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

#include <bits/stdc++.h>
#define repl(i, l, r) for (int i = l; i < r; ++i)
#define rep(i, n) repl(i, 0, n)
#define pb push_back
#define eb emplace_back
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define chmax(x, y) x = max(x, y)
using namespace std;
using ll = long long;
using ld = long double;
using P = pair<int, int>;
using G = vector<vector<int>>;
const int MOD = 1000000007;
const int INF = 1001001001;
const int dy[] = {-1, 0, 1, 0};
const int dx[] = {0, -1, 0, 1};

struct mint {
  ll x;
  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;
  }

  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; }

const int MAX = 510000;

long long fac[MAX], finv[MAX], inv[MAX];

// テーブルを作る前処理
void COMinit() {
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (int i = 2; i < MAX; i++) {
    fac[i] = fac[i - 1] * i % MOD;
    inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
    finv[i] = finv[i - 1] * inv[i] % MOD;
  }
}

// 二項係数計算
mint COM(int n, int k) {
  if (n < k)
    return 0;
  if (n < 0 || k < 0)
    return 0;
  return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}

int main() {
  int s;
  cin >> s;
  int maxlen = s / 3;
  mint ans = 0;
  COMinit();
  for (int i = maxlen; i > 0; --i) {
    int rest = s - 3 * i;
    mint x = COM(rest + i - 1, rest);
    ans += x;
  }
  cout << ans << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#define repl(i, l, r) for (int i = l; i < r; ++i)
#define rep(i, n) repl(i, 0, n)
#define pb push_back
#define eb emplace_back
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define chmax(x, y) x = max(x, y)
using namespace std;
using ll = long long;
using ld = long double;
using P = pair<int, int>;
using G = vector<vector<int>>;
const int MOD = 1000000007;
const int INF = 1001001001;
const int dy[] = {-1, 0, 1, 0};
const int dx[] = {0, -1, 0, 1};

struct mint {
  ll x;
  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;
  }

  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; }

mint comb(int n, int r) {
  vector<vector<mint>> v(n + 1, vector<mint>(n + 1, 0));
  for (int i = 0; i < v.size(); i += 1) {
    v[i][0] = 1;
    v[i][i] = 1;
  }
  for (int j = 1; j < v.size(); j += 1) {
    for (int k = 1; k < j; k += 1) {
      v[j][k] = (v[j - 1][k - 1] + v[j - 1][k]);
    }
  }
  return v[n][r];
}

int main() {
  ll s;
  cin >> s;
  ll maxlen = s / 3;
  mint ans = 0;
  for (ll i = maxlen; i > 0; --i) {
    ll rest = s - 3 * i;
    mint x = comb(rest + i - 1, rest);
    ans += x;
  }
  cout << ans << endl;
  return 0;
}