verify/data-structure/LC_segment_add_get_min.test.cpp

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Last update: 2026-08-11 23:01:09+09:00
Problem: https://judge.yosupo.jp/problem/segment_add_get_min

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"

#include "template/template.hpp"
#include "data-structure/li-chao-tree.hpp"

int main() {
  const ll INF = 1LL << 62;
  int n, q;
  in(n, q);
  vector<tuple<ll, ll, ll, ll>> init(n);
  rep(i, 0, n) {
    ll l, r, a, b;
    in(l, r, a, b);
    init[i] = {l, r, a, b};
  }
  vector<tuple<int, ll, ll, ll, ll>> query;
  vector<ll> xs;
  rep(i, 0, q) {
    int type;
    in(type);
    if (type == 0) {
      ll l, r, a, b;
      in(l, r, a, b);
      query.emplace_back(type, l, r, a, b);
    } else {
      ll p;
      in(p);
      query.emplace_back(type, p, 0, 0, 0);
      xs.push_back(p);
    }
  }
  LiChaoTree<ll> cht(xs, INF);
  for (auto [l, r, a, b] : init) cht.add_segment(l, r, a, b);
  for (auto [type, l, r, a, b] : query) {
    if (type == 0) {
      cht.add_segment(l, r, a, b);
    } else {
      ll ans = cht.get(l);
      if (ans == INF)
        out("INFINITY");
      else
        out(ans);
    }
  }
}

#line 1 "verify/data-structure/LC_segment_add_get_min.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/segment_add_get_min"

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"

#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using priority_queue_asc = priority_queue<T, vector<T>, greater<T>>;

template <class T, class S = T>
S SUM(const vector<T>& a) {
  return accumulate(ALL(a), S(0));
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmin_opt(optional<T1>& a, T2 b) {
  if (!a || a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax_opt(optional<T1>& a, T2 b) {
  if (!a || a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"

#line 2 "template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

ostream& operator<<(ostream& os, __uint128_t x) {
  char buf[40];
  size_t k = 0;
  while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
  if (k == 0) buf[k++] = '0';
  while (k) os << buf[--k];
  return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
  return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
  for (auto& v : a) is >> v;
  return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
  cin >> t;
  in(u...);
}
template <class... T>
void in_zip(int n, T&... t) {
  assert(n >= 0 && ((size(t) >= static_cast<size_t>(n)) && ...));
  for (int i = 0; i < n; i++) in(t[i]...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}
template <class T, class U>
void out_opt(const optional<T>& opt, const U& fallback, ostream& os = cout) {
  if (opt.has_value())
    os << opt.value();
  else
    os << fallback;
  os << "\n";
}
template <class T, class U>
void out_opt(const vector<optional<T>>& vec, const U& fallback, ostream& os = cout) {
  for (auto it = vec.begin(); it != vec.end();) {
    if ((*it).has_value())
      os << (*it).value();
    else
      os << fallback;
    if (++it != vec.end()) os << " ";
  }
  os << "\n";
}

namespace IO {
template <class T, class... U>
T read(U&&... u) {
  T t = T(forward<U>(u)...);
  in(t);
  return t;
}
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    u -= offset, v -= offset;
    g[u].push_back(v);
    if (!directed) g[v].push_back(u);
  }
  return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<pair<int, T>>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    T w;
    cin >> u >> v >> w;
    u -= offset, v -= offset;
    g[u].push_back({v, w});
    if (!directed) g[v].push_back({u, w});
  }
  return g;
}
}  // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
  return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
  return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 1; i < n; i++) {
    int p;
    cin >> p;
    p -= offset;
    if (to_root) g[i].push_back(p);
    if (to_leaf) g[p].push_back(i);
  }
  return g;
}
}  // namespace Tree
}  // namespace IO
#line 10 "template/template.hpp"

#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int, T) {
  cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1& a, const T2& b, const T3&... c) {
  for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
  cerr << ":" << b << " ";
  _show(i + 1, a, c...);
}
#line 2 "data-structure/li-chao-tree.hpp"

template <class T>
struct LiChaoTree {
  struct Line {
    T a, b;
    Line() : a(0), b(0) {}
    Line(T a_, T b_) : a(a_), b(b_) {}
    T get(T x) const { return a * x + b; }
  };

  LiChaoTree() : n(0), inf(numeric_limits<T>::max() / 4) {}
  LiChaoTree(vector<T> xs_, T inf_ = numeric_limits<T>::max() / 4) : inf(inf_) {
    sort(xs_.begin(), xs_.end());
    xs_.erase(unique(xs_.begin(), xs_.end()), xs_.end());
    xs = xs_;
    n = xs.size();
    seg.assign(n * 4 + 1, Line());
    used.assign(n * 4 + 1, false);
  }

  void add_line(T a, T b) { add_line(Line(a, b)); }
  void add_line(Line line) {
    if (n == 0) return;
    add_line(line, 1, 0, n);
  }
  void add_segment(T l, T r, T a, T b) { add_segment(l, r, Line(a, b)); }
  void add_segment(T l, T r, Line line) {
    if (n == 0) return;
    int il = lower_bound(xs.begin(), xs.end(), l) - xs.begin();
    int ir = lower_bound(xs.begin(), xs.end(), r) - xs.begin();
    add_segment(line, il, ir, 1, 0, n);
  }
  T get(T x) const {
    int k = lower_bound(xs.begin(), xs.end(), x) - xs.begin();
    assert(k < n && xs[k] == x);
    return get(x, k, 1, 0, n);
  }

 private:
  int n;
  T inf;
  vector<T> xs;
  vector<Line> seg;
  vector<bool> used;

  void add_line(Line line, int k, int l, int r) {
    if (!used[k]) {
      used[k] = true;
      seg[k] = line;
      return;
    }
    int m = (l + r) >> 1;
    T xl = xs[l], xm = xs[m], xr = xs[r - 1];
    Line low = seg[k], high = line;
    if (low.get(xm) > high.get(xm)) swap(low, high);
    seg[k] = low;
    if (r - l == 1) return;
    if (low.get(xl) > high.get(xl)) {
      add_line(high, k << 1, l, m);
    } else if (low.get(xr) > high.get(xr)) {
      add_line(high, k << 1 | 1, m, r);
    }
  }
  void add_segment(Line line, int ql, int qr, int k, int l, int r) {
    if (qr <= l || r <= ql) return;
    if (ql <= l && r <= qr) {
      add_line(line, k, l, r);
      return;
    }
    int m = (l + r) >> 1;
    add_segment(line, ql, qr, k << 1, l, m);
    add_segment(line, ql, qr, k << 1 | 1, m, r);
  }
  T get(T x, int p, int k, int l, int r) const {
    T ret = used[k] ? seg[k].get(x) : inf;
    if (r - l == 1) return ret;
    int m = (l + r) >> 1;
    if (p < m) return min(ret, get(x, p, k << 1, l, m));
    return min(ret, get(x, p, k << 1 | 1, m, r));
  }
};

/**
 * @brief Li Chao Tree
 * @docs docs/data-structure/li-chao-tree.md
 */
#line 5 "verify/data-structure/LC_segment_add_get_min.test.cpp"

int main() {
  const ll INF = 1LL << 62;
  int n, q;
  in(n, q);
  vector<tuple<ll, ll, ll, ll>> init(n);
  rep(i, 0, n) {
    ll l, r, a, b;
    in(l, r, a, b);
    init[i] = {l, r, a, b};
  }
  vector<tuple<int, ll, ll, ll, ll>> query;
  vector<ll> xs;
  rep(i, 0, q) {
    int type;
    in(type);
    if (type == 0) {
      ll l, r, a, b;
      in(l, r, a, b);
      query.emplace_back(type, l, r, a, b);
    } else {
      ll p;
      in(p);
      query.emplace_back(type, p, 0, 0, 0);
      xs.push_back(p);
    }
  }
  LiChaoTree<ll> cht(xs, INF);
  for (auto [l, r, a, b] : init) cht.add_segment(l, r, a, b);
  for (auto [type, l, r, a, b] : query) {
    if (type == 0) {
      cht.add_segment(l, r, a, b);
    } else {
      ll ans = cht.get(l);
      if (ans == INF)
        out("INFINITY");
      else
        out(ans);
    }
  }
}