Problem p02608 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#define LOCAL
using namespace std;
template <typename A, typename B>
ostream &operator<<(ostream &out, const pair<A, B> &a) {
  out << "(" << a.first << "," << a.second << ")";
  return out;
}
template <typename T, size_t N>
ostream &operator<<(ostream &out, const array<T, N> &a) {
  out << "[";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "]";
  return out;
}
template <typename T> ostream &operator<<(ostream &out, const vector<T> &a) {
  out << "[";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "]";
  return out;
}
template <typename T, class Cmp>
ostream &operator<<(ostream &out, const set<T, Cmp> &a) {
  out << "{";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "}";
  return out;
}
template <typename U, typename T, class Cmp>
ostream &operator<<(ostream &out, const map<U, T, Cmp> &a) {
  out << "{";
  bool first = true;
  for (auto &p : a) {
    out << (first ? "" : ", ");
    out << p.first << ":" << p.second;
    first = 0;
  }
  out << "}";
  return out;
}
#ifdef LOCAL
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
#else
#define trace(...) 42
#endif
template <typename Arg1> void __f(const char *name, Arg1 &&arg1) {
  cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char *names, Arg1 &&arg1, Args &&...args) {
  const char *comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << ": " << arg1 << " |";
  __f(comma + 1, args...);
}
#define rep(i, n) for (int i = 0; i < (n); i++)
using ll = long long;
#define int long long
using P = pair<int, int>;
// #########################################
signed main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    // f[i]
    bool found = false;
    int ans = 0;
    for (int x = 1; x * x <= i; x++) {
      for (int y = x; y * y <= i; y++) {
        for (int z = y; z * z <= i; z++) {
          // trace(x,y,z,i);
          if (x * x + y * y + z * z + x * y + y * z + z * x > i)
            continue;
          else if (x * x + y * y + z * z + x * y + y * z + z * x == i) {
            if (x == y && y == z)
              ans++;
            else if (x == y || y == z) {
              ans += 3;
            } else
              ans += 6;
          }
        }
      }
    }
    cout << ans << endl;
  }
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
#define LOCAL
using namespace std;
template <typename A, typename B>
ostream &operator<<(ostream &out, const pair<A, B> &a) {
  out << "(" << a.first << "," << a.second << ")";
  return out;
}
template <typename T, size_t N>
ostream &operator<<(ostream &out, const array<T, N> &a) {
  out << "[";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "]";
  return out;
}
template <typename T> ostream &operator<<(ostream &out, const vector<T> &a) {
  out << "[";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "]";
  return out;
}
template <typename T, class Cmp>
ostream &operator<<(ostream &out, const set<T, Cmp> &a) {
  out << "{";
  bool first = true;
  for (auto &v : a) {
    out << (first ? "" : ", ");
    out << v;
    first = 0;
  }
  out << "}";
  return out;
}
template <typename U, typename T, class Cmp>
ostream &operator<<(ostream &out, const map<U, T, Cmp> &a) {
  out << "{";
  bool first = true;
  for (auto &p : a) {
    out << (first ? "" : ", ");
    out << p.first << ":" << p.second;
    first = 0;
  }
  out << "}";
  return out;
}
#ifdef LOCAL
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
#else
#define trace(...) 42
#endif
template <typename Arg1> void __f(const char *name, Arg1 &&arg1) {
  cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char *names, Arg1 &&arg1, Args &&...args) {
  const char *comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << ": " << arg1 << " |";
  __f(comma + 1, args...);
}
#define rep(i, n) for (int i = 0; i < (n); i++)
using ll = long long;
#define int long long
using P = pair<int, int>;
// #########################################
signed main() {
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    // f[i]
    bool found = false;
    int ans = 0;
    for (int x = 1; x * x <= i; x++) {
      for (int y = 1; y * y <= i; y++) {
        for (int z = 1; z * z <= i; z++) {
          // trace(x,y,z,i);
          if (x * x + y * y + z * z + x * y + y * z + z * x == i) {
            ans++;
          }
        }
      }
    }
    cout << ans << endl;
  }
  return 0;
}