cp-algo/structures/treap/metas/reverse.hpp

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Last update: 2024-11-12 02:11:35+01:00
Include: #include "cp-algo/structures/treap/metas/reverse.hpp"

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#ifndef CP_ALGO_STRUCTURES_TREAP_METAS_REVERSE_HPP
#define CP_ALGO_STRUCTURES_TREAP_METAS_REVERSE_HPP
#include "base.hpp"
#include "../../../math/affine.hpp"
#include <algorithm>
namespace cp_algo::structures::treap::metas {
        template<typename base>
        struct reverse_meta: base_meta {
            using lin = math::lin<base>;
            base val;
            size_t sz = 1;
            bool reverse = false;
            base sum = val;
            
            lin to_push = {};

            reverse_meta(base val): val(val) {}

            void pull(auto const L, auto const R) {
                sum = val + _safe_meta(L, sum) + _safe_meta(R, sum);
                sz = 1 + _safe_meta(L, sz) + _safe_meta(R, sz);
            }
            void add_push(lin const& t) {
                val = t.eval(val);
                sum = t.a * sum + t.b * sz;
                to_push.prepend(t);
            }
            void push(auto &L, auto &R) {
                if(reverse) {
                    reverse = false;
                    std::swap(L, R);
                    _safe_meta(L, reverse ^= 1);
                    _safe_meta(R, reverse ^= 1);
                }
                if(to_push.a != 1 || to_push.b != 0) {
                    _safe_meta(L, add_push(to_push));
                    _safe_meta(R, add_push(to_push));
                    to_push = {};
                }
            }
        };
}
#endif // CP_ALGO_STRUCTURES_TREAP_METAS_REVERSE_HPP

#line 1 "cp-algo/structures/treap/metas/reverse.hpp"


#line 1 "cp-algo/structures/treap/metas/base.hpp"


#line 1 "cp-algo/structures/treap/common.hpp"


#define _safe(t, op) (t ? t->op : typename std::remove_reference_t<decltype(t->op)>())

#line 4 "cp-algo/structures/treap/metas/base.hpp"
#include <functional>
#include <algorithm>
#include <cstdint>
#define _safe_meta(i, op) _safe(i, _meta.op)
namespace cp_algo::structures::treap::metas {
    struct base_meta {
        void pull(auto const, auto const){}
        void push(auto&, auto&){}
    };
}

#line 1 "cp-algo/math/affine.hpp"


#include <optional>
#include <utility>
#include <cassert>
#include <tuple>
namespace cp_algo::math {
    // a * x + b
    template<typename base>
    struct lin {
        base a = 1, b = 0;
        std::optional<base> c;
        lin() {}
        lin(base b): a(0), b(b) {}
        lin(base a, base b): a(a), b(b) {}
        lin(base a, base b, base _c): a(a), b(b), c(_c) {}

        // polynomial product modulo x^2 - c
        lin operator * (const lin& t) {
            assert(c && t.c && *c == *t.c);
            return {a * t.b + b * t.a, b * t.b + a * t.a * (*c), *c};
        }

        // a * (t.a * x + t.b) + b
        lin apply(lin const& t) const {
            return {a * t.a, a * t.b + b};
        }

        void prepend(lin const& t) {
            *this = t.apply(*this);
        }

        base eval(base x) const {
            return a * x + b;
        }
    };

    // (ax+b) / (cx+d)
    template<typename base>
    struct linfrac {
        base a, b, c, d;
        linfrac(): a(1), b(0), c(0), d(1) {} // x, identity for composition
        linfrac(base a): a(a), b(1), c(1), d(0) {} // a + 1/x, for continued fractions
        linfrac(base a, base b, base c, base d): a(a), b(b), c(c), d(d) {}

        // composition of two linfracs
        linfrac operator * (linfrac t) const {
            return t.prepend(linfrac(*this));
        }

        linfrac operator-() const {
            return {-a, -b, -c, -d};
        }

        linfrac adj() const {
            return {d, -b, -c, a};
        }
        
        linfrac& prepend(linfrac const& t) {
            t.apply(a, c);
            t.apply(b, d);
            return *this;
        }

        // apply linfrac to A/B
        void apply(base &A, base &B) const {
            std::tie(A, B) = std::pair{a * A + b * B, c * A + d * B};
        }
    };
}

#line 6 "cp-algo/structures/treap/metas/reverse.hpp"
namespace cp_algo::structures::treap::metas {
        template<typename base>
        struct reverse_meta: base_meta {
            using lin = math::lin<base>;
            base val;
            size_t sz = 1;
            bool reverse = false;
            base sum = val;
            
            lin to_push = {};

            reverse_meta(base val): val(val) {}

            void pull(auto const L, auto const R) {
                sum = val + _safe_meta(L, sum) + _safe_meta(R, sum);
                sz = 1 + _safe_meta(L, sz) + _safe_meta(R, sz);
            }
            void add_push(lin const& t) {
                val = t.eval(val);
                sum = t.a * sum + t.b * sz;
                to_push.prepend(t);
            }
            void push(auto &L, auto &R) {
                if(reverse) {
                    reverse = false;
                    std::swap(L, R);
                    _safe_meta(L, reverse ^= 1);
                    _safe_meta(R, reverse ^= 1);
                }
                if(to_push.a != 1 || to_push.b != 0) {
                    _safe_meta(L, add_push(to_push));
                    _safe_meta(R, add_push(to_push));
                    to_push = {};
                }
            }
        };
}