Problem p02555 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < n; i++)
#define FOR(i, start, end) for (int i = start; i <= end; i++)
const int INF = 1001001001;
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define Sort(a) sort(a.begin(), a.end())
#define Rort(a) sort(a.rbegin(), a.rend())
typedef long long ll;
const ll MOD = 1000000007;
using namespace std;
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> auto MAX(const T &a) {
  return *max_element(a.begin(), a.end());
}
template <class T> auto MIN(const T &a) {
  return *min_element(a.begin(), a.end());
}
template <class T, class U> U SUM(const T &a, const U &v) {
  return accumulate(a.begin(), a.end(), v);
}
template <class T, class U> U COUNT(const T &a, const U &v) {
  return count(a.begin(), a.end(), v);
}
template <class T, class U> int LOWER(const T &a, const U &v) {
  return lower_bound(a.begin(), a.end(), v) - a.begin();
}
template <class T, class U> int UPPER(const T &a, const U &v) {
  return upper_bound(a.begin(), a.end(), v) - a.begin();
}
int GCD(int a, int b) { return b ? GCD(b, a % b) : a; }
int LCM(int a, int b) {
  int g = GCD(a, b);
  return a / g * b;
}
typedef long double ld;
typedef unsigned long long int ull;
typedef pair<int, int> P;
typedef vector<int> vi;
typedef vector<char> vc;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<ll> vll;
typedef vector<pair<int, int>> vpii;
typedef vector<pair<ll, ll>> vpll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vc> vvc;
typedef vector<vs> vvs;
typedef vector<vll> vvll;
typedef map<int, int> mii;
typedef set<int> si;
//---------------------------------------------------------------------------------------------------

int dp[1000][2004];

int main(void) {
  // Your code here!
  int s;
  cin >> s;
  memset(dp, 0, sizeof(dp));
  FOR(i, 3, 2000) dp[0][i] = 1;
  FOR(i, 1, s / 3 + 1) {
    FOR(j, 3, 2000) {
      FOR(k, 3, j - 3) {
        dp[i][j] += dp[i - 1][j - k];
        dp[i][j] %= MOD;
      }
    }
  }
  ll ans = 0;
  rep(i, 668) {
    ans += dp[i][s];
    ans %= MOD;
  }
  cout << ans << endl;
}


Fixed submission:
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < n; i++)
#define FOR(i, start, end) for (int i = start; i <= end; i++)
const int INF = 1001001001;
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define Sort(a) sort(a.begin(), a.end())
#define Rort(a) sort(a.rbegin(), a.rend())
typedef long long ll;
const ll MOD = 1000000007;
using namespace std;
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> auto MAX(const T &a) {
  return *max_element(a.begin(), a.end());
}
template <class T> auto MIN(const T &a) {
  return *min_element(a.begin(), a.end());
}
template <class T, class U> U SUM(const T &a, const U &v) {
  return accumulate(a.begin(), a.end(), v);
}
template <class T, class U> U COUNT(const T &a, const U &v) {
  return count(a.begin(), a.end(), v);
}
template <class T, class U> int LOWER(const T &a, const U &v) {
  return lower_bound(a.begin(), a.end(), v) - a.begin();
}
template <class T, class U> int UPPER(const T &a, const U &v) {
  return upper_bound(a.begin(), a.end(), v) - a.begin();
}
int GCD(int a, int b) { return b ? GCD(b, a % b) : a; }
int LCM(int a, int b) {
  int g = GCD(a, b);
  return a / g * b;
}
typedef long double ld;
typedef unsigned long long int ull;
typedef pair<int, int> P;
typedef vector<int> vi;
typedef vector<char> vc;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<ll> vll;
typedef vector<pair<int, int>> vpii;
typedef vector<pair<ll, ll>> vpll;
typedef vector<vi> vvi;
typedef vector<vvi> vvvi;
typedef vector<vc> vvc;
typedef vector<vs> vvs;
typedef vector<vll> vvll;
typedef map<int, int> mii;
typedef set<int> si;
//---------------------------------------------------------------------------------------------------

int dp[1000][2004];

int main(void) {
  // Your code here!
  int s;
  cin >> s;
  memset(dp, 0, sizeof(dp));
  FOR(i, 3, 2000) dp[0][i] = 1;
  FOR(i, 1, s / 3 + 1) {
    FOR(j, 3, 2000) {
      dp[i][j] = dp[i][j - 1] + dp[i - 1][j - 3];
      dp[i][j] %= MOD;
      // FOR(k,3,j-3){
      //     dp[i][j] += dp[i-1][j-k];
      //     dp[i][j] %= MOD;
      // }
    }
  }
  ll ans = 0;
  rep(i, 668) {
    ans += dp[i][s];
    ans %= MOD;
  }
  cout << ans << endl;
}