Problem p00712 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>

using namespace std;

inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
template <class T> inline T sqr(T x) { return x * x; }

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<string> vs;
typedef pair<int, int> pii;
typedef long long ll;

#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define pb push_back
#define mp make_pair
#define each(i, c)                                                             \
  for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define exist(s, e) ((s).find(e) != (s).end())
#define range(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(i, n) range(i, 0, n)
#define clr(a, b) memset((a), (b), sizeof(a))
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;

const double eps = 1e-10;
const double pi = acos(-1.0);
const ll INF = 1LL << 62;
const int inf = 1 << 29;

int dfs(int p, int q, int a, int n, int cur = 0, int pro = 1, int start = 1) {
  if (p < 0 || cur > n || pro > a)
    return 0;
  if (p == 0)
    return 1;
  int res = 0;
  for (int i = start; i <= a / pro; ++i) {
    int nq = q * i;
    int np = p * i - q;
    int g = __gcd(np, nq);
    np /= g, nq /= g;
    if (nq < 0)
      nq *= -1, np *= -1;
    res += dfs(np, nq, a, n, cur + 1, pro * i, i);
  }
  return res;
}

int main(void) {
  int p, q, a, n;
  while (cin >> p >> q >> a >> n) {
    if (p == 0)
      break;
    cout << dfs(p, q, a, n) << endl;
  }
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>

using namespace std;

inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
template <class T> inline T sqr(T x) { return x * x; }

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<string> vs;
typedef pair<int, int> pii;
typedef long long ll;

#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define pb push_back
#define mp make_pair
#define each(i, c)                                                             \
  for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define exist(s, e) ((s).find(e) != (s).end())
#define range(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(i, n) range(i, 0, n)
#define clr(a, b) memset((a), (b), sizeof(a))
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \
       << " " << __FILE__ << endl;

const double eps = 1e-10;
const double pi = acos(-1.0);
const ll INF = 1LL << 62;
const int inf = 1 << 29;

int dfs(int p, int q, int a, int n, int cur = 0, int pro = 1, int start = 1) {
  if (p < 0 || cur > n || pro > a)
    return 0;
  if (p == 0)
    return 1;
  int res = 0;
  for (int i = start; i <= a / pro; ++i) {
    if (p * i > q * (n - cur))
      break;
    int nq = q * i;
    int np = p * i - q;
    int g = __gcd(np, nq);
    np /= g, nq /= g;
    if (nq < 0)
      nq *= -1, np *= -1;
    res += dfs(np, nq, a, n, cur + 1, pro * i, i);
  }
  return res;
}

int main(void) {
  int p, q, a, n;
  while (cin >> p >> q >> a >> n) {
    if (p == 0)
      break;
    cout << dfs(p, q, a, n) << endl;
  }
  return 0;
}