Problem p02608 (C++)

Buggy submission (status: Time Limit Exceeded):
#include "bits/stdc++.h"
#define rep(i, j) for (int i = 0; i < j; i++)
using namespace std;
using ll = long long;
using P = pair<int, int>;
using ull = unsigned long long;

ll gcd(ll x, ll y);
int fac(ll n, vector<int> num);

const int INF = 1001001001;

// mint�p�̒萔 (10��9��)
const int mod = 1000000007;

struct mint {
  ll x; // typedef long long ll;
  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;
  }

  // for prime mod
  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, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

int main() {
  int n;
  cin >> n;

  for (int i = 1; i <= n; i++) {
    int ans = 0;

    for (int j = 1; j < sqrt(i); j++) {
      for (int k = 1; k < sqrt(i); k++) {
        for (int l = 1; l < sqrt(i); l++) {
          if (j * j + k * k + l * l + j * k + k * l + l * j == i) {
            ans++;
            break;
          }
        }
      }
    }
    cout << ans << endl;
  }
  return 0;
}

/*���C�u�����ő����*/
// ���[�O���b�h�̌ݏ��@
ll gcd(ll x, ll y) {
  ll num[3];
  num[0] = (x > y) ? x : y;
  num[1] = (x <= y) ? x : y;
  num[2] = num[0] % num[1];

  while (num[2]) {
    num[0] = num[1];
    num[1] = num[2];
    num[2] = num[0] % num[1];
  }

  return num[1];
}

/*�f��������*/
// ���색�C�u����
int fac(ll n, vector<int> num) {
  ll kazu = n;
  for (int i = 2; i <= sqrt(n); i++) {
    while (1) {
      if (kazu % i != 0)
        break;

      kazu /= i;
      num[i]++;
    }
  }
  if (kazu == n && n != 1)
    return 1;
  int ans = 0;
  if (kazu != 1)
    ans++;
  for (int i = 2; i <= sqrt(n); i++) {
    for (int j = 1; j <= num[i]; j++) {
      num[i] -= j;
      ans++;
    }
  }
  return ans;
}

Fixed submission:
#include "bits/stdc++.h"
#define rep(i, j) for (int i = 0; i < j; i++)
using namespace std;
using ll = long long;
using P = pair<int, int>;
using ull = unsigned long long;

ll gcd(ll x, ll y);
int fac(ll n, vector<int> num);

const int INF = 1001001001;

// mint�p�̒萔 (10��9��)
const int mod = 1000000007;

struct mint {
  ll x; // typedef long long ll;
  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;
  }

  // for prime mod
  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, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

int main() {
  int n;
  cin >> n;

  for (int i = 1; i <= n; i++) {
    int ans = 0;

    for (int j = 1; j < sqrt(i); j++) {
      for (int k = 1; k < sqrt(i); k++) {
        int ok = 1, ng = sqrt(i) + 1;
        while (ng - ok > 1) {
          int mid = (ok + ng) / 2;
          if (j * j + k * k + mid * mid + j * k + j * mid + k * mid <= i)
            ok = mid;
          else
            ng = mid;
        }
        if (j * j + k * k + ok * ok + j * k + j * ok + k * ok == i) {
          ans++;
        }
      }
    }
    cout << ans << endl;
  }
  return 0;
}

/*���C�u�����ő����*/
// ���[�O���b�h�̌ݏ��@
ll gcd(ll x, ll y) {
  ll num[3];
  num[0] = (x > y) ? x : y;
  num[1] = (x <= y) ? x : y;
  num[2] = num[0] % num[1];

  while (num[2]) {
    num[0] = num[1];
    num[1] = num[2];
    num[2] = num[0] % num[1];
  }

  return num[1];
}

/*�f��������*/
// ���색�C�u����
int fac(ll n, vector<int> num) {
  ll kazu = n;
  for (int i = 2; i <= sqrt(n); i++) {
    while (1) {
      if (kazu % i != 0)
        break;

      kazu /= i;
      num[i]++;
    }
  }
  if (kazu == n && n != 1)
    return 1;
  int ans = 0;
  if (kazu != 1)
    ans++;
  for (int i = 2; i <= sqrt(n); i++) {
    for (int j = 1; j <= num[i]; j++) {
      num[i] -= j;
      ans++;
    }
  }
  return ans;
}