Submission #763779

#	Time	Username	Problem	Language	Result	Execution time	Memory
763779		Sam_a17	Star Trek (CEOI20_startrek)	C++17	100 / 100	86 ms	29064 KiB

startrek

#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 (stderr)

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
• 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