Problem p03966 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
#include <unistd.h>

#define fi first
#define se second
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (n); ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define ALL(a) a.begin(), a.end()
#define pb push_back
#define dame                                                                   \
  {                                                                            \
    puts("-1");                                                                \
    return 0;                                                                  \
  }
#define show(x) cerr << #x << " = " << x << endl;

using namespace std;
using ll = long long;
using ld = long double;
using pl = pair<ll, ll>;
ll LINF = 1000000000000000000;

typedef vector<ll> vl;
typedef vector<pl> vp;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

struct UnionFind {
  vector<int> d;
  UnionFind(int n = 0) : d(n, -1) {}
  int root(int x) {
    if (d[x] < 0)
      return x;
    return d[x] = root(d[x]);
  }
  bool unite(int x, int y) {
    x = root(x);
    y = root(y);
    if (x == y)
      return false;
    if (d[x] > d[y])
      swap(x, y);
    d[x] += d[y];
    d[y] = x;
    return true;
  }
  bool same(int x, int y) { return root(x) == root(y); }
  int size(int x) { return -d[root(x)]; }
  int factor_size() {
    int ans = 0;
    rep(i, d.size()) {
      if (d[i] < 0) {
        ans++;
      }
    }
    return ans;
  }
};

ll d[201][201];

void warshall_floyd(ll n) {
  rep(k, n) {
    rep(i, n) {
      rep(j, n) { d[i][j] = min(d[i][j], d[i][k] + d[k][j]); }
    }
  }
}

struct edge {
  ll to, cost;
};

struct dijkstra {
  ll V;
  vector<vector<edge>> G;
  vector<ll> d;

  dijkstra(ll n) { init(n); }

  void init(ll n) {
    V = n;
    G.resize(V);
    d.resize(V);
    rep(i, V) { d[i] = LINF; }
  }

  void add_edge(ll s, ll t, ll cost) {
    edge e;
    e.to = t, e.cost = cost;
    G[s].push_back(e);
  }

  void run(ll s) {
    rep(i, V) { d[i] = LINF; }
    d[s] = 0;
    priority_queue<pl, vector<pl>, greater<pl>> que;
    que.push(pl(0, s));
    while (!que.empty()) {
      pl p = que.top();
      que.pop();
      ll v = p.second;
      if (d[v] < p.first)
        continue;
      for (auto e : G[v]) {
        if (d[e.to] > d[v] + e.cost) {
          d[e.to] = d[v] + e.cost;
          que.push(pl(d[e.to], e.to));
        }
      }
    }
  }
};
// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const ll mod = 7;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
// struct combination {
//   vector<mint> fact, ifact;
//   combination(int n):fact(n+1),ifact(n+1) {
//     assert(n < mod);
//     fact[0] = 1;
//     for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i;
//     ifact[n] = fact[n].inv();
//     for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i;
//   }
//   mint operator()(int n, int k) {
//     if (k < 0 || k > n) return 0;
//     return fact[n]*ifact[k]*ifact[n-k];
//   }
// } c(200005);

// Sieve of Eratosthenes
// https://youtu.be/UTVg7wzMWQc?t=2774
struct Sieve {
  int n;
  vector<int> f, primes;
  Sieve(int n = 1) : n(n), f(n + 1) {
    f[0] = f[1] = -1;
    for (ll i = 2; i <= n; ++i) {
      if (f[i])
        continue;
      primes.push_back(i);
      f[i] = i;
      for (ll j = i * i; j <= n; j += i) {
        if (!f[j])
          f[j] = i;
      }
    }
  }
  bool isPrime(int x) { return f[x] == x; }
  vector<int> factorList(int x) {
    vector<int> res;
    while (x != 1) {
      res.push_back(f[x]);
      x /= f[x];
    }
    return res;
  }
  vector<pl> factor(int x) {
    vector<int> fl = factorList(x);
    if (fl.size() == 0)
      return {};
    vector<pl> res(1, pl(fl[0], 0));
    for (int p : fl) {
      if (res.back().first == p) {
        res.back().second++;
      } else {
        res.emplace_back(p, 1);
      }
    }
    return res;
  }
  vector<pair<ll, int>> factor(ll x) {
    vector<pair<ll, int>> res;
    for (int p : primes) {
      int y = 0;
      while (x % p == 0)
        x /= p, ++y;
      if (y != 0)
        res.emplace_back(p, y);
    }
    if (x != 1)
      res.emplace_back(x, 1);
    return res;
  }
};

using data = pair<ll, vector<ll>>;

ll ans;
int C;

void dfs(vector<int> &w, vector<vector<int>> &v) {
  // rep(i, w.size()) show(w[i]);
  // show("----------------------------");
  if (w.size() == 3) {
    ll ret = 0;
    rep(i, 3) ret += ll(v[i][w[i]]);
    chmin(ans, ret);
    // return;
  } else {
    rep(i, C) {
      bool f = false;
      rep(j, w.size()) if (w[j] == i) f = true;

      if (f)
        continue;
      w.pb(i);
      dfs(w, v);
      w.pop_back();
    }
  }
}

int main() {
  int n;
  cin >> n;

  ll t, a, T = 1, A = 1;
  rep(i, n) {
    cin >> t >> a;
    ll ind = min(1LL, max(T / t, A / a));
    //    show(ind);
    while (true) {
      if (t * ind >= T and a * ind >= A)
        break;
      ind++;
    }
    T = t * ind;
    A = a * ind;
  }

  ll ans = A + T;
  // cout << -1 << endl;
  cout << ans << endl;
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
#include <unistd.h>

#define fi first
#define se second
#define rep(i, n) for (ll i = 0; i < (n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (n); ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define ALL(a) a.begin(), a.end()
#define pb push_back
#define dame                                                                   \
  {                                                                            \
    puts("-1");                                                                \
    return 0;                                                                  \
  }
#define show(x) cerr << #x << " = " << x << endl;

using namespace std;
using ll = long long;
using ld = long double;
using pl = pair<ll, ll>;
ll LINF = 1000000000000000000;

typedef vector<ll> vl;
typedef vector<pl> vp;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

struct UnionFind {
  vector<int> d;
  UnionFind(int n = 0) : d(n, -1) {}
  int root(int x) {
    if (d[x] < 0)
      return x;
    return d[x] = root(d[x]);
  }
  bool unite(int x, int y) {
    x = root(x);
    y = root(y);
    if (x == y)
      return false;
    if (d[x] > d[y])
      swap(x, y);
    d[x] += d[y];
    d[y] = x;
    return true;
  }
  bool same(int x, int y) { return root(x) == root(y); }
  int size(int x) { return -d[root(x)]; }
  int factor_size() {
    int ans = 0;
    rep(i, d.size()) {
      if (d[i] < 0) {
        ans++;
      }
    }
    return ans;
  }
};

ll d[201][201];

void warshall_floyd(ll n) {
  rep(k, n) {
    rep(i, n) {
      rep(j, n) { d[i][j] = min(d[i][j], d[i][k] + d[k][j]); }
    }
  }
}

struct edge {
  ll to, cost;
};

struct dijkstra {
  ll V;
  vector<vector<edge>> G;
  vector<ll> d;

  dijkstra(ll n) { init(n); }

  void init(ll n) {
    V = n;
    G.resize(V);
    d.resize(V);
    rep(i, V) { d[i] = LINF; }
  }

  void add_edge(ll s, ll t, ll cost) {
    edge e;
    e.to = t, e.cost = cost;
    G[s].push_back(e);
  }

  void run(ll s) {
    rep(i, V) { d[i] = LINF; }
    d[s] = 0;
    priority_queue<pl, vector<pl>, greater<pl>> que;
    que.push(pl(0, s));
    while (!que.empty()) {
      pl p = que.top();
      que.pop();
      ll v = p.second;
      if (d[v] < p.first)
        continue;
      for (auto e : G[v]) {
        if (d[e.to] > d[v] + e.cost) {
          d[e.to] = d[v] + e.cost;
          que.push(pl(d[e.to], e.to));
        }
      }
    }
  }
};
// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const ll mod = 7;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
// struct combination {
//   vector<mint> fact, ifact;
//   combination(int n):fact(n+1),ifact(n+1) {
//     assert(n < mod);
//     fact[0] = 1;
//     for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i;
//     ifact[n] = fact[n].inv();
//     for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i;
//   }
//   mint operator()(int n, int k) {
//     if (k < 0 || k > n) return 0;
//     return fact[n]*ifact[k]*ifact[n-k];
//   }
// } c(200005);

// Sieve of Eratosthenes
// https://youtu.be/UTVg7wzMWQc?t=2774
struct Sieve {
  int n;
  vector<int> f, primes;
  Sieve(int n = 1) : n(n), f(n + 1) {
    f[0] = f[1] = -1;
    for (ll i = 2; i <= n; ++i) {
      if (f[i])
        continue;
      primes.push_back(i);
      f[i] = i;
      for (ll j = i * i; j <= n; j += i) {
        if (!f[j])
          f[j] = i;
      }
    }
  }
  bool isPrime(int x) { return f[x] == x; }
  vector<int> factorList(int x) {
    vector<int> res;
    while (x != 1) {
      res.push_back(f[x]);
      x /= f[x];
    }
    return res;
  }
  vector<pl> factor(int x) {
    vector<int> fl = factorList(x);
    if (fl.size() == 0)
      return {};
    vector<pl> res(1, pl(fl[0], 0));
    for (int p : fl) {
      if (res.back().first == p) {
        res.back().second++;
      } else {
        res.emplace_back(p, 1);
      }
    }
    return res;
  }
  vector<pair<ll, int>> factor(ll x) {
    vector<pair<ll, int>> res;
    for (int p : primes) {
      int y = 0;
      while (x % p == 0)
        x /= p, ++y;
      if (y != 0)
        res.emplace_back(p, y);
    }
    if (x != 1)
      res.emplace_back(x, 1);
    return res;
  }
};

using data = pair<ll, vector<ll>>;

ll ans;
int C;

void dfs(vector<int> &w, vector<vector<int>> &v) {
  // rep(i, w.size()) show(w[i]);
  // show("----------------------------");
  if (w.size() == 3) {
    ll ret = 0;
    rep(i, 3) ret += ll(v[i][w[i]]);
    chmin(ans, ret);
    // return;
  } else {
    rep(i, C) {
      bool f = false;
      rep(j, w.size()) if (w[j] == i) f = true;

      if (f)
        continue;
      w.pb(i);
      dfs(w, v);
      w.pop_back();
    }
  }
}

int main() {
  int n;
  cin >> n;

  ll t, a, T = 1, A = 1;
  rep(i, n) {
    cin >> t >> a;
    ll ind = max(1LL, max(T / t, A / a));
    //    show(ind);
    while (true) {
      if (t * ind >= T and a * ind >= A)
        break;
      ind++;
    }
    T = t * ind;
    A = a * ind;
  }

  ll ans = A + T;
  // cout << -1 << endl;
  cout << ans << endl;
  return 0;
}