Problem p02728 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// #include "atcoder/all"

using namespace std;

const double PI = 3.14159265358979323846;
typedef long long ll;
const double EPS = 1e-9;
#define rep(i, n) for (int i = 0; i < (n); ++i)
typedef pair<ll, ll> P;
const ll INF = 10e17;
#define cmin(x, y) x = min(x, y)
#define cmax(x, y) x = max(x, y)
#define ret() return 0;

double equal(double a, double b) { return fabs(a - b) < DBL_EPSILON; }

std::istream &operator>>(std::istream &in, set<int> &o) {
  int a;
  in >> a;
  o.insert(a);
  return in;
}

std::istream &operator>>(std::istream &in, queue<int> &o) {
  ll a;
  in >> a;
  o.push(a);
  return in;
}

bool contain(set<int> &s, int a) { return s.find(a) != s.end(); }

typedef priority_queue<ll, vector<ll>, greater<ll>> PQ_ASK;
const int mod = 1000000007;

struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}

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

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

  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }

  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }

  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }

  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }

  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }

  mint &operator/=(const mint a) { return (*this) *= a.inv(); }

  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }

  friend std::istream &operator>>(std::istream &in, mint &o) {
    ll a;
    in >> a;
    o = a;
    return in;
  }

  friend std::ostream &operator<<(std::ostream &out, const mint &o) {
    out << o.x;
    return out;
  }
};

struct Triangle {
  int parent;
  vector<int> children;
};

class Tree {
  vector<vector<int>> edges;

public:
  Tree(int n) : edges(n) {}

  void edge(int i, int j) {
    edges[i].push_back(j);
    edges[j].push_back(i);
  }

  vector<Triangle> root(int r) {
    vector<Triangle> leafs;

    queue<int> vs;
    vs.push(r);
    vector<bool> check(edges.size(), false);
    check[r] = true;
    while (!vs.empty()) {
      int k = vs.front();
      Triangle triangle;
      triangle.parent = k;

      for (int i : edges[k]) {
        if (check[i])
          continue;
        check[i] = true;
        triangle.children.push_back(i);
        vs.push(i);
      }
      vs.pop();
      leafs.push_back(triangle);
    }

    reverse(leafs.begin(), leafs.end());
    return leafs;
  }
};

struct combination {
  vector<mint> fact, ifact;

  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }

  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
} combination(1000000);

mint factor(int i) { return combination.fact[i]; }

int main() {
  int n;
  cin >> n;
  vector<P> v(n - 1);
  for (P &p : v)
    cin >> p.first >> p.second, p.first--, p.second--;

  Tree tree(n);
  for (P p : v)
    tree.edge(p.first, p.second);

  rep(i, n) {
    auto leafs = tree.root(i);

    vector<int> child_counts(n);
    for (Triangle &t : leafs) {

      int parent = t.parent;
      for (int child : t.children) {
        child_counts[parent] += child_counts[child];
        child_counts[parent]++;
      }
    }

    vector<mint> dp(n, 1);
    for (Triangle &t : leafs) {
      int parent = t.parent;

      mint parent_factor = factor(child_counts[parent]);
      mint child_factor = 1;
      mint child_comb = 1;

      for (int child : t.children) {
        child_factor *= factor(child_counts[child] + 1);
      }

      for (int child : t.children) {
        child_comb *= dp[child];
      }

      mint now = parent_factor * child_comb / child_factor;

      dp[parent] = now;
    }

    cout << dp[i] << endl;
  }
}


Fixed submission:
#include <bits/stdc++.h>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// #include "atcoder/all"

using namespace std;

const double PI = 3.14159265358979323846;
typedef long long ll;
const double EPS = 1e-9;
#define rep(i, n) for (int i = 0; i < (n); ++i)
typedef pair<ll, ll> P;
const ll INF = 10e17;
#define cmin(x, y) x = min(x, y)
#define cmax(x, y) x = max(x, y)
#define ret() return 0;

double equal(double a, double b) { return fabs(a - b) < DBL_EPSILON; }

std::istream &operator>>(std::istream &in, set<int> &o) {
  int a;
  in >> a;
  o.insert(a);
  return in;
}

std::istream &operator>>(std::istream &in, queue<int> &o) {
  ll a;
  in >> a;
  o.push(a);
  return in;
}

bool contain(set<int> &s, int a) { return s.find(a) != s.end(); }

typedef priority_queue<ll, vector<ll>, greater<ll>> PQ_ASK;
const int mod = 1000000007;

struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}

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

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

  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }

  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }

  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }

  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }

  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }

  mint &operator/=(const mint a) { return (*this) *= a.inv(); }

  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }

  friend std::istream &operator>>(std::istream &in, mint &o) {
    ll a;
    in >> a;
    o = a;
    return in;
  }

  friend std::ostream &operator<<(std::ostream &out, const mint &o) {
    out << o.x;
    return out;
  }
};

struct Triangle {
  int parent;
  vector<int> children;
};

class Tree {
  vector<vector<int>> edges;

public:
  Tree(int n) : edges(n) {}

  void edge(int i, int j) {
    edges[i].push_back(j);
    edges[j].push_back(i);
  }

  vector<Triangle> root(int r) {
    vector<Triangle> leafs;

    queue<int> vs;
    vs.push(r);
    vector<bool> check(edges.size(), false);
    check[r] = true;
    while (!vs.empty()) {
      int k = vs.front();
      Triangle triangle;
      triangle.parent = k;

      for (int i : edges[k]) {
        if (check[i])
          continue;
        check[i] = true;
        triangle.children.push_back(i);
        vs.push(i);
      }
      vs.pop();
      leafs.push_back(triangle);
    }

    reverse(leafs.begin(), leafs.end());
    return leafs;
  }
};

struct combination {
  vector<mint> fact, ifact;

  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }

  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
} combination(1000000);

mint factor(int i) { return combination.fact[i]; }

int main() {
  int n;
  cin >> n;
  vector<P> v(n - 1);
  for (P &p : v)
    cin >> p.first >> p.second, p.first--, p.second--;

  Tree tree(n);
  for (P p : v)
    tree.edge(p.first, p.second);

  auto leafs = tree.root(0);

  vector<int> child_counts(n);
  for (Triangle &t : leafs) {

    int parent = t.parent;
    for (int child : t.children) {
      child_counts[parent] += child_counts[child];
      child_counts[parent]++;
    }
  }
  vector<mint> dp(n, 1);
  vector<mint> child_factor_muls(n);
  vector<mint> child_dp_muls(n);
  vector<int> parents(n, -1);

  for (Triangle &t : leafs) {
    int parent = t.parent;

    mint parent_factor = factor(child_counts[parent]);
    mint child_factor_mul = 1;
    mint child_dp_mul = 1;

    for (int child : t.children) {
      child_factor_mul *= factor(child_counts[child] + 1);
    }

    for (int child : t.children) {
      child_dp_mul *= dp[child];
    }

    for (int child : t.children) {
      parents[child] = t.parent;
    }

    child_factor_muls[parent] = child_factor_mul;
    child_dp_muls[parent] = child_dp_mul;
    mint now = parent_factor * child_dp_mul / child_factor_mul;
    dp[parent] = now;
  }
  vector<mint> ans(n);
  ans[0] = dp[0];

  reverse(leafs.begin(), leafs.end());

  auto calc_new_dp = [&](int prev_root, int new_root) -> mint {
    mint prev_root_factor_muls = child_factor_muls[prev_root];
    mint exclude_factor = factor(child_counts[new_root] + 1);
    mint factor_mul = prev_root_factor_muls / exclude_factor;
    mint dp_mul = child_dp_muls[prev_root] / dp[new_root];
    mint all_factor = factor(n - 2 - child_counts[new_root]);
    mint now = all_factor * dp_mul / factor_mul;
    return now;
  };

  auto calc_new_leaf_size = [&](int prev_root, int new_root) -> int {
    return n - 1 - child_counts[new_root];
  };

  auto move_root = [&](int new_root) {
    int prev_root = parents[new_root];
    if (prev_root == -1)
      return;
    //        child_counts[new_root] = n - 1;
    mint next = calc_new_dp(prev_root, new_root);
    child_dp_muls[new_root] *= next;
    child_factor_muls[new_root] *=
        factor(calc_new_leaf_size(prev_root, new_root));

    mint dp_mul = child_dp_muls[new_root];
    mint factor_mul = child_factor_muls[new_root];

    mint now = factor(n - 1) * dp_mul / factor_mul;
    ans[new_root] = now;
    dp[new_root] = now;
  };

  for (Triangle &t : leafs) {
    move_root(t.parent);
  }

  for (mint a : ans)
    cout << a << endl;
}