oj.uz

Submission #763779

# Submission time Handle Problem Language Result Execution time Memory
763779 2023-06-22T20:58:50 Z Sam_a17 Star Trek (CEOI20_startrek) C++17
100 / 100
 86 ms 29064 KB 
#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
// #include <atcoder/all>
#include <cstdio>
using namespace std;
 
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x <<" "; print(x); cerr << endl;
#else
#define dbg(x)
#endif
 
#define sz(x) (int((x).size()))
#define len(x) (int)x.length()
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define clr(x) (x).clear()
#define uniq(x) x.resize(unique(all(x)) - x.begin());
 
#define pb push_back
#define popf pop_front
#define popb pop_back
#define ld long double
#define ll long long
 
void print(long long t) {cerr << t;}
void print(int t) {cerr << t;}
void print(string t) {cerr << t;}
void print(char t) {cerr << t;}
void print(double t) {cerr << t;}
void print(unsigned long long t) {cerr << t;}
void print(long double t) {cerr << t;}
 
template <class T, class V> void print(pair <T, V> p);
template <class T> void print(vector <T> v);
template <class T> void print(set <T> v);
template <class T, class V> void print(map <T, V> v);
template <class T> void print(multiset <T> v);
template <class T> void print(T v[],T n) {cerr << "["; for(int i = 0; i < n; i++) {cerr << v[i] << " ";} cerr << "]";}
template <class T, class V> void print(pair <T, V> p) {cerr << "{"; print(p.first); cerr << ","; print(p.second); cerr << "}";}
template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(deque <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(set <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(multiset <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void print(map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]";}
 
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define nl '\n'
 
// for random generations
mt19937 myrand(chrono::steady_clock::now().time_since_epoch().count());
// mt19937 myrand(131);
 
// for grid problems
int dx[8] = {-1,0,1,0,1,-1,1,-1};
int dy[8] = {0,1,0,-1,1,1,-1,-1};
 
long long ka() {
	long long x = 0;
	bool z = false;
	while (1)
	{
		char y = getchar();
		if (y == '-')
			z = true;
		else if ('0' <= y && y <= '9')
			x = x * 10 + y - '0';
		else
		{
			if (z)
				x *= -1;
			return x;
		}
	}
}
 
// lowest / (1 << 17) >= 1e5 / (1 << 18) >= 2e5 / (1 << 21) >= 1e6
void fastIO() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr); cout.tie(nullptr);
}
// file in/out
void setIO(string str = "") {
  fastIO();
 
  if (str != "") {
    freopen((str + ".in").c_str(), "r", stdin);
    freopen((str + ".out").c_str(), "w", stdout);
  } else if(str == "input") {
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
  }
}
 
// Indexed Set
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const long long mod = 1e9 + 7;
const int N = 2e5 + 10, M = 2e5 + 10;
vector<int> adj[N];
long long n, d;
 
long long binPowByMod(long long a, long long b) {
  a %= mod;
  long long res = 1;
  while (b > 0) {
    if (b & 1)
      res = res * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return res;
}
 
long long add(long long a, long long b) {
  return (a + b) % mod;
}
 
long long mult(long long a, long long b) {
  return (a * b) % mod;
}
 
long long sub(long long a, long long b) {
  return (a - b + 2 * mod) % mod;
}

long long c[N], win, lose;

bool lw[N], curr[N];

int dfs_win(int node, int parent) {
  int ok = 0;
  for(auto i: adj[node]) {
    if(i == parent) continue;
    int cur = dfs_win(i, node);
    if(!cur) ok = 1;
  }
  curr[node] = ok;
  return ok;
}

void dfs_up(int node, int parent, bool par) {
  int on = 0, off = 0;
  for(auto i: adj[node]) {
    if(i == parent) continue;
    if(curr[i]) on++;
    else off++;
  }
 
  if(par) on++;
  else off++;
 
  if(off) {
    lw[node] = 1;
    win++;
  }
  else lose++;
 
  for(auto i: adj[node]) {
    if(i == parent) continue;
    if(curr[i]) on--;
    else off--;
 
    if(off) dfs_up(i, node, true);
    else dfs_up(i, node, false);
 
    if(curr[i]) on++;
    else off++;
  }
}

long long cc = 0;

struct tp {
  bool valid, state;
  int crit;
};

tp dp[N], ans[N];

void dfs_ct(int node, int parent) {
  dp[node].valid = true;
  dp[node].state = 0;
  dp[node].crit = 1;

  int los = 0;
  for(auto i: adj[node]) {
    if(i == parent) continue;
    dfs_ct(i, node);

    if(dp[i].state == 0) {
      dp[node].state = 1;
      los++;
    }
  }

  if(los >= 2) {
    dp[node].valid = false;
    dp[node].crit = 0;
  } else if(los == 1) {
    dp[node].crit = 0;
    for(auto i: adj[node]) {
      if(i == parent) continue;
      if(dp[i].state == dp[node].state) {
        continue;
      }
      dp[node].crit += dp[i].crit;
    }
  } else if(los == 0) {
    for(auto i: adj[node]) {
      if(i == parent) continue;
      dp[node].crit += dp[i].crit;
    }
  }
}

void dfs_ct_up(int node, int parent, tp par) {
  int los = 0;
  
  ans[node].valid = true;
  ans[node].state = 0;
  ans[node].crit = 1;

  vector<pair<long long, long long>> pri;
  for(auto i: adj[node]) {
    if(i == parent) continue;
    if(dp[i].state == 0) {
      ans[node].state = 1;
      pri.emplace_back(i, dp[i].crit);
      los++;
    }
  }

  if(par.state == 0) {
    ans[node].state = 1;
    pri.emplace_back(n + 1, par.crit);
    los++;
  }

  long long lans = 0;
  if(los >= 2) {
    ans[node].valid = false;
    ans[node].crit = 0;
  } else if(los == 1) {
    ans[node].crit = 0;
    for(auto i: adj[node]) {
      if(i == parent) continue;

      if(dp[i].state == ans[node].state) {
        lans += dp[i].crit;
        continue;
      }
      lans += dp[i].crit;
      ans[node].crit += dp[i].crit;
    }

    lans += par.crit;
    if(ans[node].state != par.state) {
      ans[node].crit += par.crit;
    }
  } else if(los == 0) {
    for(auto i: adj[node]) {
      if(i == parent) continue;
      ans[node].crit += dp[i].crit;
    }
    ans[node].crit += par.crit;
  }


  for(auto i: adj[node]) {
    if(i == parent) continue;
    
    auto curent = ans[node];

    if(dp[i].state == 0) {
      los--;

      if(los >= 2) {
        assert(curent.valid == false);
        assert(curent.crit == 0);
        assert(curent.state == 1);

        dfs_ct_up(i, node, curent);
      } else if(los == 1) {
        curent.valid = true;
        curent.crit = 0;
        curent.state = 1;

        for(auto j: pri) {
          if(j.first == i) continue;
          curent.crit += j.second;
        }

        dfs_ct_up(i, node, curent);
      } else {
        
        curent.valid = true;
        curent.state = 0;
        curent.crit = 1;

        curent.crit += lans;
        curent.crit -= dp[i].crit;

        dfs_ct_up(i, node, curent);
      }

      los++;
    } else {
      if(los == 0) {
        curent.crit -= dp[i].crit;
      }
      dfs_ct_up(i, node, curent);
    }
  }
}

struct Matrix {
  long long a[2][2] = {{0, 0}, {0, 0}};
 
  Matrix operator *(const Matrix& another) {
    Matrix product;
    for(int i = 0; i < 2; i++) {
      for(int j = 0; j < 2; j++) {
        for(int k = 0; k < 2; k++) {
          long long cur = mult(a[i][j], another.a[j][k]);
          product.a[i][k] = add(product.a[i][k], cur); 
        }
      }
    }
    return product;
  }
 
};
 
Matrix binpow(Matrix a, long long power) {
  power--;
  Matrix answ = a;
 
  while(power > 0) {
    if(power & 1) {
      answ = answ * a;
    }
 
    a = a * a;
    power /= 2;
  }
 
  return answ;
}

void solve_() {
  cin >> n >> d;
 
  for(int i = 1; i <= n - 1; i++) {
    int a, b; cin >> a >> b;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }

  // calc win_lose
  int cur = dfs_win(1, 0);
  dfs_up(1, 0, true);

  dfs_ct(1, 0);
  dfs_ct_up(1, 0, {0, 1, 0});

  // calc crit
  long long E = 0;
  for(int i = 1; i <= n; i++) {
    c[i] = ans[i].crit;

    if(lw[i]) {
      E += c[i];
      E %= mod;
    } else {
      E -= c[i];
      E += 2 * mod;
      E %= mod;
    }
  }

  E += 2 * mod;
  E %= mod;

  long long answ = 0;
  Matrix mt;
  mt.a[0][0] = (n * n) % mod, mt.a[0][1] = 0;
  mt.a[1][0] = lose, mt.a[1][1] = E;

  mt = binpow(mt, d);

  mt.a[1][0] %= mod;
  if(lw[1]) {
    answ = sub(binPowByMod(n, 2 * d), mult(c[1], mt.a[1][0]));
  } else {
    answ = add(answ, mult(c[1], mt.a[1][0]));
  }
  cout << answ << '\n';
}
 
int main() {
  setIO();
 
  auto solve = [&](int test_case)-> void {
    while(test_case--) {
      solve_();
    }
  };
 
  int test_cases = 1; 
  // cin >> test_cases;
  solve(test_cases);
 
  return 0;
}

Compilation message

startrek.cpp: In function 'void solve_()':
startrek.cpp:361:7: warning: unused variable 'cur' [-Wunused-variable]
  361 |   int cur = dfs_win(1, 0);
      |       ^~~
startrek.cpp: In function 'void setIO(std::string)':
startrek.cpp:88:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   88 |     freopen((str + ".in").c_str(), "r", stdin);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
startrek.cpp:89:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   89 |     freopen((str + ".out").c_str(), "w", stdout);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
startrek.cpp:91:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   91 |     freopen("input.txt", "r", stdin);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
startrek.cpp:92:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   92 |     freopen("output.txt", "w", stdout);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~

Subtask #1
0.0 / 0.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 4 ms 5076 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 5028 KB Output is correct
2 Correct 2 ms 5076 KB Output is correct
3 Correct 4 ms 5024 KB Output is correct
4 Correct 3 ms 5028 KB Output is correct
5 Correct 2 ms 4948 KB Output is correct

Subtask #3
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 4 ms 4948 KB Output is correct
3 Correct 4 ms 4948 KB Output is correct
4 Correct 4 ms 4948 KB Output is correct
5 Correct 3 ms 5032 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct

Subtask #4
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 4 ms 4948 KB Output is correct
3 Correct 4 ms 4948 KB Output is correct
4 Correct 4 ms 4948 KB Output is correct
5 Correct 3 ms 5032 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 3 ms 5076 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5036 KB Output is correct

Subtask #5
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 4 ms 4948 KB Output is correct
3 Correct 4 ms 4948 KB Output is correct
4 Correct 4 ms 4948 KB Output is correct
5 Correct 3 ms 5032 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 3 ms 5076 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5036 KB Output is correct
12 Correct 67 ms 19720 KB Output is correct
13 Correct 66 ms 29064 KB Output is correct
14 Correct 32 ms 11828 KB Output is correct
15 Correct 63 ms 11940 KB Output is correct
16 Correct 60 ms 11852 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 4 ms 4948 KB Output is correct
3 Correct 4 ms 4948 KB Output is correct
4 Correct 4 ms 4948 KB Output is correct
5 Correct 3 ms 5032 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 3 ms 5076 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5036 KB Output is correct
12 Correct 3 ms 4948 KB Output is correct
13 Correct 3 ms 5028 KB Output is correct
14 Correct 2 ms 4948 KB Output is correct
15 Correct 3 ms 5024 KB Output is correct
16 Correct 3 ms 5028 KB Output is correct
17 Correct 3 ms 5020 KB Output is correct
18 Correct 3 ms 4948 KB Output is correct
19 Correct 3 ms 4948 KB Output is correct
20 Correct 2 ms 4948 KB Output is correct
21 Correct 3 ms 5160 KB Output is correct
22 Correct 4 ms 5204 KB Output is correct
23 Correct 4 ms 5076 KB Output is correct
24 Correct 3 ms 5028 KB Output is correct
25 Correct 4 ms 5028 KB Output is correct
26 Correct 3 ms 5076 KB Output is correct
27 Correct 3 ms 5204 KB Output is correct
28 Correct 2 ms 5076 KB Output is correct
29 Correct 2 ms 5088 KB Output is correct
30 Correct 3 ms 5032 KB Output is correct

Subtask #7
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 4 ms 4948 KB Output is correct
3 Correct 4 ms 4948 KB Output is correct
4 Correct 4 ms 4948 KB Output is correct
5 Correct 3 ms 5032 KB Output is correct
6 Correct 3 ms 4948 KB Output is correct
7 Correct 3 ms 5204 KB Output is correct
8 Correct 3 ms 5204 KB Output is correct
9 Correct 3 ms 5076 KB Output is correct
10 Correct 3 ms 5076 KB Output is correct
11 Correct 3 ms 5036 KB Output is correct
12 Correct 67 ms 19720 KB Output is correct
13 Correct 66 ms 29064 KB Output is correct
14 Correct 32 ms 11828 KB Output is correct
15 Correct 63 ms 11940 KB Output is correct
16 Correct 60 ms 11852 KB Output is correct
17 Correct 3 ms 4948 KB Output is correct
18 Correct 3 ms 5028 KB Output is correct
19 Correct 2 ms 4948 KB Output is correct
20 Correct 3 ms 5024 KB Output is correct
21 Correct 3 ms 5028 KB Output is correct
22 Correct 3 ms 5020 KB Output is correct
23 Correct 3 ms 4948 KB Output is correct
24 Correct 3 ms 4948 KB Output is correct
25 Correct 2 ms 4948 KB Output is correct
26 Correct 3 ms 5160 KB Output is correct
27 Correct 4 ms 5204 KB Output is correct
28 Correct 4 ms 5076 KB Output is correct
29 Correct 3 ms 5028 KB Output is correct
30 Correct 4 ms 5028 KB Output is correct
31 Correct 3 ms 5076 KB Output is correct
32 Correct 3 ms 5204 KB Output is correct
33 Correct 2 ms 5076 KB Output is correct
34 Correct 2 ms 5088 KB Output is correct
35 Correct 3 ms 5032 KB Output is correct
36 Correct 49 ms 19676 KB Output is correct
37 Correct 65 ms 28980 KB Output is correct
38 Correct 32 ms 11812 KB Output is correct
39 Correct 41 ms 11892 KB Output is correct
40 Correct 56 ms 11836 KB Output is correct
41 Correct 52 ms 24588 KB Output is correct
42 Correct 68 ms 26888 KB Output is correct
43 Correct 40 ms 11048 KB Output is correct
44 Correct 64 ms 11876 KB Output is correct
45 Correct 43 ms 11832 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 4948 KB Output is correct
2 Correct 4 ms 5076 KB Output is correct
3 Correct 4 ms 5028 KB Output is correct
4 Correct 2 ms 5076 KB Output is correct
5 Correct 4 ms 5024 KB Output is correct
6 Correct 3 ms 5028 KB Output is correct
7 Correct 2 ms 4948 KB Output is correct
8 Correct 3 ms 4948 KB Output is correct
9 Correct 4 ms 4948 KB Output is correct
10 Correct 4 ms 4948 KB Output is correct
11 Correct 4 ms 4948 KB Output is correct
12 Correct 3 ms 5032 KB Output is correct
13 Correct 3 ms 4948 KB Output is correct
14 Correct 3 ms 5204 KB Output is correct
15 Correct 3 ms 5204 KB Output is correct
16 Correct 3 ms 5076 KB Output is correct
17 Correct 3 ms 5076 KB Output is correct
18 Correct 3 ms 5036 KB Output is correct
19 Correct 67 ms 19720 KB Output is correct
20 Correct 66 ms 29064 KB Output is correct
21 Correct 32 ms 11828 KB Output is correct
22 Correct 63 ms 11940 KB Output is correct
23 Correct 60 ms 11852 KB Output is correct
24 Correct 3 ms 4948 KB Output is correct
25 Correct 3 ms 5028 KB Output is correct
26 Correct 2 ms 4948 KB Output is correct
27 Correct 3 ms 5024 KB Output is correct
28 Correct 3 ms 5028 KB Output is correct
29 Correct 3 ms 5020 KB Output is correct
30 Correct 3 ms 4948 KB Output is correct
31 Correct 3 ms 4948 KB Output is correct
32 Correct 2 ms 4948 KB Output is correct
33 Correct 3 ms 5160 KB Output is correct
34 Correct 4 ms 5204 KB Output is correct
35 Correct 4 ms 5076 KB Output is correct
36 Correct 3 ms 5028 KB Output is correct
37 Correct 4 ms 5028 KB Output is correct
38 Correct 3 ms 5076 KB Output is correct
39 Correct 3 ms 5204 KB Output is correct
40 Correct 2 ms 5076 KB Output is correct
41 Correct 2 ms 5088 KB Output is correct
42 Correct 3 ms 5032 KB Output is correct
43 Correct 49 ms 19676 KB Output is correct
44 Correct 65 ms 28980 KB Output is correct
45 Correct 32 ms 11812 KB Output is correct
46 Correct 41 ms 11892 KB Output is correct
47 Correct 56 ms 11836 KB Output is correct
48 Correct 52 ms 24588 KB Output is correct
49 Correct 68 ms 26888 KB Output is correct
50 Correct 40 ms 11048 KB Output is correct
51 Correct 64 ms 11876 KB Output is correct
52 Correct 43 ms 11832 KB Output is correct
53 Correct 56 ms 29004 KB Output is correct
54 Correct 86 ms 25532 KB Output is correct
55 Correct 38 ms 10484 KB Output is correct
56 Correct 48 ms 19328 KB Output is correct
57 Correct 41 ms 11912 KB Output is correct
58 Correct 58 ms 11904 KB Output is correct
59 Correct 41 ms 11832 KB Output is correct
60 Correct 46 ms 11904 KB Output is correct