Problem p02728 (C++)

Buggy submission (status: Runtime Error):


#include <algorithm>
#include <array>
#include <assert.h>
#include <bitset>
#include <climits>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <math.h>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>

#define FOR(i, a, n) for (int i = (a); i < (n); ++i)
#define FOE(i, a) for (auto i : a)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define SUM(x) std::accumulate(ALL(x), 0LL)
#define MIN(v) *std::min_element(v.begin(), v.end())
#define MAX(v) *std::max_element(v.begin(), v.end())
#define EXIST(v, x) (std::find(v.begin(), v.end(), x) != v.end())
#define IS_BIT_ON(bit, i) (bit & (1 << i))
#define BIT_ON(bit, i) (bit |= (1 << i))
#define BIT_OFF(bit, i) (bit &= ~(1 << i))
#define BIT_COUNT(bit) (__builtin_popcount(bit))

typedef long long LL;

template <typename T> std::vector<T> make_v(size_t a) {
  return std::vector<T>(a);
}

template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return std::vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
} // C++14
template <typename T, typename V>
typename std::enable_if<std::is_class<T>::value == 0>::type fill_v(T &t,
                                                                   const V &v) {
  t = v;
}

template <typename T, typename V>
typename std::enable_if<std::is_class<T>::value != 0>::type fill_v(T &t,
                                                                   const V &v) {
  for (auto &e : t)
    fill_v(e, v);
}

template <class T> inline T ceil(T a, T b) { return (a + b - 1) / b; }

void print() { std::cout << std::endl; }

template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
  std::cout << head;
  if (sizeof...(tail) != 0) {
    std::cout << " ";
  }
  print(std::forward<Tail>(tail)...);
}

template <class T> void print(std::vector<T> &v) {
  for (auto &a : v) {
    std::cout << a;
    if (&a != &v.back()) {
      std::cout << " ";
    }
  }
  std::cout << std::endl;
}

template <class T> void print(std::vector<std::vector<T>> &vv) {
  for (auto &v : vv) {
    print(v);
  }
}

void debug() { std::cerr << std::endl; }

template <class Head, class... Tail> void debug(Head &&head, Tail &&...tail) {
  std::cerr << head;
  if (sizeof...(tail) != 0) {
    std::cerr << " ";
  }
  print(std::forward<Tail>(tail)...);
}

template <class T> void debug(std::vector<T> &v) {
  for (auto &a : v) {
    std::cerr << a;
    if (&a != &v.back()) {
      std::cerr << " ";
    }
  }
  std::cerr << std::endl;
}

template <class T> void debug(std::vector<std::vector<T>> &vv) {
  for (auto &v : vv) {
    print(v);
  }
}

inline bool inside(long long y, long long x, long long H, long long W) {
  return 0 <= y and y < H and 0 <= x and x < W;
}

template <class T> inline double euclidean_distance(T y1, T x1, T y2, T x2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}

template <class T> inline double manhattan_distance(T y1, T x1, T y2, T x2) {
  return abs(x1 - x2) + abs(y1 - y2);
}

template <typename T> T &chmin(T &a, const T &b) { return a = std::min(a, b); }

template <typename T> T &chmax(T &a, const T &b) { return a = std::max(a, b); }

template <class T> inline std::vector<T> unique(std::vector<T> v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
  return v;
}

long long sum_of_arithmetic_progression(long long s, long long d, long long n) {
  return n * (2 * s + (n - 1) * d) / 2;
}

bool is_power_of_two(long long x) { return !(x & (x - 1)); }

long long gcd(long long a, long long b) {
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b);
}

long long gcd(std::vector<long long> &v) {
  long long ans = v[0];
  for (int i = 1; i < (int)v.size(); ++i) {
    ans = gcd(ans, v[i]);
  }
  return ans;
}

long long lcm(long long a, long long b) {
  long long g = gcd(a, b);
  return a / g * b;
}

const int INF = 1u << 30u;
const long long LINF = 1ull << 58u;
const double EPS = 1e-9;
const long double PI = acos(-1.0);
const std::vector<int> dy2 = {0, 1}, dx2 = {1, 0};
const std::vector<int> dy4 = {0, 1, 0, -1}, dx4 = {1, 0, -1, 0};
const std::vector<int> dy8 = {0, -1, 0, 1, 1, -1, -1, 1},
                       dx8 = {1, 0, -1, 0, 1, 1, -1, -1};

using namespace std;

const int MOD = 1000000000 + 7;

template <int mod> struct mint {
  long long x;

  mint(long long x = 0) : x(x % 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(long long 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;
  }
};

long long modpow(long long base, long long exp, long long mod) {
  base %= mod;
  long long result = 1;
  while (exp > 0) {
    if (exp & 1) {
      result = (result * base) % mod;
    }
    base = (base * base) % mod;
    exp >>= 1;
  }
  return result;
}

long long combination(long long n, long long r) {
  uint64_t ans = 1;
  for (uint64_t d = 1; d <= r; ++d) {
    ans *= n--;
    ans /= d;
  }
  return ans;
}

class Combination {
public:
  int mod;
  vector<long long> fact;
  vector<long long> inv;

  Combination(int n, int mod) : mod(mod) {
    assert(0 < n);
    this->fact.resize(n + 1, 1);
    this->inv.resize(n + 1, 1);

    for (int i = 1; i < fact.size(); ++i) {
      this->fact[i] = (i * this->fact[i - 1]) % this->mod;
      this->inv[i] = modpow(this->fact[i], this->mod - 2, this->mod);
    }
  }

  long long nCr(int n, int k) {
    assert(0 <= n and n < this->fact.size() and 0 <= k);
    assert(n >= k);
    auto a = this->fact[n];
    auto b = (this->inv[k] * this->inv[n - k]) % this->mod;
    return (a * b) % this->mod;
  }

  long long nHr(int n, int k) { return nCr(n + k - 1, k); }
};

Combination comb(150000, MOD);

// 全方位木DP
template <typename T> class Rerooting {
public:
  const int num_of_nodes;
  std::vector<T> ans;

private:
  std::vector<std::vector<int>> tree;
  std::vector<std::vector<int>> children; // children[u] = [c1, c2, ...]

  // 問題特有のデータ
  std::vector<std::unordered_map<int, T>>
      dp; // dp[u][parent] =
          // 親がparentであるときのノードuの目的値(uが根のときはparentはnum_of_nodesとなる)
  vector<int> num_children;

public:
  Rerooting(const int num_of_nodes) : num_of_nodes(num_of_nodes) {
    this->ans.resize(this->num_of_nodes);
    this->tree.resize(this->num_of_nodes);
    this->children.resize(this->num_of_nodes + 1);
    this->dp.resize(this->num_of_nodes);
    this->num_children.resize(this->num_of_nodes);
  }

  void add_undirected_edge(const int u, const int v) {
    this->tree[u].emplace_back(v);
    this->tree[v].emplace_back(u);
  }

  void solve() {
    const int root = 0;

    // rootを固定したときの，各ノードの値を求める
    vector<int> num_children(this->num_of_nodes);
    dfs(root, this->num_of_nodes);

    // 各ノードをrootとしたときの値を求める
    dfs2(root, this->num_of_nodes, 1);
  }

  // dfs1をすべてのノードに対して行う
  void debug() {
    for (int root = 0; root < this->num_of_nodes; ++root) {
      dfs(root, this->num_of_nodes);
      this->ans[root] = dp[root][this->num_of_nodes];
    }
  }

private:
  void dfs(const int u, const int parent) {
    this->children[parent].emplace_back(u);

    this->num_children[u] = 0;
    this->dp[u][parent] = 1;
    for (int i = 0; i < this->tree[u].size(); ++i) {
      const int v = this->tree[u][i];
      if (v == parent) {
        continue;
      }

      this->dfs(v, u);

      this->num_children[u] += this->num_children[v];
      dp[u][parent] *= dp[v][u] * comb.nCr(num_children[u], num_children[v]);
    }

    this->num_children[u]++;
  }

  void dfs2(const int u, const int parent, mint<MOD> t) {

    this->ans[u] =
        dp[u][parent] * t *
        comb.nCr(this->num_of_nodes - 1, this->num_of_nodes - num_children[u]);

    for (int v : this->children[u]) {
      auto t2 =
          ans[u] / dp[v][u] / comb.nCr(num_of_nodes - 1, this->num_children[v]);
      dfs2(v, u, t2);
    }
  }
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  int N;
  cin >> N;

  Rerooting<mint<MOD>> rr(N);

  auto tree = make_v<int>(N, 0);
  FOR(i, 0, N - 1) {
    int A, B;
    cin >> A >> B;
    A--;
    B--;
    rr.add_undirected_edge(A, B);
  }

  rr.solve();
  //    rr.debug();

  FOR(i, 0, N) { print(rr.ans[i].x); }

  return 0;
}


Fixed submission:


#include <algorithm>
#include <array>
#include <assert.h>
#include <bitset>
#include <climits>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <math.h>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>

#define FOR(i, a, n) for (int i = (a); i < (n); ++i)
#define FOE(i, a) for (auto i : a)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define SUM(x) std::accumulate(ALL(x), 0LL)
#define MIN(v) *std::min_element(v.begin(), v.end())
#define MAX(v) *std::max_element(v.begin(), v.end())
#define EXIST(v, x) (std::find(v.begin(), v.end(), x) != v.end())
#define IS_BIT_ON(bit, i) (bit & (1 << i))
#define BIT_ON(bit, i) (bit |= (1 << i))
#define BIT_OFF(bit, i) (bit &= ~(1 << i))
#define BIT_COUNT(bit) (__builtin_popcount(bit))

typedef long long LL;

template <typename T> std::vector<T> make_v(size_t a) {
  return std::vector<T>(a);
}

template <typename T, typename... Ts> auto make_v(size_t a, Ts... ts) {
  return std::vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
} // C++14
template <typename T, typename V>
typename std::enable_if<std::is_class<T>::value == 0>::type fill_v(T &t,
                                                                   const V &v) {
  t = v;
}

template <typename T, typename V>
typename std::enable_if<std::is_class<T>::value != 0>::type fill_v(T &t,
                                                                   const V &v) {
  for (auto &e : t)
    fill_v(e, v);
}

template <class T> inline T ceil(T a, T b) { return (a + b - 1) / b; }

void print() { std::cout << std::endl; }

template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
  std::cout << head;
  if (sizeof...(tail) != 0) {
    std::cout << " ";
  }
  print(std::forward<Tail>(tail)...);
}

template <class T> void print(std::vector<T> &v) {
  for (auto &a : v) {
    std::cout << a;
    if (&a != &v.back()) {
      std::cout << " ";
    }
  }
  std::cout << std::endl;
}

template <class T> void print(std::vector<std::vector<T>> &vv) {
  for (auto &v : vv) {
    print(v);
  }
}

void debug() { std::cerr << std::endl; }

template <class Head, class... Tail> void debug(Head &&head, Tail &&...tail) {
  std::cerr << head;
  if (sizeof...(tail) != 0) {
    std::cerr << " ";
  }
  print(std::forward<Tail>(tail)...);
}

template <class T> void debug(std::vector<T> &v) {
  for (auto &a : v) {
    std::cerr << a;
    if (&a != &v.back()) {
      std::cerr << " ";
    }
  }
  std::cerr << std::endl;
}

template <class T> void debug(std::vector<std::vector<T>> &vv) {
  for (auto &v : vv) {
    print(v);
  }
}

inline bool inside(long long y, long long x, long long H, long long W) {
  return 0 <= y and y < H and 0 <= x and x < W;
}

template <class T> inline double euclidean_distance(T y1, T x1, T y2, T x2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}

template <class T> inline double manhattan_distance(T y1, T x1, T y2, T x2) {
  return abs(x1 - x2) + abs(y1 - y2);
}

template <typename T> T &chmin(T &a, const T &b) { return a = std::min(a, b); }

template <typename T> T &chmax(T &a, const T &b) { return a = std::max(a, b); }

template <class T> inline std::vector<T> unique(std::vector<T> v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
  return v;
}

long long sum_of_arithmetic_progression(long long s, long long d, long long n) {
  return n * (2 * s + (n - 1) * d) / 2;
}

bool is_power_of_two(long long x) { return !(x & (x - 1)); }

long long gcd(long long a, long long b) {
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b);
}

long long gcd(std::vector<long long> &v) {
  long long ans = v[0];
  for (int i = 1; i < (int)v.size(); ++i) {
    ans = gcd(ans, v[i]);
  }
  return ans;
}

long long lcm(long long a, long long b) {
  long long g = gcd(a, b);
  return a / g * b;
}

const int INF = 1u << 30u;
const long long LINF = 1ull << 58u;
const double EPS = 1e-9;
const long double PI = acos(-1.0);
const std::vector<int> dy2 = {0, 1}, dx2 = {1, 0};
const std::vector<int> dy4 = {0, 1, 0, -1}, dx4 = {1, 0, -1, 0};
const std::vector<int> dy8 = {0, -1, 0, 1, 1, -1, -1, 1},
                       dx8 = {1, 0, -1, 0, 1, 1, -1, -1};

using namespace std;

const int MOD = 1000000000 + 7;

template <int mod> struct mint {
  long long x;

  mint(long long x = 0) : x(x % 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(long long 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;
  }
};

long long modpow(long long base, long long exp, long long mod) {
  base %= mod;
  long long result = 1;
  while (exp > 0) {
    if (exp & 1) {
      result = (result * base) % mod;
    }
    base = (base * base) % mod;
    exp >>= 1;
  }
  return result;
}

long long combination(long long n, long long r) {
  uint64_t ans = 1;
  for (uint64_t d = 1; d <= r; ++d) {
    ans *= n--;
    ans /= d;
  }
  return ans;
}

class Combination {
public:
  int mod;
  vector<long long> fact;
  vector<long long> inv;

  Combination(int n, int mod) : mod(mod) {
    assert(0 < n);
    this->fact.resize(n + 1, 1);
    this->inv.resize(n + 1, 1);

    for (int i = 1; i < fact.size(); ++i) {
      this->fact[i] = (i * this->fact[i - 1]) % this->mod;
      this->inv[i] = modpow(this->fact[i], this->mod - 2, this->mod);
    }
  }

  long long nCr(int n, int k) {
    assert(0 <= n and n < this->fact.size() and 0 <= k);
    assert(n >= k);
    auto a = this->fact[n];
    auto b = (this->inv[k] * this->inv[n - k]) % this->mod;
    return (a * b) % this->mod;
  }

  long long nHr(int n, int k) { return nCr(n + k - 1, k); }
};

Combination comb(250000, MOD);

// 全方位木DP
template <typename T> class Rerooting {
public:
  const int num_of_nodes;
  std::vector<T> ans;

private:
  std::vector<std::vector<int>> tree;
  std::vector<std::vector<int>> children; // children[u] = [c1, c2, ...]

  // 問題特有のデータ
  std::vector<std::unordered_map<int, T>>
      dp; // dp[u][parent] =
          // 親がparentであるときのノードuの目的値(uが根のときはparentはnum_of_nodesとなる)
  vector<int> num_children;

public:
  Rerooting(const int num_of_nodes) : num_of_nodes(num_of_nodes) {
    this->ans.resize(this->num_of_nodes);
    this->tree.resize(this->num_of_nodes);
    this->children.resize(this->num_of_nodes + 1);
    this->dp.resize(this->num_of_nodes);
    this->num_children.resize(this->num_of_nodes);
  }

  void add_undirected_edge(const int u, const int v) {
    this->tree[u].emplace_back(v);
    this->tree[v].emplace_back(u);
  }

  void solve() {
    const int root = 0;

    // rootを固定したときの，各ノードの値を求める
    vector<int> num_children(this->num_of_nodes);
    dfs(root, this->num_of_nodes);

    // 各ノードをrootとしたときの値を求める
    dfs2(root, this->num_of_nodes, 1);
  }

  // dfs1をすべてのノードに対して行う
  void debug() {
    for (int root = 0; root < this->num_of_nodes; ++root) {
      dfs(root, this->num_of_nodes);
      this->ans[root] = dp[root][this->num_of_nodes];
    }
  }

private:
  void dfs(const int u, const int parent) {
    this->children[parent].emplace_back(u);

    this->num_children[u] = 0;
    this->dp[u][parent] = 1;
    for (int i = 0; i < this->tree[u].size(); ++i) {
      const int v = this->tree[u][i];
      if (v == parent) {
        continue;
      }

      this->dfs(v, u);

      this->num_children[u] += this->num_children[v];
      dp[u][parent] *= dp[v][u] * comb.nCr(num_children[u], num_children[v]);
    }

    this->num_children[u]++;
  }

  void dfs2(const int u, const int parent, mint<MOD> t) {

    this->ans[u] =
        dp[u][parent] * t *
        comb.nCr(this->num_of_nodes - 1, this->num_of_nodes - num_children[u]);

    for (int v : this->children[u]) {
      auto t2 =
          ans[u] / dp[v][u] / comb.nCr(num_of_nodes - 1, this->num_children[v]);
      dfs2(v, u, t2);
    }
  }
};

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  int N;
  cin >> N;

  Rerooting<mint<MOD>> rr(N);

  auto tree = make_v<int>(N, 0);
  FOR(i, 0, N - 1) {
    int A, B;
    cin >> A >> B;
    A--;
    B--;
    rr.add_undirected_edge(A, B);
  }

  rr.solve();
  //    rr.debug();

  FOR(i, 0, N) { print(rr.ans[i].x); }

  return 0;
}