Problem p02555 (C++) — buggy submission, verdict: Time Limit Exceeded

#include "bits/stdc++.h"
using namespace std;
typedef long long ll;

template <typename T>
void print_vec(const vector<T> &v, bool is_reverse = false, int num = 0) {
  if (num == 0)
    num = (int)v.size();
  if (is_reverse)
    for (int i = num - 1; i >= 0; i--) {
      cout << v[i];
      if (i != 0)
        cout << " ";
    }
  else
    for (int i = 0; i < num; i++) {
      cout << v[i];
      if (i != num - 1)
        cout << " ";
    }
  cout << endl;
}

template <typename T> void print_pairvec(const vector<T> &v, int num = 0) {
  if (num == 0)
    num = (int)v.size();
  cout << endl;
  for (int i = 0; i < num; i++) {
    cout << v[i].first << " " << v[i].second << endl;
  }
}

template <typename TYPE> void print_vec2(const vector<vector<TYPE>> &v) {
  cout << endl;
  cout << "       ";
  for (int i = 0; i < v[0].size(); i++)
    cout << i << "   ";
  cout << endl;
  for (int i = 0; i < v.size(); i++) {
    cout << "i=" << i << ":   ";
    for (int j = 0; j < v[i].size(); j++) {
      if (v[i][j] == 0)
        cout << "\\x1B[0m" << v[i][j] << "   ";
      else
        cout << "\\x1B[31m" << v[i][j]
             << "   "; // https://stackoverrun.com/ja/q/12618775
    }
    cout << "\\x1B[0m" << endl;
  }
}

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 1000000007;
// const int mod = 998244353;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  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 { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll 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 { return mint(*this) /= a; }
};
istream &operator>>(istream &is, mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};

int main() {
  int S;
  cin >> S;

  const int DIGIT = 667;
  const int MAX = 2000;
  combination comb(MAX + 5);

  mint ans = 0;
  for (int i = 0; i <= DIGIT; i++) {
    int tmp = S - 3 * (i + 1);
    // cout << " i: " << i << " tmp: " << tmp << " comb(tmp, i): " << comb(tmp,
    // i) << endl;
    ans += comb(tmp + i, i);
  }
  cout << ans << endl;

  // TLE解答
  // const int DIGIT = 667;
  // const int MAX = 2000;
  // vector<vector<mint>> dp(DIGIT+5, vector<mint>(MAX+5, 0));
  // dp[0][0] = 1;
  // for(int i=0; i<=DIGIT; i++){
  //   for(int j=0; j<=MAX; j++){
  //     for(int num=3; num<=MAX; num++){
  //       if(num+j <= MAX) dp[i+1][j+num] += dp[i][j];
  //     }
  //   }
  // }

  // mint ans = 0;
  // for(int i=0; i<=DIGIT; i++) ans += dp[i][S];
  // cout << ans << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include "bits/stdc++.h"
using namespace std;
typedef long long ll;

template <typename T>
void print_vec(const vector<T> &v, bool is_reverse = false, int num = 0) {
  if (num == 0)
    num = (int)v.size();
  if (is_reverse)
    for (int i = num - 1; i >= 0; i--) {
      cout << v[i];
      if (i != 0)
        cout << " ";
    }
  else
    for (int i = 0; i < num; i++) {
      cout << v[i];
      if (i != num - 1)
        cout << " ";
    }
  cout << endl;
}

template <typename T> void print_pairvec(const vector<T> &v, int num = 0) {
  if (num == 0)
    num = (int)v.size();
  cout << endl;
  for (int i = 0; i < num; i++) {
    cout << v[i].first << " " << v[i].second << endl;
  }
}

template <typename TYPE> void print_vec2(const vector<vector<TYPE>> &v) {
  cout << endl;
  cout << "       ";
  for (int i = 0; i < v[0].size(); i++)
    cout << i << "   ";
  cout << endl;
  for (int i = 0; i < v.size(); i++) {
    cout << "i=" << i << ":   ";
    for (int j = 0; j < v[i].size(); j++) {
      if (v[i][j] == 0)
        cout << "\\x1B[0m" << v[i][j] << "   ";
      else
        cout << "\\x1B[31m" << v[i][j]
             << "   "; // https://stackoverrun.com/ja/q/12618775
    }
    cout << "\\x1B[0m" << endl;
  }
}

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 1000000007;
// const int mod = 998244353;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  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 { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll 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 { return mint(*this) /= a; }
};
istream &operator>>(istream &is, mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

int main() {
  int S;
  cin >> S;

  const int DIGIT = 667;
  const int MAX = 2000;
  vector<vector<mint>> dp(DIGIT + 5, vector<mint>(MAX + 5, 0));
  dp[0][0] = 1;
  for (int i = 0; i <= DIGIT; i++) {
    for (int j = 0; j <= MAX; j++) {
      for (int num = 3; num <= MAX; num++) {
        if (num + j <= MAX)
          dp[i + 1][j + num] += dp[i][j];
      }
    }
  }

  mint ans = 0;
  for (int i = 0; i <= DIGIT; i++)
    ans += dp[i][S];
  cout << ans << endl;
  return 0;
}