Problem p00009 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <cassert>
#include <cctype>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>

#define REP(i, m, n) for (int i = m; i < n; i++)
#define rep(i, n) for (int i = 0; i < n; i++)
#define rp(i, c) rep(i, (int)c.size())
#define fr(i, c)                                                               \\
  for (__typeof((c).begin()) i = (c).begin(); i != (c).end(); i++)
#define mp make_pair
#define pb push_back
#define all(c) (c).begin(), (c).end()
#define rall(u) (u).rbegin(), (u).rend()
#define dbg(x) cerr << #x << " = " << (x) << endl
#define v_delete(a, b) (a).erase(remove((a).begin(), (a).end(), b), (a).end())
#define v_unique(a) (a).erase(unique((a).begin(), (a).end()), (a).end())
#define VV(T) vector<vector<T>>
#define init(a, b) memset((a), (b), sizeof((a)))
using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pi;
const int inf = 1 << 28;
const double INF = 1e10, EPS = 1e-9;

template <class T> int SIZE(T a) { return a.size(); }
template <class T> string IntToString(T num) {
  string res;
  stringstream ss;
  ss << num;
  return ss.str();
}
template <class T> T StringToInt(string str) {
  T res = 0;
  for (int i = 0; i < SIZE(str); i++)
    res = (res * 10 + str[i] - '0');
  return res;
}
template <class T> T gcd(T a, T b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}
template <class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

template <class T> void input(T &a, int n) {
  for (int i = 0; i < n; ++i)
    cin >> a[i];
}
template <class T> void input(T *a, int n) {
  for (int i = 0; i < n; ++i)
    cin >> a[i];
}
typedef pair<int, int> pii;

inline bool IN(int x, int y, int w, int h) {
  return 0 <= x && x < w && 0 <= y && y < h;
}

int main() {
  int n;
  vi pn(1000000, 1);
  pn[0] = 0;
  pn[1] = 0;
  for (int i = 2; i <= 1000000 / 2; i++) {
    if (pn[i] == 1) {
      for (int j = 2; j <= 1000000 / i; j++) {
        pn[j * i] = 0;
      }
    }
  }
  while (cin >> n) {
    int ans = 0;
    rep(i, n + 1) {
      if (pn[i])
        ans++;
    }
    cout << ans << endl;
  }
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <cassert>
#include <cctype>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>

#define REP(i, m, n) for (int i = m; i < n; i++)
#define rep(i, n) for (int i = 0; i < n; i++)
#define rp(i, c) rep(i, (int)c.size())
#define fr(i, c)                                                               \\
  for (__typeof((c).begin()) i = (c).begin(); i != (c).end(); i++)
#define mp make_pair
#define pb push_back
#define all(c) (c).begin(), (c).end()
#define rall(u) (u).rbegin(), (u).rend()
#define dbg(x) cerr << #x << " = " << (x) << endl
#define v_delete(a, b) (a).erase(remove((a).begin(), (a).end(), b), (a).end())
#define v_unique(a) (a).erase(unique((a).begin(), (a).end()), (a).end())
#define VV(T) vector<vector<T>>
#define init(a, b) memset((a), (b), sizeof((a)))
using namespace std;

typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pi;
const int inf = 1 << 28;
const double INF = 1e10, EPS = 1e-9;

template <class T> int SIZE(T a) { return a.size(); }
template <class T> string IntToString(T num) {
  string res;
  stringstream ss;
  ss << num;
  return ss.str();
}
template <class T> T StringToInt(string str) {
  T res = 0;
  for (int i = 0; i < SIZE(str); i++)
    res = (res * 10 + str[i] - '0');
  return res;
}
template <class T> T gcd(T a, T b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}
template <class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

template <class T> void input(T &a, int n) {
  for (int i = 0; i < n; ++i)
    cin >> a[i];
}
template <class T> void input(T *a, int n) {
  for (int i = 0; i < n; ++i)
    cin >> a[i];
}
typedef pair<int, int> pii;

inline bool IN(int x, int y, int w, int h) {
  return 0 <= x && x < w && 0 <= y && y < h;
}

int main() {
  int n;
  while (cin >> n) {
    vi pn(1000000, 1);
    pn[0] = 0;
    pn[1] = 0;
    int ans = 0;
    for (int i = 2; i <= n; i++) {
      if (pn[i] == 1) {
        for (int j = i + 1; j <= n; j++) {
          if (!(j % i)) {
            pn[j] = 0;
          }
        }
      }
    }
    rep(i, n + 1) {
      if (pn[i])
        ans++;
    }
    cout << ans << endl;
  }
}