 73 ms 7240 KB Output is correct
22 Correct 100 ms 7204 KB Output is correct
23 Correct 79 ms 7176 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 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 3 ms 2644 KB Output is correct
33 Correct 3 ms 2772 KB Output is correct
34 Correct 2 ms 2772 KB Output is correct
35 Correct 2 ms 2676 KB Output is correct
36 Correct 3 ms 2644 KB Output is correct
37 Correct 2 ms 2684 KB Output is correct
38 Correct 2 ms 2772 KB Output is correct
39 Correct 3 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 2656 KB Output is correct
43 Correct 127 ms 14344 KB Output is correct
44 Correct 142 ms 22704 KB Output is correct
45 Correct 84 ms 7392 KB Output is correct
46 Correct 74 ms 7272 KB Output is correct
47 Correct 89 ms 7356 KB Output is correct
48 Correct 123 ms 18972 KB Output is correct
49 Correct 119 ms 21324 KB Output is correct
50 Correct 52 ms 7044 KB Output is correct
51 Correct 72 ms 7380 KB Output is correct
52 Correct 94 ms 7580 KB Output is correct
53 Correct 142 ms 23304 KB Output is correct
54 Correct 138 ms 20120 KB Output is correct
55 Correct 50 ms 6840 KB Output is correct
56 Correct 117 ms 14844 KB Output is correct
57 Correct 79 ms 7888 KB Output is correct
58 Correct 119 ms 7756 KB Output is correct
59 Correct 125 ms 7788 KB Output is correct
60 Correct 122 ms 7608 KB Output is correct