Problem p03492 (C++)

Buggy submission (status: Runtime Error):
const long long MOD = 1e9 + 7;
const int N = 1044;

#include <algorithm>
#include <bitset>
#include <cmath>
#include <deque>
#include <iostream>
#include <map>
#include <set>
#include <string>
#include <time.h>
#include <unordered_set>
#include <vector>

using namespace std;

#define int long long
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<ll> vi;

#define forn(i, n) for (int(i) = 0; (i) != (n); (i)++)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define popcount(x) __builtin_popcount(x)
#define popcountll(x) __builtin_popcountll(x)
#define fi first
#define se second
#define re return
#define uniq(x)                                                                \
  sort(all(x));                                                                \
  (x).resize(unique(all(x)) - (x).begin())

#ifdef LOCAL
#define dbg(x) cerr << __LINE__ << " " << #x << " " << x << endl
#define ln cerr << __LINE__ << endl
#else
#define dbg(x) void(0)
#define ln void(0)
#endif // LOCAL

int cx[4] = {-1, 0, 1, 0};
int cy[4] = {0, -1, 0, 1};

ll inq(ll x, ll y) {
  if (!y)
    re 1 % MOD;
  ll l = inq(x, y / 2);
  if (y % 2)
    re l *l % MOD *x % MOD;
  re l *l % MOD;
}

ll rev(ll x) { return inq(x, MOD - 2); }

bool __precomputed_combinatorics = 0;
vector<ll> __fact, __ufact, __rev;

void __precompute_combinatorics() {
  __precomputed_combinatorics = 1;
  __fact.resize(N);
  __ufact.resize(N);
  __rev.resize(N);
  __rev[1] = 1;
  for (int i = 2; i < N; i++)
    __rev[i] = MOD - __rev[MOD % i] * (MOD / i) % MOD;
  __fact[0] = 1, __ufact[0] = 1;
  for (int i = 1; i < N; i++)
    __fact[i] = __fact[i - 1] * i % MOD,
    __ufact[i] = __ufact[i - 1] * __rev[i] % MOD;
}

ll fact(int x) {
  if (!__precomputed_combinatorics)
    __precompute_combinatorics();
  return __fact[x];
}

ll cnk(int n, int k) {
  if (!__precomputed_combinatorics)
    __precompute_combinatorics();
  return __fact[n] * __ufact[n - k] % MOD * __ufact[k] % MOD;
}

int n;
vector<int> graph[N];
int sz[N];

void dfs(int v, int p = 1) {
  sz[v] = 1;
  for (auto u : graph[v])
    if (u != p) {
      dfs(u, v);
      sz[v] += sz[u];
    }
}

signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  vector<vector<ll>> perm_n_objects_exactly_k_on_thier_places(N, vector<ll>(N));
  perm_n_objects_exactly_k_on_thier_places[1][1] = 1;
  perm_n_objects_exactly_k_on_thier_places[0][0] = 1;
  for (int len = 2; len < N; len++) {
    for (int k = 1; k <= len; k++) {
      perm_n_objects_exactly_k_on_thier_places[len][k] =
          cnk(len, k) * perm_n_objects_exactly_k_on_thier_places[len - k][0] %
          MOD;
    }
    perm_n_objects_exactly_k_on_thier_places[len][0] = fact(len);
    for (int k = 1; k <= len; k++) {
      perm_n_objects_exactly_k_on_thier_places[len][0] =
          (perm_n_objects_exactly_k_on_thier_places[len][0] + MOD -
           perm_n_objects_exactly_k_on_thier_places[len][k]) %
          MOD;
    }
  }
  cin >> n;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    graph[a].push_back(b);
    graph[b].push_back(a);
  }
  dfs(1);
  vector<int> cen;
  for (int i = 1; i <= n; i++) {
    int t = 1;
    if (2 * (n - sz[i]) <= n) {
      for (auto u : graph[i]) {
        if (sz[u] < sz[i] && 2 * sz[u] > n)
          t = 0;
      }
    } else
      t = 0;
    if (t)
      cen.push_back(i);
  }
  if (cen.size() == 2) {
    long long ans = 1;
    for (int i = 1; i <= n / 2; i++)
      ans = ans * i % MOD * i % MOD;
    cout << ans;
    return 0;
  }
  int C = cen[0];
  vector<int> sizes;
  for (auto u : graph[C]) {
    if (sz[u] < sz[C])
      sizes.push_back(sz[u]);
    else
      sizes.push_back(n - sz[C]);
  }
  vector<ll> dp(n);
  dp[0] = 1;
  for (int i = 0; i < sizes.size(); i++) {
    for (int have = n - 1 - sizes[i]; have >= 0; have--) {
      for (int sel = sizes[i]; sel > 0; sel--) {
        dp[have + sel] =
            (dp[have + sel] + dp[have] * cnk(sizes[i], sel) % MOD *
                                  cnk(sizes[i], sel) % MOD * fact(sel)) %
            MOD;
      }
    }
  }
  // for (int i = 0; i < n; i++) cout << dp[i] << " "; cout << "\n";
  ll ans = 0;
  for (int i = 0; i < n; i++) {
    if (i % 2 == 0) {
      ans = (ans + dp[i] * fact(n - i)) % MOD;
    } else {
      ans = (ans + MOD * MOD - dp[i] * fact(n - i)) % MOD;
    }
  }
  cout << ans;
}

/* Note:
Check constants at the beginning of the code.
    N is set to 4e5 but be careful in problems with large constant factor.
    Setting N in every problem is more effective.
Check corner cases.
    N = 1
No def int long long for now.
Add something here.
*/


Fixed submission:
const long long MOD = 1e9 + 7;
const int N = 6044;

#include <algorithm>
#include <bitset>
#include <cmath>
#include <deque>
#include <iostream>
#include <map>
#include <set>
#include <string>
#include <time.h>
#include <unordered_set>
#include <vector>

using namespace std;

#define int long long
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<ll> vi;

#define forn(i, n) for (int(i) = 0; (i) != (n); (i)++)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define popcount(x) __builtin_popcount(x)
#define popcountll(x) __builtin_popcountll(x)
#define fi first
#define se second
#define re return
#define uniq(x)                                                                \
  sort(all(x));                                                                \
  (x).resize(unique(all(x)) - (x).begin())

#ifdef LOCAL
#define dbg(x) cerr << __LINE__ << " " << #x << " " << x << endl
#define ln cerr << __LINE__ << endl
#else
#define dbg(x) void(0)
#define ln void(0)
#endif // LOCAL

int cx[4] = {-1, 0, 1, 0};
int cy[4] = {0, -1, 0, 1};

ll inq(ll x, ll y) {
  if (!y)
    re 1 % MOD;
  ll l = inq(x, y / 2);
  if (y % 2)
    re l *l % MOD *x % MOD;
  re l *l % MOD;
}

ll rev(ll x) { return inq(x, MOD - 2); }

bool __precomputed_combinatorics = 0;
vector<ll> __fact, __ufact, __rev;

void __precompute_combinatorics() {
  __precomputed_combinatorics = 1;
  __fact.resize(N);
  __ufact.resize(N);
  __rev.resize(N);
  __rev[1] = 1;
  for (int i = 2; i < N; i++)
    __rev[i] = MOD - __rev[MOD % i] * (MOD / i) % MOD;
  __fact[0] = 1, __ufact[0] = 1;
  for (int i = 1; i < N; i++)
    __fact[i] = __fact[i - 1] * i % MOD,
    __ufact[i] = __ufact[i - 1] * __rev[i] % MOD;
}

ll fact(int x) {
  if (!__precomputed_combinatorics)
    __precompute_combinatorics();
  return __fact[x];
}

ll cnk(int n, int k) {
  if (!__precomputed_combinatorics)
    __precompute_combinatorics();
  return __fact[n] * __ufact[n - k] % MOD * __ufact[k] % MOD;
}

int n;
vector<int> graph[N];
int sz[N];

void dfs(int v, int p = 1) {
  sz[v] = 1;
  for (auto u : graph[v])
    if (u != p) {
      dfs(u, v);
      sz[v] += sz[u];
    }
}

signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  vector<vector<ll>> perm_n_objects_exactly_k_on_thier_places(N, vector<ll>(N));
  perm_n_objects_exactly_k_on_thier_places[1][1] = 1;
  perm_n_objects_exactly_k_on_thier_places[0][0] = 1;
  for (int len = 2; len < N; len++) {
    for (int k = 1; k <= len; k++) {
      perm_n_objects_exactly_k_on_thier_places[len][k] =
          cnk(len, k) * perm_n_objects_exactly_k_on_thier_places[len - k][0] %
          MOD;
    }
    perm_n_objects_exactly_k_on_thier_places[len][0] = fact(len);
    for (int k = 1; k <= len; k++) {
      perm_n_objects_exactly_k_on_thier_places[len][0] =
          (perm_n_objects_exactly_k_on_thier_places[len][0] + MOD -
           perm_n_objects_exactly_k_on_thier_places[len][k]) %
          MOD;
    }
  }
  cin >> n;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    graph[a].push_back(b);
    graph[b].push_back(a);
  }
  dfs(1);
  vector<int> cen;
  for (int i = 1; i <= n; i++) {
    int t = 1;
    if (2 * (n - sz[i]) <= n) {
      for (auto u : graph[i]) {
        if (sz[u] < sz[i] && 2 * sz[u] > n)
          t = 0;
      }
    } else
      t = 0;
    if (t)
      cen.push_back(i);
  }
  if (cen.size() == 2) {
    long long ans = 1;
    for (int i = 1; i <= n / 2; i++)
      ans = ans * i % MOD * i % MOD;
    cout << ans;
    return 0;
  }
  int C = cen[0];
  vector<int> sizes;
  for (auto u : graph[C]) {
    if (sz[u] < sz[C])
      sizes.push_back(sz[u]);
    else
      sizes.push_back(n - sz[C]);
  }
  vector<ll> dp(n);
  dp[0] = 1;
  for (int i = 0; i < sizes.size(); i++) {
    for (int have = n - 1 - sizes[i]; have >= 0; have--) {
      for (int sel = sizes[i]; sel > 0; sel--) {
        dp[have + sel] =
            (dp[have + sel] + dp[have] * cnk(sizes[i], sel) % MOD *
                                  cnk(sizes[i], sel) % MOD * fact(sel)) %
            MOD;
      }
    }
  }
  // for (int i = 0; i < n; i++) cout << dp[i] << " "; cout << "\n";
  ll ans = 0;
  for (int i = 0; i < n; i++) {
    if (i % 2 == 0) {
      ans = (ans + dp[i] * fact(n - i)) % MOD;
    } else {
      ans = (ans + MOD * MOD - dp[i] * fact(n - i)) % MOD;
    }
  }
  cout << ans;
}

/* Note:
Check constants at the beginning of the code.
    N is set to 4e5 but be careful in problems with large constant factor.
    Setting N in every problem is more effective.
Check corner cases.
    N = 1
No def int long long for now.
Add something here.
*/