#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif plint rdpl() { lint a, b; cin >> a >> b; return {a, b}; } using Tri = pair; Tri read_tri() { plint A = rdpl(); plint B = rdpl(); plint C = rdpl(); auto d1 = B - A, d2 = C - A; const lint S = abs(d1.first * d2.second - d2.first * d1.second); const lint lo = min({A.first, B.first, C.first}), hi = max({A.first, B.first, C.first}); return {{lo, hi}, S}; } #ifndef ATCODER_INTERNAL_BITOP_HPP #define ATCODER_INTERNAL_BITOP_HPP 1 #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { // @param n `0 <= n` // @return minimum non-negative `x` s.t. `n <= 2**x` int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace atcoder #endif // ATCODER_INTERNAL_BITOP_HPP #ifndef ATCODER_SEGTREE_HPP #define ATCODER_SEGTREE_HPP 1 #include #include #include // #include "atcoder/internal_bit" namespace atcoder { template struct segtree { public: segtree() : segtree(0) {} explicit segtree(int n) : segtree(std::vector(n, e())) {} explicit segtree(const std::vector& v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector(2 * size, e()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) const { assert(0 <= p && p < _n); return d[p + size]; } S prod(int l, int r) const { assert(0 <= l && l <= r && r <= _n); S sml = e(), smr = e(); l += size; r += size; while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() const { return d[1]; } template int max_right(int l) const { return max_right(l, [](S x) { return f(x); }); } template int max_right(int l, F f) const { assert(0 <= l && l <= _n); assert(f(e())); if (l == _n) return _n; l += size; S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!f(op(sm, d[l]))) { while (l < size) { l = (2 * l); if (f(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template int min_left(int r) const { return min_left(r, [](S x) { return f(x); }); } template int min_left(int r, F f) const { assert(0 <= r && r <= _n); assert(f(e())); if (r == 0) return 0; r += size; S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!f(op(d[r], sm))) { while (r < size) { r = (2 * r + 1); if (f(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; std::vector d; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } }; } // namespace atcoder #endif // ATCODER_SEGTREE_HPP lint op(lint l, lint r) { return max(l, r); } lint e() { return -1; } // Reference: https://atcoder.github.io/ac-library/document_ja/segtree.html /* usage: struct S { long long su; int nb; }; S e() { return {0, 0}; } S op(S l, S r) { return {l.su + r.su, l.nb + r.nb}; } vector seginit(100000, e()); atcoder::segtree segtree(seginit); */ std::vector segtree_range_covering_nodes(int N, int l, int r) { std::vector ret, ret_rev; l += N, r += N; while (l < r) { if (l & 1) ret.push_back(l++); if (r & 1) ret_rev.push_back(--r); l >>= 1, r >>= 1; } std::reverse(ret_rev.begin(), ret_rev.end()); ret.insert(ret.end(), ret_rev.begin(), ret_rev.end()); return ret; } int main() { int N, Q; cin >> N >> Q; vector tris(N); for (auto &x : tris) x = read_tri(); vector TP(Q); vector tris_add(Q); vector qs(Q); REP(q, Q) { int tp; cin >> tp; TP[q] = tp; if (tp == 1) tris_add[q] = read_tri(); else { int l, r; cin >> l >> r; qs[q] = {l, r}; } } vector xs; for (auto triv : {tris, tris_add}) { for (auto [lh, S] : triv) { auto [l, h] = lh; xs.push_back(l), xs.push_back(h + 1); } } xs = sort_unique(xs); const int K = xs.size(); vector> x2y(K * 2); dbg(xs); dbg(tris); dbg(tris_add); for (const auto trivec : {tris, tris_add}) { for (const auto [lh, S] : trivec) { const auto [l, h] = lh; int i = arglb(xs, int(l)) + K; // int j = arglb(xs, int(h + 1)); while (i) { x2y[i].push_back(h); i /= 2; } // for (auto k : segtree_range_covering_nodes(K, i, j)) { // x2y[k].push_back(h); // } } } for (auto &v : x2y) v = sort_unique(v); dbg(x2y); using Tree = atcoder::segtree; vector trees; for (auto v : x2y) trees.push_back(Tree(v.size())); auto add_tri = [&](Tri tri) { const auto [lr, S] = tri; const auto [l, r] = lr; int k = arglb(xs, l) + K; while (k) { auto x = arglb(x2y[k], int(r)); if (trees[k].get(x) < S) { } trees[k].set(x, S); k /= 2; } // const int j = arglb(xs, r + 1); // for (auto k : segtree_range_covering_nodes(K, i, j)) { // } }; dbg(tris); for (auto tri : tris) add_tri(tri); REP(q, Q) { if (TP[q] == 1) { add_tri(tris_add[q]); } else { auto [l, r] = qs[q]; int i = arglb(xs, l); int j = arglb(xs, r + 1); lint ret = -1; for (auto k : segtree_range_covering_nodes(K, i, j)) { int rr = argub(x2y[k], int(r)); chmax(ret, trees[k].prod(0, rr)); } cout << ret << '\n'; } } }