Problem p02728 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;

typedef unsigned long ul;
typedef unsigned long long ull;
typedef long long ll;
typedef vector<ll> vint;
typedef vector<vector<ll>> vvint;
typedef vector<vector<vector<ll>>> vvvint;
typedef vector<string> vstring;
typedef vector<vector<string>> vvstring;
typedef vector<char> vchar;
typedef vector<vector<char>> vvchar;
typedef vector<long double> vdouble;
typedef vector<vector<long double>> vvdouble;
typedef vector<vector<vector<long double>>> vvvdouble;
typedef pair<ll, ll> pint;
typedef vector<pint> vpint;
typedef vector<bool> vbool;

#define rep(i, n) for (ll i = 0; i < n; i++)
#define repf(i, f, n) for (ll i = f; i < n; i++)
#define repr(i, n) for (ll i = n - 1; i >= 0; i--)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define ALL(obj) (obj).begin(), (obj).end()
// #define LLONG_MAX 9223372036854775806
#define vmax(vec) *max_element(vec.begin(), vec.end())
#define vmin(vec) *min_element(vec.begin(), vec.end())
#define vsort(vec) sort(vec.begin(), vec.end())
#define vsortgr(vec) sort(vec.begin(), vec.end(), greater<ll>())
#define MOD 1000000007
// #define MOD 998244353
// #define MOD LLONG_MAX
const double PI = 3.14159265358979323846;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

int dy[] = {0, 0, 1, -1};
int dx[] = {
    1,
    -1,
    0,
    0,
};

void printv(vint &v) {
  for (auto e : v)
    cout << e << " ";
  cout << endl;
}

// 繰り返し二乗法
ll power(ll a, ll b) {
  if (a == 1)
    return a;
  // if(a==0)re
  ll res = 1;
  while (b > 0) {
    if (b & 1)
      res = res * a % MOD;
    a = a * a % MOD;
    b >>= 1;
  }
  return res;
}

const int MAX = 2100000;

ll fact[MAX], fact_inv[MAX];

void init_fact(ll n) {
  fact[0] = 1;
  // 階乗の計算
  for (ll i = 0; i < n; i++)
    fact[i + 1] = fact[i] * (i + 1) % MOD;
  fact_inv[n] = power(fact[n], MOD - 2);
  // 逆元の計算
  for (ll i = n - 1; i >= 0; i--)
    fact_inv[i] = fact_inv[i + 1] * (i + 1) % MOD;
}

ll comb(ll n, ll r) {
  return (fact[n] * fact_inv[r]) % MOD * fact_inv[n - r] % MOD;
}

ll perm(ll n, ll r) { return (fact[n] * fact_inv[n - r]) % MOD; }
template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt<(int)(1e9 + 7)>;

ll n;
vvint edges;
map<pint, pair<ll, modint>> dp;

void treeDP(ll src, ll to) {
  if (dp.count(mp(src, to)))
    return;
  ll x;
  modint y;
  if (dp.count(mp(0, to))) {
    // puts("yay");
    // cout<<src<<" "<<to<<endl;
    // cout<<dp[mp(0,to)].first<<" "<<dp[mp(0,to)].second<<endl;
    tie(x, y) = dp[mp(0, to)];
    y *= fact_inv[n - 1];
    y *= fact[n - 1 - dp[mp(to, src)].first];
    y *= fact[dp[mp(to, src)].first];
    y /= dp[mp(to, src)].second;
    x = n - dp[mp(to, src)].first;
    // cout<<x<<" "<<y<<endl<<endl;
  } else {
    x = 0;
    y = 1;
    for (auto e : edges[to]) {
      if (e == src)
        continue;
      if (dp.count(mp(to, e)) == 0)
        treeDP(to, e);
      ll dx;
      modint dy;
      tie(dx, dy) = dp[mp(to, e)];
      x += dx;
      y *= dy;
      y *= fact_inv[dx];
    }
    y *= fact[x];
    x++;
  }
  dp[mp(src, to)] = mp(x, y);
}

int main() {
  cout << fixed << setprecision(10);

  cin >> n;
  edges.resize(n + 1);
  rep(i, n - 1) {
    ll a, b;
    cin >> a >> b;
    edges[a].push_back(b);
    edges[b].push_back(a);
  }

  init_fact(2e5 + 100);

  queue<ll> q;
  q.push(1);
  set<ll> used;
  while (!q.empty()) {
    ll src = q.front();
    q.pop();
    if (used.count(src))
      continue;
    used.insert(src);
    treeDP(0, src);
    for (auto to : edges[src]) {
      if (used.count(to))
        continue;
      q.push(to);
    }
  }

  rep(i, n) { cout << dp[mp(0, i + 1)].second << endl; }

  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;

typedef unsigned long ul;
typedef unsigned long long ull;
typedef long long ll;
typedef vector<ll> vint;
typedef vector<vector<ll>> vvint;
typedef vector<vector<vector<ll>>> vvvint;
typedef vector<string> vstring;
typedef vector<vector<string>> vvstring;
typedef vector<char> vchar;
typedef vector<vector<char>> vvchar;
typedef vector<long double> vdouble;
typedef vector<vector<long double>> vvdouble;
typedef vector<vector<vector<long double>>> vvvdouble;
typedef pair<ll, ll> pint;
typedef vector<pint> vpint;
typedef vector<bool> vbool;

#define rep(i, n) for (ll i = 0; i < n; i++)
#define repf(i, f, n) for (ll i = f; i < n; i++)
#define repr(i, n) for (ll i = n - 1; i >= 0; i--)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define ALL(obj) (obj).begin(), (obj).end()
// #define LLONG_MAX 9223372036854775806
#define vmax(vec) *max_element(vec.begin(), vec.end())
#define vmin(vec) *min_element(vec.begin(), vec.end())
#define vsort(vec) sort(vec.begin(), vec.end())
#define vsortgr(vec) sort(vec.begin(), vec.end(), greater<ll>())
#define MOD 1000000007
// #define MOD 998244353
// #define MOD LLONG_MAX
const double PI = 3.14159265358979323846;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
  return 0;
}

int dy[] = {0, 0, 1, -1};
int dx[] = {
    1,
    -1,
    0,
    0,
};

void printv(vint &v) {
  for (auto e : v)
    cout << e << " ";
  cout << endl;
}

// 繰り返し二乗法
ll power(ll a, ll b) {
  if (a == 1)
    return a;
  // if(a==0)re
  ll res = 1;
  while (b > 0) {
    if (b & 1)
      res = res * a % MOD;
    a = a * a % MOD;
    b >>= 1;
  }
  return res;
}

const int MAX = 2100000;

ll fact[MAX], fact_inv[MAX];

void init_fact(ll n) {
  fact[0] = 1;
  // 階乗の計算
  for (ll i = 0; i < n; i++)
    fact[i + 1] = fact[i] * (i + 1) % MOD;
  fact_inv[n] = power(fact[n], MOD - 2);
  // 逆元の計算
  for (ll i = n - 1; i >= 0; i--)
    fact_inv[i] = fact_inv[i + 1] * (i + 1) % MOD;
}

ll comb(ll n, ll r) {
  return (fact[n] * fact_inv[r]) % MOD * fact_inv[n - r] % MOD;
}

ll perm(ll n, ll r) { return (fact[n] * fact_inv[n - r]) % MOD; }
template <int mod> struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if ((x += p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if ((x += mod - p.x) >= mod)
      x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int)(1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while (n > 0) {
      if (n & 1)
        ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt<mod>(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt<(int)(1e9 + 7)>;

ll n;
vvint edges;
map<pint, pair<ll, modint>> dp;

void treeDP(ll src, ll to) {
  if (dp.count(mp(src, to)))
    return;
  ll x;
  modint y;
  if (dp.count(mp(0, to))) {
    // puts("yay");
    // cout<<src<<" "<<to<<endl;
    // cout<<dp[mp(0,to)].first<<" "<<dp[mp(0,to)].second<<endl;
    tie(x, y) = dp[mp(0, to)];
    y *= fact_inv[n - 1];
    y *= fact[n - 1 - dp[mp(to, src)].first];
    y *= fact[dp[mp(to, src)].first];
    y /= dp[mp(to, src)].second;
    x = n - dp[mp(to, src)].first;
    // cout<<x<<" "<<y<<endl<<endl;
  } else {
    x = 0;
    y = 1;
    for (auto e : edges[to]) {
      if (e == src)
        continue;
      if (dp.count(mp(to, e)) == 0)
        treeDP(to, e);
      ll dx;
      modint dy;
      tie(dx, dy) = dp[mp(to, e)];
      x += dx;
      y *= dy;
      y *= fact_inv[dx];
    }
    y *= fact[x];
    x++;
  }
  dp[mp(src, to)] = mp(x, y);
}

int main() {
  cout << fixed << setprecision(10);

  cin >> n;
  edges.resize(n + 1);
  rep(i, n - 1) {
    ll a, b;
    cin >> a >> b;
    edges[a].push_back(b);
    edges[b].push_back(a);
  }

  init_fact(2e5 + 100);

  rep(i, n) {
    treeDP(0, i + 1);
    cout << dp[mp(0, i + 1)].second << endl;
  }

  return 0;
}