Problem p03492 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <cassert>
#include <cstdio>
#include <functional>
#include <iostream>
#include <map>
#include <set>
#include <vector>
using namespace std;

const int MOD = 1e9 + 7;

const int N = 5000001;
long long fact[N];
long long invfact[N];
long long inv[N];
void init() {
  fact[0] = fact[1] = 1;
  for (int i = 2; i < N; i++)
    fact[i] = fact[i - 1] * i % MOD;
  inv[1] = 1;
  for (int i = 2; i < N; i++)
    inv[i] = (MOD - MOD / i) * inv[MOD % i] % MOD;
  invfact[0] = invfact[1] = 1;
  for (int i = 2; i < N; i++)
    invfact[i] = invfact[i - 1] * inv[i] % MOD;
}
long long C(long long n, long long r) {
  if (n < 0 || r < 0 || n < r)
    return 0;
  return fact[n] * invfact[n - r] % MOD * invfact[r] % MOD;
}

vector<int> Centroid(int root, const vector<vector<int>> &g,
                     const vector<bool> &dead) {
  int alive_cnt = 0;
  map<int, int> alive_node;
  function<void(int, int)> count_alive = [&](int u, int prev) {
    alive_node[u] = alive_cnt++;
    for (auto v : g[u])
      if (v != prev && !dead[v]) {
        count_alive(v, u);
      }
  };
  count_alive(root, -1);
  vector<int> centroid;
  vector<int> sz(alive_cnt);
  function<void(int, int)> dfs = [&](int u, int prev) {
    int x = alive_node[u];
    sz[x] = 1;
    bool is_centroid = true;
    for (auto v : g[u])
      if (v != prev && !dead[v]) {
        dfs(v, u);
        int y = alive_node[v];
        sz[x] += sz[y];
        if (sz[y] > alive_cnt / 2)
          is_centroid = false;
      }
    if (alive_cnt - sz[x] > alive_cnt / 2)
      is_centroid = false;
    if (is_centroid)
      centroid.push_back(u);
  };
  dfs(root, -1);
  return centroid;
}

int main() {
  init();
  int n;
  scanf("%d", &n);
  vector<vector<int>> g(n);
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    a--, b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  vector<bool> dead(n);
  auto get = Centroid(0, g, dead);
  if (get.size() == 2) {
    long long ans = fact[n / 2] * fact[n / 2] % MOD;
    printf("%lld\n", ans);
    return 0;
  }
  int centroid = get[0];
  vector<int> sz(n);
  function<void(int, int)> get_size = [&](int u, int prev) {
    sz[u] = 1;
    for (auto v : g[u])
      if (v != prev) {
        get_size(v, u);
        sz[u] += sz[v];
      }
  };
  get_size(centroid, -1);
  vector<int> subtrees;
  for (auto v : g[centroid])
    subtrees.push_back(sz[v]);
  int k = (int)subtrees.size();
  vector<vector<long long>> dp(k + 1, vector<long long>(n + 1, 0));
  dp[0][1] = 1;
  for (int i = 0; i < k; i++) {
    int num = subtrees[i];
    for (int j = 0; j <= n; j++) {
      for (int l = 0; l <= num; l++) {
        if (l & 1) {
          (dp[i + 1][j + num - l] -= dp[i][j] * C(num, l) % MOD * fact[num] %
                                     MOD * invfact[num - l] % MOD) %= MOD;
        } else {
          (dp[i + 1][j + num - l] += dp[i][j] * C(num, l) % MOD * fact[num] %
                                     MOD * invfact[num - l] % MOD) %= MOD;
        }
      }
    }
  }
  long long ans = 0;
  for (int i = 0; i <= n; i++) {
    (ans += dp[k][i] * fact[i] % MOD) %= MOD;
  }
  ans = ((ans % MOD) + MOD) % MOD;
  printf("%lld\n", ans);
  return 0;
}


Fixed submission:
#include <algorithm>
#include <cassert>
#include <cstdio>
#include <functional>
#include <iostream>
#include <map>
#include <set>
#include <vector>
using namespace std;

const int MOD = 1e9 + 7;

const int N = 5000001;
long long fact[N];
long long invfact[N];
long long inv[N];
void init() {
  fact[0] = fact[1] = 1;
  for (int i = 2; i < N; i++)
    fact[i] = fact[i - 1] * i % MOD;
  inv[1] = 1;
  for (int i = 2; i < N; i++)
    inv[i] = (MOD - MOD / i) * inv[MOD % i] % MOD;
  invfact[0] = invfact[1] = 1;
  for (int i = 2; i < N; i++)
    invfact[i] = invfact[i - 1] * inv[i] % MOD;
}
long long C(long long n, long long r) {
  if (n < 0 || r < 0 || n < r)
    return 0;
  return fact[n] * invfact[n - r] % MOD * invfact[r] % MOD;
}

vector<int> Centroid(int root, const vector<vector<int>> &g,
                     const vector<bool> &dead) {
  int alive_cnt = 0;
  map<int, int> alive_node;
  {
    function<void(int, int)> count_alive = [&](int u, int prev) {
      alive_node[u] = alive_cnt++;
      for (auto v : g[u])
        if (v != prev && !dead[v]) {
          count_alive(v, u);
        }
    };
    count_alive(root, -1);
  }
  vector<int> centroid;
  vector<int> sz(alive_cnt);
  function<void(int, int)> dfs = [&](int u, int prev) {
    int x = alive_node[u];
    sz[x] = 1;
    bool is_centroid = true;
    for (auto v : g[u])
      if (v != prev && !dead[v]) {
        dfs(v, u);
        int y = alive_node[v];
        sz[x] += sz[y];
        if (sz[y] > alive_cnt / 2)
          is_centroid = false;
      }
    if (alive_cnt - sz[x] > alive_cnt / 2)
      is_centroid = false;
    if (is_centroid)
      centroid.push_back(u);
  };
  dfs(root, -1);
  return centroid;
}

int main() {
  init();
  int n;
  scanf("%d", &n);
  vector<vector<int>> g(n);
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    a--, b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  vector<bool> dead(n);
  auto get = Centroid(0, g, dead);
  if (get.size() == 2) {
    long long ans = fact[n / 2] * fact[n / 2] % MOD;
    printf("%lld\n", ans);
    return 0;
  }
  int centroid = get[0];
  vector<int> sz(n);
  function<void(int, int)> get_size = [&](int u, int prev) {
    sz[u] = 1;
    for (auto v : g[u])
      if (v != prev) {
        get_size(v, u);
        sz[u] += sz[v];
      }
  };
  get_size(centroid, -1);
  vector<int> subtrees;
  for (auto v : g[centroid])
    subtrees.push_back(sz[v]);
  int k = (int)subtrees.size();
  vector<vector<long long>> dp(k + 1, vector<long long>(n + 1, 0));
  dp[0][1] = 1;
  for (int i = 0; i < k; i++) {
    int num = subtrees[i];
    for (int j = 0; j <= n; j++) {
      for (int l = 0; l <= num; l++) {
        if (l & 1) {
          (dp[i + 1][j + num - l] -= dp[i][j] * C(num, l) % MOD * fact[num] %
                                     MOD * invfact[num - l] % MOD) %= MOD;
        } else {
          (dp[i + 1][j + num - l] += dp[i][j] * C(num, l) % MOD * fact[num] %
                                     MOD * invfact[num - l] % MOD) %= MOD;
        }
      }
    }
  }
  long long ans = 0;
  for (int i = 0; i <= n; i++) {
    (ans += dp[k][i] * fact[i] % MOD) %= MOD;
  }
  ans = ((ans % MOD) + MOD) % MOD;
  printf("%lld\n", ans);
  return 0;
}