Problem p02666 (C++) — buggy submission, verdict: Time Limit Exceeded

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

#define LL long long
// #define LL __int64
typedef pair<int, int> pii;
typedef pair<LL, LL> pLL;
typedef vector<int> VI;
typedef vector<vector<int>> VVI;

template <typename T> inline void read(T &x) {
  static char _c;
  static bool _f;

  x = 0;
  _f = 0;
  _c = getchar();

  while (_c < '0' || '9' < _c) {
    if (_c == '-')
      _f = true;
    _c = getchar();
  }
  while ('0' <= _c && _c <= '9') {
    x = (x << 1) + (x << 3) + (_c & 15);
    _c = getchar();
  }
  if (_f)
    x = -x;
}
template <typename T, typename... Args> inline void read(T &x, Args &...args) {
  read(x);
  read(args...);
}

template <typename T> inline void Min(T &x, T y) {
  if (y < x)
    x = y;
}
template <typename T> inline void Max(T &x, T y) {
  if (x < y)
    x = y;
}

#define lowbit(x) ((x) & -(x))
#define lson l, mid, id << 1
#define rson mid + 1, r, id << 1 | 1
#define ls id << 1
#define rs id << 1 | 1
#define MID(l, r) ((l) + (((r) - (l)) >> 1))
#define fi first
#define se second
#define mk make_pair
#define mt make_tuple
#define pb push_back
#define all(a) a.begin(), a.end()

const int INF = 0x3f3f3f3f;
const LL LINF = 0x3f3f3f3f3f3f3f3f;
const double pi = (double)acos(-1.0);
const double eps = (double)1e-8;
const int e5 = (int)1e5 + 5;
// const int MOD = (int) 1e9 + 7;
const int MOD = (int)1000000007;
// const int MOD = 998244353;

template <typename T0, typename T1>
inline void depair(T0 &x, T1 &y, pair<T0, T1> &p) {
  x = p.fi, y = p.se;
}
inline int sig(double x) { return x < -eps ? -1 : eps < x; }
LL fp(LL a, LL n, LL mod = MOD) {
  if (n < 0)
    a = fp(a, mod - 2, mod), n = -n;
  LL res = 1;
  for (; n; n >>= 1, a = a * a % mod)
    if (n & 1)
      res = res * a % mod;
  return res;
}

struct Mint {
  int x;
  Mint() : x(0) {}
  Mint(int _x) : x(_x) {
    if (x >= MOD)
      x %= MOD;
    else if (x < 0)
      x = (x % MOD + MOD) % MOD;
  }
  Mint operator-() const { return Mint(MOD - x); }
  Mint operator+(const Mint &rhs) const {
    return Mint(x + rhs.x >= MOD ? x - MOD + rhs.x : x + rhs.x);
  }
  Mint operator-(const Mint &rhs) const {
    return Mint(x - rhs.x < 0 ? x - rhs.x + MOD : x - rhs.x);
  }
  Mint operator*(const Mint &rhs) const { return Mint((LL)x * rhs.x % MOD); }
  Mint operator/(const Mint &rhs) const {
    return Mint((LL)x * fp(rhs.x, -1) % MOD);
  }
  Mint &operator+=(const Mint &rhs) {
    x += rhs.x;
    if (x >= MOD)
      x -= MOD;
    return *this;
  }
  Mint &operator-=(const Mint &rhs) {
    x -= rhs.x;
    if (x < 0)
      x += MOD;
    return *this;
  }
  Mint &operator*=(const Mint &rhs) {
    x = ((LL)x * rhs.x) % MOD;
    return *this;
  }
  Mint &operator/=(const Mint &rhs) {
    x = (LL)x * fp(rhs.x, -1) % MOD;
    return *this;
  }
  bool operator==(const Mint &rhs) const { return x == rhs.x; }
  bool operator!=(const Mint &rhs) const { return x != rhs.x; }
  friend ostream &operator<<(ostream &out, const Mint &rhs) {
    return out << rhs.x;
  }
  friend istream &operator>>(istream &in, Mint &rhs) { return in >> rhs.x; }

  Mint rev() { return Mint(fp(x, -1)); }
  Mint pow(int k) { return Mint(fp(x, k)); }
  Mint pow(const Mint &t) { return Mint(fp(x, t.x)); }
};

const int maxn = (int)1e5 + 20;
const int maxm = (int)1e6 + 20;

void work() {
  int n;
  cin >> n;
  vector<int> a(n), f(n), sz(n, 1);

  for (int i = 0; i < n; i++) {
    cin >> a[i];
    f[i] = i;

    if (a[i] > 0)
      a[i]--;
  }

  function<int(int)> find_f = [&](int x) {
    if (x == f[x])
      return x;
    return f[x] = find_f(f[x]);
  };
  auto mer = [&](int x, int y) {
    x = find_f(x);
    y = find_f(y);

    if (x == y)
      return 0;
    return f[y] = x, sz[x] += sz[y], 1;
  };

  int e = 0, c = 0;
  for (int i = 0; i < n; i++) {
    if (a[i] == -1)
      c++;
    else
      e += mer(i, a[i]);
  }

  vector<Mint> dp(n + 1);
  dp[0] = 1;

  Mint rv = Mint(n - 1).rev();
  for (int i = 0; i < n; i++) {
    if (a[i] == -1) {
      int s = sz[find_f(i)];
      for (int j = n; j; j--)
        dp[j] += dp[j - 1] * Mint(s) * rv;
    }
  }

  Mint fac = 1;
  Mint tmp = 0;
  for (int i = 1; i <= n; i++) {
    tmp += dp[i] * fac;
    fac *= i;
  }

  Mint ans = (Mint(c) / Mint(n - 1) - tmp + e + c) * Mint(n - 1).pow(c);

  cout << ans << endl;
}

int main(int argc, char **argv) {
#ifdef yukihana0416
  freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
#endif // yukihana0416
       //    get_prime();
       //    pre();
  int tc = 1;
  //    read(tc);
  for (int ca = 1; ca <= tc; ca++) {
    //        printf("Case #%d: ", ca);
    work();
  }
  return 0;
}


Error: TLE

Fixed submission:

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

#define LL long long
// #define LL __int64
typedef pair<int, int> pii;
typedef pair<LL, LL> pLL;
typedef vector<int> VI;
typedef vector<vector<int>> VVI;

template <typename T> inline void read(T &x) {
  static char _c;
  static bool _f;

  x = 0;
  _f = 0;
  _c = getchar();

  while (_c < '0' || '9' < _c) {
    if (_c == '-')
      _f = true;
    _c = getchar();
  }
  while ('0' <= _c && _c <= '9') {
    x = (x << 1) + (x << 3) + (_c & 15);
    _c = getchar();
  }
  if (_f)
    x = -x;
}
template <typename T, typename... Args> inline void read(T &x, Args &...args) {
  read(x);
  read(args...);
}

template <typename T> inline void Min(T &x, T y) {
  if (y < x)
    x = y;
}
template <typename T> inline void Max(T &x, T y) {
  if (x < y)
    x = y;
}

#define lowbit(x) ((x) & -(x))
#define lson l, mid, id << 1
#define rson mid + 1, r, id << 1 | 1
#define ls id << 1
#define rs id << 1 | 1
#define MID(l, r) ((l) + (((r) - (l)) >> 1))
#define fi first
#define se second
#define mk make_pair
#define mt make_tuple
#define pb push_back
#define all(a) a.begin(), a.end()

const int INF = 0x3f3f3f3f;
const LL LINF = 0x3f3f3f3f3f3f3f3f;
const double pi = (double)acos(-1.0);
const double eps = (double)1e-8;
const int e5 = (int)1e5 + 5;
// const int MOD = (int) 1e9 + 7;
const int MOD = (int)1000000007;
// const int MOD = 998244353;

template <typename T0, typename T1>
inline void depair(T0 &x, T1 &y, pair<T0, T1> &p) {
  x = p.fi, y = p.se;
}
inline int sig(double x) { return x < -eps ? -1 : eps < x; }
LL fp(LL a, LL n, LL mod = MOD) {
  if (n < 0)
    a = fp(a, mod - 2, mod), n = -n;
  LL res = 1;
  for (; n; n >>= 1, a = a * a % mod)
    if (n & 1)
      res = res * a % mod;
  return res;
}

struct Mint {
  int x;
  Mint() : x(0) {}
  Mint(int _x) : x(_x) {
    if (x >= MOD)
      x %= MOD;
    else if (x < 0)
      x = (x % MOD + MOD) % MOD;
  }
  Mint operator-() const { return Mint(MOD - x); }
  Mint operator+(const Mint &rhs) const {
    return Mint(x + rhs.x >= MOD ? x - MOD + rhs.x : x + rhs.x);
  }
  Mint operator-(const Mint &rhs) const {
    return Mint(x - rhs.x < 0 ? x - rhs.x + MOD : x - rhs.x);
  }
  Mint operator*(const Mint &rhs) const { return Mint((LL)x * rhs.x % MOD); }
  Mint operator/(const Mint &rhs) const {
    return Mint((LL)x * fp(rhs.x, -1) % MOD);
  }
  Mint &operator+=(const Mint &rhs) {
    x += rhs.x;
    if (x >= MOD)
      x -= MOD;
    return *this;
  }
  Mint &operator-=(const Mint &rhs) {
    x -= rhs.x;
    if (x < 0)
      x += MOD;
    return *this;
  }
  Mint &operator*=(const Mint &rhs) {
    x = ((LL)x * rhs.x) % MOD;
    return *this;
  }
  Mint &operator/=(const Mint &rhs) {
    x = (LL)x * fp(rhs.x, -1) % MOD;
    return *this;
  }
  bool operator==(const Mint &rhs) const { return x == rhs.x; }
  bool operator!=(const Mint &rhs) const { return x != rhs.x; }
  friend ostream &operator<<(ostream &out, const Mint &rhs) {
    return out << rhs.x;
  }
  friend istream &operator>>(istream &in, Mint &rhs) { return in >> rhs.x; }

  Mint rev() { return Mint(fp(x, -1)); }
  Mint pow(int k) { return Mint(fp(x, k)); }
  Mint pow(const Mint &t) { return Mint(fp(x, t.x)); }
};

const int maxn = (int)1e5 + 20;
const int maxm = (int)1e6 + 20;

void work() {
  int n;
  cin >> n;
  vector<int> a(n), f(n), sz(n, 1);

  for (int i = 0; i < n; i++) {
    cin >> a[i];
    f[i] = i;

    if (a[i] > 0)
      a[i]--;
  }

  function<int(int)> find_f = [&](int x) {
    if (x == f[x])
      return x;
    return f[x] = find_f(f[x]);
  };
  auto mer = [&](int x, int y) {
    x = find_f(x);
    y = find_f(y);

    if (x == y)
      return 0;
    return f[y] = x, sz[x] += sz[y], 1;
  };

  int e = 0, c = 0;
  for (int i = 0; i < n; i++) {
    if (a[i] == -1)
      c++;
    else
      e += mer(i, a[i]);
  }

  vector<Mint> dp(n + 1);
  dp[0] = 1;
  for (int i = 0; i < n; i++) {
    if (a[i] == -1) {
      int s = sz[find_f(i)];
      for (int j = n; j; j--)
        dp[j] += dp[j - 1] * Mint(s) / (n - 1);
    }
  }

  Mint fac = 1;
  Mint tmp = 0;
  for (int i = 1; i <= n; i++) {
    tmp += dp[i] * fac;
    fac *= i;
  }

  Mint ans = (Mint(c) / Mint(n - 1) - tmp + e + c) * Mint(n - 1).pow(c);

  cout << ans << endl;
}

int main(int argc, char **argv) {
#ifdef yukihana0416
  freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
#endif // yukihana0416
       //    get_prime();
       //    pre();
  int tc = 1;
  //    read(tc);
  for (int ca = 1; ca <= tc; ca++) {
    //        printf("Case #%d: ", ca);
    work();
  }
  return 0;
}