Problem p03202 (C++)

Buggy submission (status: Time Limit Exceeded):
#include "bits/stdc++.h"
using namespace std;
using LL = long long;
using ULL = unsigned long long;
const double PI = acos(-1);
template <class T> constexpr T INF() { return ::std::numeric_limits<T>::max(); }
template <class T> constexpr T HINF() { return INF<T>() / 2; }
template <typename T_char> T_char TL(T_char cX) { return tolower(cX); };
template <typename T_char> T_char TU(T_char cX) { return toupper(cX); };
typedef pair<LL, LL> pii;
const int vy[] = {-1, -1, -1, 0, 1, 1, 1, 0},
          vx[] = {-1, 0, 1, 1, 1, 0, -1, -1};
const int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
int popcnt(unsigned long long n) {
  int cnt = 0;
  for (int i = 0; i < 64; i++)
    if ((n >> i) & 1)
      cnt++;
  return cnt;
}
int d_sum(LL n) {
  int ret = 0;
  while (n > 0) {
    ret += n % 10;
    n /= 10;
  }
  return ret;
}
int d_cnt(LL n) {
  int ret = 0;
  while (n > 0) {
    ret++;
    n /= 10;
  }
  return ret;
}
LL gcd(LL a, LL b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
};
LL lcm(LL a, LL b) {
  LL g = gcd(a, b);
  return a / g * b;
};
#define ALL(qpqpq) (qpqpq).begin(), (qpqpq).end()
#define UNIQUE(wpwpw)                                                          \
  sort(ALL((wpwpw)));                                                          \
  (wpwpw).erase(unique(ALL((wpwpw))), (wpwpw).end())
#define LOWER(epepe) transform(ALL((epepe)), (epepe).begin(), TL<char>)
#define UPPER(rprpr) transform(ALL((rprpr)), (rprpr).begin(), TU<char>)
#define FOR(i, tptpt, ypypy) for (LL i = (tptpt); i < (ypypy); i++)
#define REP(i, upupu) FOR(i, 0, upupu)
#define INIT                                                                   \
  std::ios::sync_with_stdio(false);                                            \
  std::cin.tie(0)

int n;
int a[202020];
map<int, int> num;
bool calc(int mid) {
  num.erase(ALL(num));
  for (int i = 1; i < n; i++) {
    if (a[i - 1] >= a[i]) {
      if (num.empty()) {
        num[a[i]] = 1;
      } else {
        auto it = num.upper_bound(a[i]);
        num.erase(it, num.end());
        num[a[i]]++;
        int d = a[i];
        while (num[d] == mid) {
          if (d == 1)
            return false;
          num.erase(d);
          d--;
          num[d]++;
        }
      }
    }
  }
  return true;
}

int lis(vector<LL> &v) {
  vector<LL> ans(v.size(), HINF<LL>());
  for (int i = 0; i < v.size(); i++) {
    (*lower_bound(ans.begin(), ans.end(), v[i])) = v[i];
  }
  return lower_bound(ans.begin(), ans.end(), HINF<LL>()) - ans.begin();
}

vector<LL> v;

int main() {
  INIT;
  cin >> n;
  REP(i, n) {
    cin >> a[i];
    v.emplace_back(a[i]);
  }
  if (lis(v) == n) {
    cout << 1 << endl;
    return 0;
  }
  int ng = 0, ok = n + 1;
  while (ok - ng > 1) {
    int mid = (ok + ng) / 2;
    if (calc(mid)) {
      ok = mid;
    } else {
      ng = mid;
    }
  }
  cout << ok << endl;
}

Fixed submission:
#include "bits/stdc++.h"
using namespace std;
using LL = long long;
using ULL = unsigned long long;
const double PI = acos(-1);
template <class T> constexpr T INF() { return ::std::numeric_limits<T>::max(); }
template <class T> constexpr T HINF() { return INF<T>() / 2; }
template <typename T_char> T_char TL(T_char cX) { return tolower(cX); };
template <typename T_char> T_char TU(T_char cX) { return toupper(cX); };
typedef pair<LL, LL> pii;
const int vy[] = {-1, -1, -1, 0, 1, 1, 1, 0},
          vx[] = {-1, 0, 1, 1, 1, 0, -1, -1};
const int dx[4] = {0, 1, 0, -1}, dy[4] = {1, 0, -1, 0};
int popcnt(unsigned long long n) {
  int cnt = 0;
  for (int i = 0; i < 64; i++)
    if ((n >> i) & 1)
      cnt++;
  return cnt;
}
int d_sum(LL n) {
  int ret = 0;
  while (n > 0) {
    ret += n % 10;
    n /= 10;
  }
  return ret;
}
int d_cnt(LL n) {
  int ret = 0;
  while (n > 0) {
    ret++;
    n /= 10;
  }
  return ret;
}
LL gcd(LL a, LL b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
};
LL lcm(LL a, LL b) {
  LL g = gcd(a, b);
  return a / g * b;
};
#define ALL(qpqpq) (qpqpq).begin(), (qpqpq).end()
#define UNIQUE(wpwpw)                                                          \
  sort(ALL((wpwpw)));                                                          \
  (wpwpw).erase(unique(ALL((wpwpw))), (wpwpw).end())
#define LOWER(epepe) transform(ALL((epepe)), (epepe).begin(), TL<char>)
#define UPPER(rprpr) transform(ALL((rprpr)), (rprpr).begin(), TU<char>)
#define FOR(i, tptpt, ypypy) for (LL i = (tptpt); i < (ypypy); i++)
#define REP(i, upupu) FOR(i, 0, upupu)
#define INIT                                                                   \
  std::ios::sync_with_stdio(false);                                            \
  std::cin.tie(0)

int n;
int a[202020];
map<int, int> num;
bool calc(int mid) {
  num.erase(ALL(num));
  for (int i = 1; i < n; i++) {
    if (a[i - 1] >= a[i]) {
      if (num.empty()) {
        num[a[i]] = 1;
      } else {
        auto it = num.upper_bound(a[i]);
        num.erase(it, num.end());
        num[a[i]]++;
        int d = a[i];
        while (num[d] == mid) {
          if (d == 1)
            return false;
          num.erase(d);
          d--;
          num[d]++;
        }
      }
    }
  }
  return true;
}

int lis(vector<LL> &v) {
  vector<LL> ans(v.size(), HINF<LL>());
  for (int i = 0; i < v.size(); i++) {
    (*lower_bound(ans.begin(), ans.end(), v[i])) = v[i];
  }
  return lower_bound(ans.begin(), ans.end(), HINF<LL>()) - ans.begin();
}

vector<LL> v;

int main() {
  INIT;
  cin >> n;
  REP(i, n) {
    cin >> a[i];
    v.emplace_back(a[i]);
  }
  if (lis(v) == n) {
    cout << 1 << endl;
    return 0;
  }
  int ng = 1, ok = n + 1;
  while (ok - ng > 1) {
    int mid = (ok + ng) / 2;
    if (calc(mid)) {
      ok = mid;
    } else {
      ng = mid;
    }
  }
  cout << ok << endl;
}