Problem p02634 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <map>
#include <set>
#include <string>
#include <vector>

#include <cmath>
#include <queue>
#include <stack>

using namespace std;

#define LL long long

const int dx[4] = {1, -1, 0, 0};
const int dy[4] = {0, 0, 1, -1};

LL mod(LL x, LL md) { return ((x % md) + md) % md; }

class Mint {
public:
  static LL md;
  LL x;
  Mint(LL _x = 0) { x = mod(_x, md); }
  Mint(const Mint &y) { x = mod(y.x, md); }
};

void MintMyExgcd(LL a, LL b, LL &x, LL &y) {
  // solve equation ax + by = 1 (mod m)
  LL md = Mint::md;
  if (b == 0) {
    y = 0;
    x = 1;
    return;
  }
  MintMyExgcd(b, a % b, x, y);
  LL t = y;
  y = mod(x - (a / b) * y, md);
  x = t;
}

LL MintNY(LL x) {
  if (x == 0) {
    return 1;
  }
  LL md = Mint::md;
  LL a, b;
  MintMyExgcd(x, md, a, b);
  while (a < 0) {
    a += md;
  }
  return a;
}

/* LL gcd(LL a, LL b) {
        if (b == 0) {
                return a;
        }
        return gcd(b, a % b);
} */

Mint operator+(Mint a, Mint b) { return Mint(mod(a.x + b.x, Mint::md)); }
Mint operator-(Mint a, Mint b) { return Mint(mod(a.x - b.x, Mint::md)); }
Mint operator*(Mint a, Mint b) { return Mint(mod(a.x * b.x, Mint::md)); }
Mint operator/(Mint a, Mint b) {
  Mint c = Mint(MintNY(b.x));
  return Mint(mod(a.x * c.x, Mint::md));
}

Mint operator-(Mint a) { return Mint(-a.x); }
bool operator==(Mint a, Mint b) { return a.x == b.x; }
bool operator!=(Mint a, Mint b) { return a.x != b.x; }
bool operator>(Mint a, Mint b) { return a.x > b.x; }
bool operator<(Mint a, Mint b) { return a.x < b.x; }
bool operator>=(Mint a, Mint b) { return a.x >= b.x; }
bool operator<=(Mint a, Mint b) { return a.x <= b.x; }

void operator+=(Mint &a, Mint b) { a = a + b; }
void operator-=(Mint &a, Mint b) { a = a - b; }
void operator*=(Mint &a, Mint b) { a = a * b; }
void operator/=(Mint &a, Mint b) { a = a / b; }

ostream &operator<<(ostream &out, Mint a) {
  out << a.x;
  return out;
}

istream &operator>>(istream &in, Mint &a) {
  in >> a.x;
  return in;
}

Mint factorial(LL n) {
  if (n == 0) {
    return Mint(1);
  }
  Mint res = 1;
  for (LL i = 1; i <= n; ++i) {
    res *= i;
  }
  return res;
}
Mint multiRange(LL s, LL t) {
  Mint res = 1;
  for (LL i = s; i <= t; ++i) {
    res *= i;
  }
  return res;
}

Mint getC(LL n, LL k) {
  if (n - k < k) {
    return getC(n, n - k);
  }
  return multiRange(n - k + 1, n) / factorial(k);
}

Mint getA(LL n, LL k) { return multiRange(n - k + 1, n); }

Mint countNonNegativeDivision(LL n, LL k) { return getC(n + k - 1, k - 1); }
Mint countPositiveDivision(LL n, LL k) {
  if (n < k) {
    return 0;
  }
  if (k <= 0) {
    return 0;
  }
  return getC(n - 1, k - 1);
}
Mint quickMod(Mint a, LL b) {
  Mint res = 1;
  while (b > 0) {
    if (b % 2) {
      res *= a;
    }
    a *= a;
    b /= 2;
  }
  return res;
}
template <class TypeName> vector<TypeName> getVector1D(int n, TypeName val) {
  return vector<TypeName>(n, val);
}
template <class TypeName>
vector<vector<TypeName>> getVector2D(int n1, int n2, TypeName val) {
  vector<vector<TypeName>> res(n1);
  for (int i = 0; i < n1; ++i) {
    res[i] = vector<TypeName>(n2, val);
  }
  return res;
}
template <class TypeName>
vector<vector<vector<TypeName>>> getVector3D(int n1, int n2, int n3,
                                             TypeName val) {
  vector<vector<vector<TypeName>>> res(n1);
  for (int i = 0; i < n1; ++i) {
    res[i] = vector<vector<TypeName>>(n2);
    for (int j = 0; j < n2; ++j) {
      res[i][j] = vector<TypeName>(n3, val);
    }
  }
  return res;
}
template <class TypeName>
vector<vector<vector<vector<TypeName>>>> getVector4D(int n1, int n2, int n3,
                                                     int n4, TypeName val) {
  vector<vector<vector<vector<TypeName>>>> res(n1);
  for (int i = 0; i < n1; ++i) {
    res[i] = vector<vector<vector<TypeName>>>(n2);
    for (int j = 0; j < n2; ++j) {
      res[i][j] = vector<vector<TypeName>>(n3);
      for (int k = 0; k < n3; ++k) {
        res[i][j][k] = vector<TypeName>(n4, val);
      }
    }
  }
  return res;
}

LL Mint::md = 998244353;
LL md = 998244353;

int main() {
  LL a, b, c, d;
  cin >> a >> b >> c >> d;

  auto f = getVector2D(c + 1, d + 1, (LL)(0)); // all cases
  // auto g = getVector2D(c + 1, d + 1, Mint(0)); // cases where (i, j) is
  // painted black
  f[a][b] = 1;
  for (LL i = a; i <= c; ++i) {
    for (LL j = b; j <= d; ++j) {
      if (i == a && j == b) {
        continue;
      }
      if (i == a) {
        f[i][j] = mod(f[i][j - 1] * a, md);
        continue;
      }
      if (j == b) {
        f[i][j] = mod(f[i - 1][j] * b, md);
        continue;
      }
      // f[i][j] = f[i - 1][j] * (b + 1) + f[i][j - 1] * (a + 1) + ((f[i][j - 1]
      // * (i - a - 1) + f[i - 1][j] * (j - b - 1)) / 2);
      f[i][j] = mod(f[i - 1][j] * j + f[i][j - 1] * i -
                        f[i - 1][j - 1] * (i - 1) * (j - 1),
                    md);
    }
  }
  cout << f[c][d] << endl;
  return 0;
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <map>
#include <set>
#include <string>
#include <vector>

#include <cmath>
#include <queue>
#include <stack>

using namespace std;

#define LL long long

const int dx[4] = {1, -1, 0, 0};
const int dy[4] = {0, 0, 1, -1};

LL mod(LL x, LL md) { return ((x % md) + md) % md; }

class Mint {
public:
  static LL md;
  LL x;
  Mint(LL _x = 0) { x = mod(_x, md); }
  Mint(const Mint &y) { x = mod(y.x, md); }
};

void MintMyExgcd(LL a, LL b, LL &x, LL &y) {
  // solve equation ax + by = 1 (mod m)
  LL md = Mint::md;
  if (b == 0) {
    y = 0;
    x = 1;
    return;
  }
  MintMyExgcd(b, a % b, x, y);
  LL t = y;
  y = mod(x - (a / b) * y, md);
  x = t;
}

LL MintNY(LL x) {
  if (x == 0) {
    return 1;
  }
  LL md = Mint::md;
  LL a, b;
  MintMyExgcd(x, md, a, b);
  while (a < 0) {
    a += md;
  }
  return a;
}

/* LL gcd(LL a, LL b) {
        if (b == 0) {
                return a;
        }
        return gcd(b, a % b);
} */

Mint operator+(Mint a, Mint b) { return Mint(mod(a.x + b.x, Mint::md)); }
Mint operator-(Mint a, Mint b) { return Mint(mod(a.x - b.x, Mint::md)); }
Mint operator*(Mint a, Mint b) { return Mint(mod(a.x * b.x, Mint::md)); }
Mint operator/(Mint a, Mint b) {
  Mint c = Mint(MintNY(b.x));
  return Mint(mod(a.x * c.x, Mint::md));
}

Mint operator-(Mint a) { return Mint(-a.x); }
bool operator==(Mint a, Mint b) { return a.x == b.x; }
bool operator!=(Mint a, Mint b) { return a.x != b.x; }
bool operator>(Mint a, Mint b) { return a.x > b.x; }
bool operator<(Mint a, Mint b) { return a.x < b.x; }
bool operator>=(Mint a, Mint b) { return a.x >= b.x; }
bool operator<=(Mint a, Mint b) { return a.x <= b.x; }

void operator+=(Mint &a, Mint b) { a = a + b; }
void operator-=(Mint &a, Mint b) { a = a - b; }
void operator*=(Mint &a, Mint b) { a = a * b; }
void operator/=(Mint &a, Mint b) { a = a / b; }

ostream &operator<<(ostream &out, Mint a) {
  out << a.x;
  return out;
}

istream &operator>>(istream &in, Mint &a) {
  in >> a.x;
  return in;
}

Mint factorial(LL n) {
  if (n == 0) {
    return Mint(1);
  }
  Mint res = 1;
  for (LL i = 1; i <= n; ++i) {
    res *= i;
  }
  return res;
}
Mint multiRange(LL s, LL t) {
  Mint res = 1;
  for (LL i = s; i <= t; ++i) {
    res *= i;
  }
  return res;
}

Mint getC(LL n, LL k) {
  if (n - k < k) {
    return getC(n, n - k);
  }
  return multiRange(n - k + 1, n) / factorial(k);
}

Mint getA(LL n, LL k) { return multiRange(n - k + 1, n); }

Mint countNonNegativeDivision(LL n, LL k) { return getC(n + k - 1, k - 1); }
Mint countPositiveDivision(LL n, LL k) {
  if (n < k) {
    return 0;
  }
  if (k <= 0) {
    return 0;
  }
  return getC(n - 1, k - 1);
}
Mint quickMod(Mint a, LL b) {
  Mint res = 1;
  while (b > 0) {
    if (b % 2) {
      res *= a;
    }
    a *= a;
    b /= 2;
  }
  return res;
}
template <class TypeName> vector<TypeName> getVector1D(int n, TypeName val) {
  return vector<TypeName>(n, val);
}
template <class TypeName>
vector<vector<TypeName>> getVector2D(int n1, int n2, TypeName val) {
  vector<vector<TypeName>> res(n1);
  for (int i = 0; i < n1; ++i) {
    res[i] = vector<TypeName>(n2, val);
  }
  return res;
}
template <class TypeName>
vector<vector<vector<TypeName>>> getVector3D(int n1, int n2, int n3,
                                             TypeName val) {
  vector<vector<vector<TypeName>>> res(n1);
  for (int i = 0; i < n1; ++i) {
    res[i] = vector<vector<TypeName>>(n2);
    for (int j = 0; j < n2; ++j) {
      res[i][j] = vector<TypeName>(n3, val);
    }
  }
  return res;
}
template <class TypeName>
vector<vector<vector<vector<TypeName>>>> getVector4D(int n1, int n2, int n3,
                                                     int n4, TypeName val) {
  vector<vector<vector<vector<TypeName>>>> res(n1);
  for (int i = 0; i < n1; ++i) {
    res[i] = vector<vector<vector<TypeName>>>(n2);
    for (int j = 0; j < n2; ++j) {
      res[i][j] = vector<vector<TypeName>>(n3);
      for (int k = 0; k < n3; ++k) {
        res[i][j][k] = vector<TypeName>(n4, val);
      }
    }
  }
  return res;
}

LL Mint::md = 998244353;

int main() {
  int a, b, c, d;
  cin >> a >> b >> c >> d;

  auto f = getVector2D(c + 1, d + 1, Mint(0)); // all cases
  // auto g = getVector2D(c + 1, d + 1, Mint(0)); // cases where (i, j) is
  // painted black
  f[a][b] = 1;
  for (int i = a; i <= c; ++i) {
    for (int j = b; j <= d; ++j) {
      if (i == a && j == b) {
        continue;
      }
      if (i == a) {
        f[i][j] = f[i][j - 1] * a;
        continue;
      }
      if (j == b) {
        f[i][j] = f[i - 1][j] * b;
        continue;
      }
      // f[i][j] = f[i - 1][j] * (b + 1) + f[i][j - 1] * (a + 1) + ((f[i][j - 1]
      // * (i - a - 1) + f[i - 1][j] * (j - b - 1)) / 2);
      f[i][j] = f[i - 1][j] * j + f[i][j - 1] * i -
                f[i - 1][j - 1] * (i - 1) * (j - 1);
    }
  }
  cout << f[c][d] << endl;
  return 0;
}