cp-algo/structures/segtree/metas/affine.hpp

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• Last update: 2024-11-21 04:16:11+01:00
• Include: #include "cp-algo/structures/segtree/metas/affine.hpp"

Depends on

• cp-algo/math/affine.hpp
• cp-algo/structures/segtree/metas/base.hpp

Verified with

• Range Affine Range Sum (verify/structures/segtree/range_affine_range_sum.test.cpp)

Code

#ifndef CP_ALGO_STRUCTURES_SEGMENT_TREE_METAS_AFFINE_HPP
#define CP_ALGO_STRUCTURES_SEGMENT_TREE_METAS_AFFINE_HPP
#include "base.hpp"
#include "../../../math/affine.hpp"
namespace cp_algo::structures::segtree::metas {
    template<typename base>
    struct affine_meta: base_meta<affine_meta<base>> {
        using meta = affine_meta;
        using lin = math::lin<base>;

        base sum = 0;
        lin to_push = {};

        affine_meta() {}
        affine_meta(base sum): sum(sum) {}

        void push(meta *L, meta *R, size_t l, size_t r) override {
            if(to_push.a != 1 || to_push.b != 0) {
                sum = to_push.a * sum + to_push.b * (r - l);
                if(r - l > 1) {
                    L->to_push.prepend(to_push);
                    R->to_push.prepend(to_push);
                }
                to_push = {};
            }
        }

        void pull(meta const& L, meta const& R, size_t, size_t) override {
            sum = L.sum + R.sum;
        }
    };
}
#endif // CP_ALGO_STRUCTURES_SEGMENT_TREE_METAS_AFFINE_HPP

#line 1 "cp-algo/structures/segtree/metas/affine.hpp"


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


#include <cstddef>
namespace cp_algo::structures::segtree::metas {
    template<typename derived_meta>
    struct base_meta {
        using meta = derived_meta;
        virtual void pull(meta const&, meta const&, size_t, size_t) {};
        virtual void push(meta*, meta*, size_t, size_t) {};
    };
}

#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 5 "cp-algo/structures/segtree/metas/affine.hpp"
namespace cp_algo::structures::segtree::metas {
    template<typename base>
    struct affine_meta: base_meta<affine_meta<base>> {
        using meta = affine_meta;
        using lin = math::lin<base>;

        base sum = 0;
        lin to_push = {};

        affine_meta() {}
        affine_meta(base sum): sum(sum) {}

        void push(meta *L, meta *R, size_t l, size_t r) override {
            if(to_push.a != 1 || to_push.b != 0) {
                sum = to_push.a * sum + to_push.b * (r - l);
                if(r - l > 1) {
                    L->to_push.prepend(to_push);
                    R->to_push.prepend(to_push);
                }
                to_push = {};
            }
        }

        void pull(meta const& L, meta const& R, size_t, size_t) override {
            sum = L.sum + R.sum;
        }
    };
}

#ifndef CP_ALGO_STRUCTURES_SEGMENT_TREE_METAS_AFFINE_HPP
#define CP_ALGO_STRUCTURES_SEGMENT_TREE_METAS_AFFINE_HPP
#include "base.hpp"
#include "../../../math/affine.hpp"
namespace cp_algo::structures::segtree::metas{template<typename base>struct affine_meta:base_meta<affine_meta<base>>{using meta=affine_meta;using lin=math::lin<base>;base sum=0;lin to_push={};affine_meta(){}affine_meta(base sum):sum(sum){}void push(meta*L,meta*R,size_t l,size_t r)override{if(to_push.a!=1||to_push.b!=0){sum=to_push.a*sum+to_push.b*(r-l);if(r-l>1){L->to_push.prepend(to_push);R->to_push.prepend(to_push);}to_push={};}}void pull(meta const&L,meta const&R,size_t,size_t)override{sum=L.sum+R.sum;}};}
#endif

#line 1 "cp-algo/structures/segtree/metas/affine.hpp"
#line 1 "cp-algo/structures/segtree/metas/base.hpp"
#include <cstddef>
namespace cp_algo::structures::segtree::metas{template<typename derived_meta>struct base_meta{using meta=derived_meta;virtual void pull(meta const&,meta const&,size_t,size_t){};virtual void push(meta*,meta*,size_t,size_t){};};}
#line 1 "cp-algo/math/affine.hpp"
#include <optional>
#include <utility>
#include <cassert>
#include <tuple>
namespace cp_algo::math{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){}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};}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;}};template<typename base>struct linfrac{base a,b,c,d;linfrac():a(1),b(0),c(0),d(1){}linfrac(base a):a(a),b(1),c(1),d(0){}linfrac(base a,base b,base c,base d):a(a),b(b),c(c),d(d){}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;}void apply(base&A,base&B)const{std::tie(A,B)=std::pair{a*A+b*B,c*A+d*B};}};}
#line 5 "cp-algo/structures/segtree/metas/affine.hpp"
namespace cp_algo::structures::segtree::metas{template<typename base>struct affine_meta:base_meta<affine_meta<base>>{using meta=affine_meta;using lin=math::lin<base>;base sum=0;lin to_push={};affine_meta(){}affine_meta(base sum):sum(sum){}void push(meta*L,meta*R,size_t l,size_t r)override{if(to_push.a!=1||to_push.b!=0){sum=to_push.a*sum+to_push.b*(r-l);if(r-l>1){L->to_push.prepend(to_push);R->to_push.prepend(to_push);}to_push={};}}void pull(meta const&L,meta const&R,size_t,size_t)override{sum=L.sum+R.sum;}};}

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