Problem p02694 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
#include <regex>
using namespace std;

// type
typedef long long int ll;
typedef pair<int, int> P;
// 定数
#define INF 1000000000000 // 10^12:∞
#define MOD 1000000007    // 10^9+7:合同式の法
#define MAXR 100000       // 10^5:配列の最大のrange
// 略記
#define PB push_back // 挿入
#define MP make_pair // pairのコンストラクタ
#define F first      // pairの一つ目の要素
#define S second     // pairの二つ目の要素
#define Z class

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { std::cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int w_ = 0; w_ < n; ++w_) {                                             \\
    MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);                                       \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { std::cin >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    std::cin >> i;
// 2d vector:  MAT(type, v, size, size);
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &R : c)                                                            \\
    for (auto &w : R)                                                          \\
      std::cin >> w;

// output
template <typename T> void MACRO_OUT(const T t) { std::cout << t; }

#define OUT(...) MACRO_OUT(__VA_ARGS__);
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define ENDL std::cout << std::endl;

#define YES() printf("YES\\n")
#define NO() printf("NO\\n")
#define isYES(x) printf("%s\\n", (x) ? "YES" : "NO")
#define Yes() printf("Yes\\n")
#define No() printf("No\\n")
#define yes() printf("yes\\n")
#define no() printf("no\\n")
#define ln cout << '\\n'
template <Z A> void pr(A a) {
  cout << a;
  ln;
}
template <Z A, Z B> void pr(A a, B b) { cout << a << ' ' << b << endl; }

// OTHER
// xの二乗を返す (関数テンプレート版)
template <typename T> T square(T x) { return x * x; }
template <class T> T GCD(T a, T b) {
  T r;
  while (a)
    r = b, b = a, a = r % a;
  return b;
}
template <class T> T LCM(T a, T b) { return a / GCD(a, b) * b; }

#define chmax(x, y) (x = max(x, y))
#define chmin(x, y) (x = min(x, y))
// loop
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define repe(i, n) for (ll i = 0; i <= (n); i++)
#define repd(i, n) for (ll i = n; i > 0; i--)
#define repde(i, n) for (ll i = n; i >= 0; i--)
#define FOR(i, a, b) for (ll i = a; i < (b); i++)
#define FORE(i, a, b) for (ll i = a; i <= (b); i++)
#define FORD(i, a, b) for (ll i = a; i >= (b); i--)
#define FORA(i, I) for (const auto &i : I)

// vector
#define ALL(x) x.begin(), x.end()
typedef vector<int> vi;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef vector<vi> vvi;
typedef vector<ll> vl;
#define ERASE(x) x.erase(unique(ALL(x)), x.end()); // erase same elements

bool yes = 0;
bool boo = 0;
int mx = -100000, mn = 100000;
int sum = 0;

int co = 0;

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
// * * * * * *
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
// * * * * * * cout << (conditon ? (result:  == 1 ): (==0)) << endl; <- output
// result of if long long 型が表せる値の上限はおよそ 9 × 10＾18 です．

// vector
// sum: accumulate(ALl(x),0)
// return last element: v.back();
//  i & 1 は偶数なら 0に 奇数なら1に

// sort (descending order) :  sort(arr, arr+n, greater<int>());

int main() {
  int ans = 0;
  VAR(long long, x);
  long long n = 100;
  while (n < x) {
    n += n / 100;
    ans++;
  }
  pr(ans);
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
#define all(x) (x).begin(), (x).end()
#define YES() printf("YES\\n")
#define NO() printf("NO\\n")
#define isYES(x) printf("%s\\n", (x) ? "YES" : "NO")
#define Yes() printf("Yes\\n")
#define No() printf("No\\n")
#define rep(i, n)for(urs(n)i=0;i<(n);++i

int main() {

  long long n;
  cin >> n;
  int x = 100;
  long long ans = 0;
  while (n >= x) {
    x *= 1.01;
    // cout << x << endl;
    ans++;
    if (n <= x) {
      cout << ans;
      return 0;
    }
  }

  return 0;
}