Problem p00904 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <cctype>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <fstream>
#include <functional>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using namespace std;
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toStr(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
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 FOR(i, a, b) for (int i = (a); i <= (b); ++i)
#define REP(i, n) FOR(i, 0, (n)-1)
const double EPS = 1e-12;
const double PI = acos(-1.0);
const int INF = INT_MAX / 10;

int main() {
  int N;
  cin >> N;
  REP(_, N) {
    int p, q;
    cin >> p >> q;
    bool ok = true;
    for (int m = -4000; m <= 4000; m++) {
      for (int n = -4000; n <= 4000; n++) {
        int a = m * m + n * n;
        if (a <= 1 || 20000 <= a) {
          continue;
        }
        int b = m * p + n * q;
        int c = m * q - n * p;
        if (b % a == 0 && c % a == 0) {
          if ((m == p && n == q) || (-n == p && m == q) ||
              (-m == p && -n == q) || (n == p && -m == q)) {
            continue;
          }
          ok = false;
          goto show;
        }
      }
    }
  show:
    cout << (ok ? 'P' : 'C') << endl;
  }
  return 0;
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <cctype>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <fstream>
#include <functional>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using namespace std;
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toStr(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
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 FOR(i, a, b) for (int i = (a); i <= (b); ++i)
#define REP(i, n) FOR(i, 0, (n)-1)
const double EPS = 1e-12;
const double PI = acos(-1.0);
const int INF = INT_MAX / 10;

int main() {
  int N;
  cin >> N;
  REP(_, N) {
    int p, q;
    cin >> p >> q;
    bool ok = true;
    for (int m = -5000; m <= 5000; m++) {
      for (int n = -5000; n <= 5000; n++) {
        int a = m * m + n * n;
        if (a <= 1 || 20000 <= a) {
          continue;
        }
        int b = m * p + n * q;
        int c = m * q - n * p;
        if (b % a == 0 && c % a == 0) {
          if ((m == p && n == q) || (-n == p && m == q) ||
              (-m == p && -n == q) || (n == p && -m == q)) {
            continue;
          }
          ok = false;
          goto show;
        }
      }
    }
  show:
    cout << (ok ? 'P' : 'C') << endl;
  }
  return 0;
}