Problem p03202 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (int)n; i++)
#define all(c) (c).begin(), (c).end()
#define pb push_back
#define dbg(...)                                                               \
  do {                                                                         \
    cerr << __LINE__ << ": ";                                                  \
    dbgprint(#__VA_ARGS__, __VA_ARGS__);                                       \
  } while (0);

using namespace std;

namespace std {
template <class S, class T> struct hash<pair<S, T>> {
  size_t operator()(const pair<S, T> &p) const {
    return ((size_t)1e9 + 7) * hash<S>()(p.first) + hash<T>()(p.second);
  }
};
template <class T> struct hash<vector<T>> {
  size_t operator()(const vector<T> &v) const {
    size_t h = 0;
    for (auto i : v)
      h = h * ((size_t)1e9 + 7) + hash<T>()(i) + 1;
    return h;
  }
};
} // namespace std
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
  os << "[ ";
  rep(i, v.size()) os << v[i] << (i == v.size() - 1 ? " ]" : ", ");
  return os;
}
template <class T> ostream &operator<<(ostream &os, const set<T> &v) {
  os << "{ ";
  for (const auto &i : v)
    os << i << ", ";
  return os << "}";
}
template <class T, class U>
ostream &operator<<(ostream &os, const map<T, U> &v) {
  os << "{";
  for (const auto &i : v)
    os << " " << i.first << ": " << i.second << ",";
  return os << "}";
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
void dbgprint(const string &fmt) { cerr << endl; }
template <class H, class... T>
void dbgprint(const string &fmt, const H &h, const T &...r) {
  cerr << fmt.substr(0, fmt.find(",")) << "= " << h << " ";
  dbgprint(fmt.substr(fmt.find(",") + 1), r...);
}
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pi;
const int inf = (int)1e9;
const double INF = 1e12, EPS = 1e-9;

int main() {
  cin.tie(0);
  cin.sync_with_stdio(0);
  int n;
  cin >> n;
  vi v(n);
  rep(i, n) cin >> v[i];
  int lo = 0, hi = n, mid;
  while (lo + 1 < hi) {
    mid = (lo + hi) / 2;
    map<int, int> p;
    rep(i, n - 1) {
      if (v[i] < v[i + 1])
        continue;
      int pos = -v[i + 1];
      while (p.size() && p.begin()->first < pos)
        p.erase(p.begin());
      while (pos < 0) {
        if (++p[pos] >= mid) {
          p.erase(pos);
          ++pos;
        } else
          break;
      }
      if (pos == 0) {
        lo = mid;
        goto END;
      }
    }
    hi = mid;
  END:;
  }
  cout << hi << endl;
  return 0;
}

Fixed submission:
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (int)n; i++)
#define all(c) (c).begin(), (c).end()
#define pb push_back
#define dbg(...)                                                               \
  do {                                                                         \
    cerr << __LINE__ << ": ";                                                  \
    dbgprint(#__VA_ARGS__, __VA_ARGS__);                                       \
  } while (0);

using namespace std;

namespace std {
template <class S, class T> struct hash<pair<S, T>> {
  size_t operator()(const pair<S, T> &p) const {
    return ((size_t)1e9 + 7) * hash<S>()(p.first) + hash<T>()(p.second);
  }
};
template <class T> struct hash<vector<T>> {
  size_t operator()(const vector<T> &v) const {
    size_t h = 0;
    for (auto i : v)
      h = h * ((size_t)1e9 + 7) + hash<T>()(i) + 1;
    return h;
  }
};
} // namespace std
template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
  os << "[ ";
  rep(i, v.size()) os << v[i] << (i == v.size() - 1 ? " ]" : ", ");
  return os;
}
template <class T> ostream &operator<<(ostream &os, const set<T> &v) {
  os << "{ ";
  for (const auto &i : v)
    os << i << ", ";
  return os << "}";
}
template <class T, class U>
ostream &operator<<(ostream &os, const map<T, U> &v) {
  os << "{";
  for (const auto &i : v)
    os << " " << i.first << ": " << i.second << ",";
  return os << "}";
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  return os << "(" << p.first << ", " << p.second << ")";
}
void dbgprint(const string &fmt) { cerr << endl; }
template <class H, class... T>
void dbgprint(const string &fmt, const H &h, const T &...r) {
  cerr << fmt.substr(0, fmt.find(",")) << "= " << h << " ";
  dbgprint(fmt.substr(fmt.find(",") + 1), r...);
}
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pi;
const int inf = (int)1e9;
const double INF = 1e12, EPS = 1e-9;

int main() {
  cin.tie(0);
  cin.sync_with_stdio(0);
  int n;
  cin >> n;
  vi v(n);
  rep(i, n) cin >> v[i];

  {
    bool ok = 1;
    rep(i, n - 1) if (v[i] >= v[i + 1]) ok = 0;
    if (ok) {
      cout << 1 << endl;
      return 0;
    }
  }

  int lo = 1, hi = n, mid;
  while (lo + 1 < hi) {
    mid = (lo + hi) / 2;
    map<int, int> p;
    rep(i, n - 1) {
      if (v[i] < v[i + 1])
        continue;
      int pos = -v[i + 1];
      while (p.size() && p.begin()->first < pos)
        p.erase(p.begin());
      while (pos < 0) {
        if (++p[pos] >= mid) {
          p.erase(pos);
          ++pos;
        } else
          break;
      }
      if (pos == 0) {
        lo = mid;
        goto END;
      }
    }
    hi = mid;
  END:;
  }
  cout << hi << endl;
  return 0;
}