Problem p00096 (C++) — buggy submission, verdict: Time Limit Exceeded

#define _crt_secure_no_warnings

#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#ifdef __GXX_EXPERIMENTAL_CXX0X__
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#ifdef __GXX_EXPERIMENTAL_CXX0X__
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <unordered_map>
#include <unordered_set>
#endif

using namespace std;

int data[4][4001] = {};

long long int saiki(int N, int x) {
  if (N < 0)
    return 0;
  if (N > x * 1000)
    return 0;
  if (x == 1 && N <= 1000)
    return 1;
  int count = 0;
  for (size_t i = 0; i <= 1000 && i <= N; i++) {
    if (!data[x - 1][N - i]) {
      data[x - 1][N - i] = saiki(N - i, x - 1);
    }
    count += data[x - 1][N - i];
  }
  return count;
}

int main() {
  int N;
  while (cin >> N) {
    cout << saiki(N, 4) << endl;
  }
}

Error: TLE

Fixed submission:

#define _crt_secure_no_warnings

#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#ifdef __GXX_EXPERIMENTAL_CXX0X__
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#ifdef __GXX_EXPERIMENTAL_CXX0X__
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <unordered_map>
#include <unordered_set>
#endif

using namespace std;

int data[4][4001] = {};

long long int saiki(int N, int x) {
  if (N < 0)
    return 0;
  if (N > x * 1000)
    return 0;
  if (x == 1 && N <= 1000)
    return 1;
  int count = 0;
  for (size_t i = 0; i <= 1000 && i <= N; i++) {
    // if (!data[x - 1][N - i])
    { data[x - 1][N - i] = saiki(N - i, x - 1); }
    count += data[x - 1][N - i];
  }
  return count;
}

int main() {
  int N;
  while (cin >> N) {
    cout << saiki(N, 4) << endl;
  }
}