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

#pragma GCC optimize("O3")
#include <algorithm>
#include <bitset>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <iomanip>
#include <iostream>
#include <istream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
#define IINF 1000000000
#define INF 3223372036854775807
#define MOD 1000000007
#define mod 1000000007
#define INT_MAX_ 2147483647
#define EPS (1e-10)
#define REP(i, a, n) fo - r(ll i = a; i < (ll)(n); i++)
#define REPE(i, a, n) for (ll i = a; i <= (ll)(n); i++)
// #define rep(i,n)for (ll i = 0; i < (ll)(n); i++)
#define rep(i, l, r) for (ll i = (l); i < (r); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define Endl endl
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define eb emplace_back
#define mmax(x, y) (x > y ? x : y)
#define mmin(x, y) (x < y ? x : y)
#define chmax(x, y) x = mmax(x, y)
#define chmin(x, y) x = mmin(x, y)
#define all(x) (x).begin(), (x).end()
#define siz(x) (ll)(x).size()
#define PI acos(-1.0)
#define me memset
#define bit(n, k) ((n >> k) & 1)
#define lg length()
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;
typedef long double ld;
typedef pair<int, int> Pin;
typedef pair<ll, ll> Pll;
template <class T> using V = vector<T>;
template <typename T>
using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
long long GCD(long long a, long long b) { return b ? GCD(b, a % b) : a; }
long long LCM(long long a, long long b) { return a / GCD(a, b) * b; }
ll pom(ll a, ll n, int m) {
  ll x = 1;
  for (a %= m; n; n /= 2)
    n & 1 ? x = x * a % m : 0, a = a * a % m;
  return x;
}
#define invp(a, p) pom(a, p - 2, p)
int dx[4] = {-1, 0, 1, 0};
int dy[4] = {0, -1, 0, 1};
int ddx[8] = {-1, 0, 1, 0, 1, 1, -1, -1};
int ddy[8] = {0, -1, 0, 1, 1, -1, 1, -1};
ll cmp1(pair<Pll, ll> a, pair<Pll, ll> b) { return a.fi.se > b.fi.se; }
ll cmp2(pair<ll, ll> a, pair<ll, ll> b) {
  if (a.fi != b.fi)
    return a.se < b.se;
  else
    return a.se > b.se;
}
//----------------------------------------------------------------------
ll color[2002][2002];
ll rres[2001];
ll dfs(ll i, ll n, ll s) {
  if (color[i][n] >= 0)
    return color[i][n];
  ll res = n + i;
  ll tmp = 0;
  if (res == s)
    return 1;
  else if (res > s - 3 && res < s)
    return 0;
  else if (res > s)
    return 0;
  return rres[s - res];

  for (ll j = 3; j <= s; j++) {
    if (res + j > s)
      break;
    if (res + j == s - 1)
      continue;
    if (res + j == s - 2)
      continue;
    tmp += dfs(j, res, s);
    tmp %= mod;
  }
  color[i][n] = tmp;
  return tmp;
}
//----------------------------------------------------------------------
int main(int argc, char *argv[]) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  //-------------------------------
  // ll begin_t=clock();
  // freopen("big.txt", "r", stdin);
  // freopen("out3.txt", "w", stdout);
  //------------------------------
  ll s;
  cin >> s;
  ll is = s;
  if (s < 3) {
    cout << 0 << endl;
    return 0;
  }
  for (ll i = 3; i <= s; i++) {
    ll aans = 0;
    for (ll y = 0; y <= i; y++) {
      for (ll j = 0; j <= i; j++) {
        color[y][j] = -1;
      }
    }
    for (ll k = 3; k <= i; k++) {
      aans += dfs(k, 0, i);
      aans %= mod;
    }
    rres[i] = aans;
    if (i == s)
      cout << rres[i] << endl;
  }
  //------------------------------
  // fclose(stdin);
  // fclose(stdout);
  // ll end_t=clock();cout<<"time="<<end_t-begin_t<<"ms"<<endl;
  //-------------------------------
  return 0;
}
//----------------------------------------------------------------------


Error: TLE

Fixed submission:

#pragma GCC optimize("O3")
#include <algorithm>
#include <bitset>
#include <cctype>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <iomanip>
#include <iostream>
#include <istream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
#define IINF 1000000000
#define INF 3223372036854775807
#define MOD 1000000007
#define mod 1000000007
#define INT_MAX_ 2147483647
#define EPS (1e-10)
#define REP(i, a, n) fo - r(ll i = a; i < (ll)(n); i++)
#define REPE(i, a, n) for (ll i = a; i <= (ll)(n); i++)
// #define rep(i,n)for (ll i = 0; i < (ll)(n); i++)
#define rep(i, l, r) for (ll i = (l); i < (r); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define Endl endl
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define eb emplace_back
#define mmax(x, y) (x > y ? x : y)
#define mmin(x, y) (x < y ? x : y)
#define chmax(x, y) x = mmax(x, y)
#define chmin(x, y) x = mmin(x, y)
#define all(x) (x).begin(), (x).end()
#define siz(x) (ll)(x).size()
#define PI acos(-1.0)
#define me memset
#define bit(n, k) ((n >> k) & 1)
#define lg length()
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;
typedef long double ld;
typedef pair<int, int> Pin;
typedef pair<ll, ll> Pll;
template <class T> using V = vector<T>;
template <typename T>
using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
long long GCD(long long a, long long b) { return b ? GCD(b, a % b) : a; }
long long LCM(long long a, long long b) { return a / GCD(a, b) * b; }
ll pom(ll a, ll n, int m) {
  ll x = 1;
  for (a %= m; n; n /= 2)
    n & 1 ? x = x * a % m : 0, a = a * a % m;
  return x;
}
#define invp(a, p) pom(a, p - 2, p)
int dx[4] = {-1, 0, 1, 0};
int dy[4] = {0, -1, 0, 1};
int ddx[8] = {-1, 0, 1, 0, 1, 1, -1, -1};
int ddy[8] = {0, -1, 0, 1, 1, -1, 1, -1};
ll cmp1(pair<Pll, ll> a, pair<Pll, ll> b) { return a.fi.se > b.fi.se; }
ll cmp2(pair<ll, ll> a, pair<ll, ll> b) {
  if (a.fi != b.fi)
    return a.se < b.se;
  else
    return a.se > b.se;
}
//----------------------------------------------------------------------
ll color[2002][2002];
ll rres[2001];
ll dfs(ll i, ll n, ll s) {
  if (color[i][n] >= 0)
    return color[i][n];
  ll res = n + i;
  ll tmp = 0;
  if (res == s)
    return 1;
  else if (res > s - 3 && res < s)
    return 0;
  else if (res > s)
    return 0;
  if (res >= s - res) {
    return rres[s - res];
  }
  for (ll j = 3; j <= s; j++) {
    if (res + j > s)
      break;
    if (res + j == s - 1)
      continue;
    if (res + j == s - 2)
      continue;
    tmp += dfs(j, res, s);
    tmp %= mod;
  }
  color[i][n] = tmp;
  return tmp;
}
//----------------------------------------------------------------------
int main(int argc, char *argv[]) {
  cin.tie(0);
  ios::sync_with_stdio(false);
  //-------------------------------
  // ll begin_t=clock();
  // freopen("big.txt", "r", stdin);
  // freopen("out3.txt", "w", stdout);
  //------------------------------
  ll s;
  cin >> s;
  ll is = s;
  if (s < 3) {
    cout << 0 << endl;
    return 0;
  }
  for (ll i = 3; i <= s; i++) {
    ll aans = 0;
    for (ll y = 0; y <= i; y++) {
      for (ll j = 0; j <= i; j++) {
        color[y][j] = -1;
      }
    }
    for (ll k = 3; k <= i; k++) {
      aans += dfs(k, 0, i);
      aans %= mod;
    }
    rres[i] = aans;
    if (i == s)
      cout << rres[i] << endl;
  }
  //------------------------------
  // fclose(stdin);
  // fclose(stdout);
  // ll end_t=clock();cout<<"time="<<end_t-begin_t<<"ms"<<endl;
  //-------------------------------
  return 0;
}
//----------------------------------------------------------------------