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aka_iterators.hh
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			/**
			* @file aka_iterators.hh
			*
			* @author Nicolas Richart <nicolas.richart@epfl.ch>
			*
			* @date creation: Fri Aug 11 2017
			* @date last modification: Mon Jan 29 2018
			*
			* @brief iterator interfaces
			*
			* @section LICENSE
			*
			* Copyright (©) 2016-2018 EPFL (Ecole Polytechnique Fédérale de Lausanne)
			* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
			*
			* Akantu is free software: you can redistribute it and/or modify it under the
			* terms of the GNU Lesser General Public License as published by the Free
			* Software Foundation, either version 3 of the License, or (at your option) any
			* later version.
			*
			* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
			* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
			* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
			* details.
			*
			* You should have received a copy of the GNU Lesser General Public License
			* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
			*
			*/

			/* -------------------------------------------------------------------------- */
			#include "aka_compatibilty_with_cpp_standard.hh"
			#include "aka_tuple_tools.hh"
			/* -------------------------------------------------------------------------- */
			#include <iterator>
			#include <tuple>
			#include <utility>

			/* -------------------------------------------------------------------------- */
			#ifndef AKANTU_AKA_ITERATORS_HH
			#define AKANTU_AKA_ITERATORS_HH

			#ifndef AKANTU_ITERATOR_NAMESPACE
			#define AKANTU_ITERATOR_NAMESPACE akantu
			#endif

			namespace AKANTU_ITERATOR_NAMESPACE {

			/* -------------------------------------------------------------------------- */
			namespace iterators {
			namespace details {
			template <typename cat1, typename cat2>
			using is_iterator_category_at_least =
			std::is_same<std::common_type_t<cat1, cat2>, cat2>;
			}

			template <class... Iterators> class ZipIterator {
			private:
			using tuple_t = std::tuple<Iterators...>;

			public:
			using value_type =
			std::tuple<typename std::iterator_traits<Iterators>::value_type...>;
			using difference_type = std::common_type_t<
			typename std::iterator_traits<Iterators>::difference_type...>;
			using pointer =
			std::tuple<typename std::iterator_traits<Iterators>::pointer...>;
			using reference =
			std::tuple<typename std::iterator_traits<Iterators>::reference...>;
			using iterator_category = // std::input_iterator_tag;
			std::common_type_t<
			typename std::iterator_traits<Iterators>::iterator_category...>;

			using nb_iterators = std::tuple_size<tuple_t>;

			public:
			explicit ZipIterator(tuple_t iterators) : iterators(std::move(iterators)) {}

			ZipIterator(const ZipIterator & other) = default;
			ZipIterator(ZipIterator && other) noexcept = default;

			ZipIterator & operator=(const ZipIterator & other) = default;
			ZipIterator & operator=(ZipIterator && other) noexcept = default;

			/* ---------------------------------------------------------------------- */
			template <class iterator_category_ = iterator_category,
			std::enable_if_t<details::is_iterator_category_at_least<
			iterator_category_,
			std::bidirectional_iterator_tag>::value> * = nullptr>
			ZipIterator & operator--() {
			tuple::foreach ([](auto && it) { --it; }, iterators);
			return *this;
			}

			template <class iterator_category_ = iterator_category,
			std::enable_if_t<details::is_iterator_category_at_least<
			iterator_category_,
			std::bidirectional_iterator_tag>::value> * = nullptr>
			ZipIterator operator--(int a) {
			auto cpy = *this;
			this->operator--();
			return cpy;
			}

			// input iterator ++it
			ZipIterator & operator++() {
			tuple::foreach ([](auto && it) { ++it; }, iterators);
			return *this;
			}

			// input iterator it++
			ZipIterator operator++(int) {
			auto cpy = *this;
			this->operator++();
			return cpy;
			}

			// input iterator it != other_it
			bool operator!=(const ZipIterator & other) const {
			// return tuple::are_not_equal(iterators, other.iterators);
			return std::get<0>(iterators) !=
			std::get<0>(other.iterators); // helps the compiler to optimize
			}

			// input iterator dereference *it
			decltype(auto) operator*() {
			return tuple::transform([](auto && it) -> decltype(auto) { return *it; },
			iterators);
			}

			template <class iterator_category_ = iterator_category,
			std::enable_if_t<details::is_iterator_category_at_least<
			iterator_category_,
			std::random_access_iterator_tag>::value> * = nullptr>
			difference_type operator-(const ZipIterator & other) {
			return std::get<0>(this->iterators) - std::get<0>(other.iterators);
			}

			// random iterator it[idx]
			template <class iterator_category_ = iterator_category,
			std::enable_if_t<details::is_iterator_category_at_least<
			iterator_category_,
			std::random_access_iterator_tag>::value> * = nullptr>
			decltype(auto) operator[](std::size_t idx) {
			return tuple::transform(
			[idx](auto && it) -> decltype(auto) { return it[idx]; }, iterators);
			}

			// random iterator it + n
			template <class iterator_category_ = iterator_category,
			std::enable_if_t<details::is_iterator_category_at_least<
			iterator_category_,
			std::random_access_iterator_tag>::value> * = nullptr>
			decltype(auto) operator+(std::size_t n) {
			return ZipIterator(std::forward<tuple_t>(tuple::transform(
			[n](auto && it) -> decltype(auto) { return it + n; }, iterators)));
			}

			// random iterator it - n
			template <class iterator_category_ = iterator_category,
			std::enable_if_t<details::is_iterator_category_at_least<
			iterator_category_,
			std::random_access_iterator_tag>::value> * = nullptr>
			decltype(auto) operator-(std::size_t n) {
			return ZipIterator(std::forward<tuple_t>(tuple::transform(
			[n](auto && it) -> decltype(auto) { return it - n; }, iterators)));
			}

			template <
			class iterator_category_ = iterator_category,
			std::enable_if_t<details::is_iterator_category_at_least<
			iterator_category_, std::forward_iterator_tag>::value> * = nullptr>
			bool operator==(const ZipIterator & other) const {
			return not tuple::are_not_equal(iterators, other.iterators);
			}

			private:
			tuple_t iterators;
			};
			} // namespace iterators

			/* -------------------------------------------------------------------------- */
			template <class... Iterators>
			decltype(auto) zip_iterator(std::tuple<Iterators...> && iterators_tuple) {
			auto zip = iterators::ZipIterator<Iterators...>(
			std::forward<decltype(iterators_tuple)>(iterators_tuple));
			return zip;
			}

			/* -------------------------------------------------------------------------- */
			namespace containers {
			template <class... Containers> class ZipContainer {
			using containers_t = std::tuple<Containers...>;

			public:
			explicit ZipContainer(Containers &&... containers)
			: containers(std::forward<Containers>(containers)...) {}

			decltype(auto) begin() const {
			return zip_iterator(
			tuple::transform([](auto && c) { return c.begin(); },
			std::forward<containers_t>(containers)));
			}

			decltype(auto) end() const {
			return zip_iterator(
			tuple::transform([](auto && c) { return c.end(); },
			std::forward<containers_t>(containers)));
			}

			decltype(auto) begin() {
			return zip_iterator(
			tuple::transform([](auto && c) { return c.begin(); },
			std::forward<containers_t>(containers)));
			}

			decltype(auto) end() {
			return zip_iterator(
			tuple::transform([](auto && c) { return c.end(); },
			std::forward<containers_t>(containers)));
			}

			// template <class Container = std::tuple_element<0, containers_t>,
			// std::enable_if_t<std::is_integral<decltype(
			// std::declval<Container>().size())>::value> * = nullptr>
			// decltype(auto) size() {
			// return std::forward<Container>(std::get<0>(containers)).size();
			// }

			private:
			containers_t containers;
			};

			template <class Iterator> class Range {
			public:
			using iterator = Iterator;
			// ugly trick
			using const_iterator = Iterator;

			explicit Range(Iterator && it1, Iterator && it2)
			: iterators(std::forward<Iterator>(it1), std::forward<Iterator>(it2)) {}

			decltype(auto) begin() const { return std::get<0>(iterators); }
			decltype(auto) begin() { return std::get<0>(iterators); }

			decltype(auto) end() const { return std::get<1>(iterators); }
			decltype(auto) end() { return std::get<1>(iterators); }

			private:
			std::tuple<Iterator, Iterator> iterators;
			};
			} // namespace containers

			/* -------------------------------------------------------------------------- */
			template <class... Containers> decltype(auto) zip(Containers &&... conts) {
			return containers::ZipContainer<Containers...>(
			std::forward<Containers>(conts)...);
			}

			template <class Iterator>
			decltype(auto) range(Iterator && it1, Iterator && it2) {
			return containers::Range<Iterator>(std::forward<Iterator>(it1),
			std::forward<Iterator>(it2));
			}
			/* -------------------------------------------------------------------------- */
			/* Arange */
			/* -------------------------------------------------------------------------- */
			namespace iterators {
			template <class T> class ArangeIterator {
			public:
			using value_type = T;
			using pointer = T *;
			using reference = T &;
			using difference_type = size_t;
			using iterator_category = std::forward_iterator_tag;

			constexpr ArangeIterator(T value, T step) : value(value), step(step) {}
			constexpr ArangeIterator(const ArangeIterator &) = default;

			constexpr ArangeIterator & operator++() {
			value += step;
			return *this;
			}

			constexpr T operator*() const { return value; }

			constexpr bool operator==(const ArangeIterator & other) const {
			return (value == other.value) and (step == other.step);
			}

			constexpr bool operator!=(const ArangeIterator & other) const {
			return not operator==(other);
			}

			private:
			T value{0};
			const T step{1};
			};
			} // namespace iterators

			namespace containers {
			template <class T> class ArangeContainer {
			public:
			using iterator = iterators::ArangeIterator<T>;
			using const_iterator = iterators::ArangeIterator<T>;

			constexpr ArangeContainer(T start, T stop, T step = 1)
			: start(start), stop((stop - start) % step == 0
			? stop
			: start + (1 + (stop - start) / step) * step),
			step(step) {}
			explicit constexpr ArangeContainer(T stop) : ArangeContainer(0, stop, 1) {}

			constexpr T operator[](size_t i) {
			T val = start + i * step;
			assert(val < stop && "i is out of range");
			return val;
			}

			constexpr T size() { return (stop - start) / step; }

			constexpr iterator begin() { return iterator(start, step); }
			constexpr iterator end() { return iterator(stop, step); }

			private:
			const T start{0}, stop{0}, step{1};
			};
			} // namespace containers

			template <class T,
			typename = std::enable_if_t<std::is_integral<std::decay_t<T>>::value>>
			inline decltype(auto) arange(const T & stop) {
			return containers::ArangeContainer<T>(stop);
			}

			template <class T1, class T2,
			typename = std::enable_if_t<
			std::is_integral<std::common_type_t<T1, T2>>::value>>
			inline constexpr decltype(auto) arange(const T1 & start, const T2 & stop) {
			return containers::ArangeContainer<std::common_type_t<T1, T2>>(start, stop);
			}

			template <class T1, class T2, class T3,
			typename = std::enable_if_t<
			std::is_integral<std::common_type_t<T1, T2, T3>>::value>>
			inline constexpr decltype(auto) arange(const T1 & start, const T2 & stop,
			const T3 & step) {
			return containers::ArangeContainer<std::common_type_t<T1, T2, T3>>(
			start, stop, step);
			}

			/* -------------------------------------------------------------------------- */
			namespace iterators {
			template <class Iterator> class EnumerateIterator {
			public:
			using value_type =
			std::tuple<size_t, typename std::iterator_traits<Iterator>::value_type>;
			using difference_type = size_t;
			using pointer =
			std::tuple<size_t, typename std::iterator_traits<Iterator>::pointer>;
			using reference =
			std::tuple<size_t, typename std::iterator_traits<Iterator>::reference>;
			using iterator_category = std::input_iterator_tag;

			public:
			explicit EnumerateIterator(Iterator && iterator) : iterator(iterator) {}

			// input iterator ++it
			EnumerateIterator & operator++() {
			++iterator;
			++index;
			return *this;
			}

			// input iterator it++
			EnumerateIterator operator++(int) {
			auto cpy = *this;
			this->operator++();
			return cpy;
			}

			// input iterator it != other_it
			bool operator!=(const EnumerateIterator & other) const {
			return iterator != other.iterator;
			}

			// input iterator dereference *it
			decltype(auto) operator*() {
			return std::tuple_cat(std::make_tuple(index), *iterator);
			}

			bool operator==(const EnumerateIterator & other) const {
			return not this->operator!=(other);
			}

			private:
			Iterator iterator;
			size_t index{0};
			};

			template <class Iterator>
			inline constexpr decltype(auto) enumerate(Iterator && iterator) {
			return EnumerateIterator<Iterator>(std::forward<Iterator>(iterator));
			}

			} // namespace iterators

			namespace containers {
			template <class... Containers> class EnumerateContainer {
			public:
			explicit EnumerateContainer(Containers &&... containers)
			: zip_container(std::forward<Containers>(containers)...) {}

			decltype(auto) begin() {
			return iterators::enumerate(zip_container.begin());
			}

			decltype(auto) begin() const {
			return iterators::enumerate(zip_container.begin());
			}

			decltype(auto) end() { return iterators::enumerate(zip_container.end()); }

			decltype(auto) end() const {
			return iterators::enumerate(zip_container.end());
			}

			private:
			ZipContainer<Containers...> zip_container;
			};
			} // namespace containers

			template <class... Container>
			inline constexpr decltype(auto) enumerate(Container &&... container) {
			return containers::EnumerateContainer<Container...>(
			std::forward<Container>(container)...);
			}

			/* -------------------------------------------------------------------------- */
			/* -------------------------------------------------------------------------- */
			namespace iterators {
			template <class iterator_t, class operator_t>
			class transform_adaptor_iterator {
			public:
			using value_type = decltype(std::declval<operator_t>()(
			std::declval<typename iterator_t::value_type>()));
			using difference_type = typename iterator_t::difference_type;
			using pointer = std::decay_t<value_type> *;
			using reference = value_type &;
			using iterator_category = typename iterator_t::iterator_category;

			transform_adaptor_iterator(iterator_t it, operator_t op)
			: it(std::move(it)), op(op) {}
			transform_adaptor_iterator(const transform_adaptor_iterator &) = default;

			transform_adaptor_iterator & operator++() {
			++it;
			return *this;
			}

			decltype(auto) operator() { return op(std::forward<decltype(it)>(*it)); }

			bool operator==(const transform_adaptor_iterator & other) const {
			return (it == other.it);
			}

			bool operator!=(const transform_adaptor_iterator & other) const {
			return not operator==(other);
			}

			template <class iterator_category_ = iterator_category,
			std::enable_if_t<details::is_iterator_category_at_least<
			iterator_category_,
			std::random_access_iterator_tag>::value> * = nullptr>
			difference_type operator-(const transform_adaptor_iterator & other) {
			return other - *this;
			}

			private:
			iterator_t it;
			operator_t op;
			};

			template <class iterator_t, class operator_t>
			decltype(auto) make_transform_adaptor_iterator(iterator_t it, operator_t op) {
			return transform_adaptor_iterator<iterator_t, operator_t>(
			it, std::forward<operator_t>(op));
			}

			} // namespace iterators

			namespace containers {
			template <class container_t, class operator_t>
			class TransformIteratorAdaptor {
			public:
			// using const_iterator = typename
			// std::decay_t<container_t>::const_iterator; using iterator = typename
			// std::decay_t<container_t>::iterator;

			TransformIteratorAdaptor(container_t && cont, operator_t op)
			: cont(std::forward<container_t>(cont)),
			op(std::forward<operator_t>(op)) {}

			decltype(auto) begin() const {
			return iterators::make_transform_adaptor_iterator(cont.begin(), op);
			}
			decltype(auto) begin() {
			return iterators::make_transform_adaptor_iterator(cont.begin(), op);
			}

			decltype(auto) end() const {
			return iterators::make_transform_adaptor_iterator(cont.end(), op);
			}
			decltype(auto) end() {
			return iterators::make_transform_adaptor_iterator(cont.end(), op);
			}

			private:
			container_t cont;
			operator_t op;
			};
			} // namespace containers

			template <class container_t, class operator_t>
			decltype(auto) make_transform_adaptor(container_t && cont, operator_t && op) {
			return containers::TransformIteratorAdaptor<container_t, operator_t>(
			std::forward<container_t>(cont), std::forward<operator_t>(op));
			}

			template <class container_t>
			decltype(auto) make_keys_adaptor(container_t && cont) {
			return make_transform_adaptor(
			std::forward<container_t>(cont),
			[](auto && pair) -> const auto & { return pair.first; });
			}

			template <class container_t>
			decltype(auto) make_values_adaptor(container_t && cont) {
			return make_transform_adaptor(
			std::forward<container_t>(cont),
			[](auto && pair) -> auto & { return pair.second; });
			}

			template <class container_t>
			decltype(auto) make_dereference_adaptor(container_t && cont) {
			return make_transform_adaptor(
			std::forward<container_t>(cont),
			[](auto && value) -> decltype(value) { return value; });
			}

			template <class... zip_container_t>
			decltype(auto) make_zip_cat(zip_container_t &&... cont) {
			return make_transform_adaptor(
			zip(std::forward<zip_container_t>(cont)...),
			[](auto && value) { return tuple::flatten(value); });
			}

			/* -------------------------------------------------------------------------- */
			namespace iterators {
			template <class filter_iterator_t, class container_iterator_t>
			class FilterIterator {
			public:
			using value_type =
			decltype(std::declval<container_iterator_t>().operator[](0));
			using difference_type = typename filter_iterator_t::difference_type;
			using pointer = std::decay_t<value_type> *;
			using reference = value_type &;
			using iterator_category = typename filter_iterator_t::iterator_category;

			FilterIterator(filter_iterator_t filter_it,
			container_iterator_t container_begin)
			: filter_it(std::move(filter_it)), container_begin(container_begin),
			container_it(container_begin) {}

			FilterIterator(const FilterIterator &) = default;

			FilterIterator & operator++() {
			++filter_it;
			container_it =
			container_begin + *filter_it; // this might return invalid iterators
			return *this;
			}

			decltype(auto) operator() { return container_it; }

			decltype(auto) operator() const { return container_it; }

			bool operator==(const FilterIterator & other) const {
			return (filter_it == other.filter_it) and
			(container_begin == other.container_begin);
			}

			bool operator!=(const FilterIterator & other) const {
			return filter_it != other.filter_it;
			}

			private:
			filter_iterator_t filter_it;
			container_iterator_t container_begin;
			container_iterator_t container_it;
			};

			template <class filter_iterator_t, class container_iterator_t>
			decltype(auto) make_filter_iterator(filter_iterator_t && filter_it,
			container_iterator_t && container_begin) {
			return FilterIterator<filter_iterator_t, container_iterator_t>(
			std::forward<filter_iterator_t>(filter_it),
			std::forward<container_iterator_t>(container_begin));
			}
			} // namespace iterators

			namespace containers {
			template <class filter_t, class Container> class FilterAdaptor {
			public:
			FilterAdaptor(filter_t && filter, Container && container)
			: filter(std::forward<filter_t>(filter)),
			container(std::forward<Container>(container)) {
			static_assert(
			std::is_same<typename decltype(container.begin())::iterator_category,
			std::random_access_iterator_tag>::value,
			"Containers must all have random iterators");
			}

			decltype(auto) begin() const {
			return iterators::make_filter_iterator(filter.begin(), container.begin());
			}
			decltype(auto) begin() {
			return iterators::make_filter_iterator(filter.begin(), container.begin());
			}

			decltype(auto) end() const {
			return iterators::make_filter_iterator(filter.end(), container.begin());
			}
			decltype(auto) end() {
			return iterators::make_filter_iterator(filter.end(), container.begin());
			}

			private:
			filter_t filter;
			Container container;
			};
			} // namespace containers

			template <class filter_t, class Container>
			decltype(auto) filter(filter_t && filter, Container && container) {
			return containers::FilterAdaptor<filter_t, Container>(
			std::forward<filter_t>(filter), std::forward<Container>(container));
			}

			} // namespace AKANTU_ITERATOR_NAMESPACE

			namespace std {
			template <typename... Its>
			struct iterator_traits<::akantu::iterators::ZipIterator<Its...>> {
			using iterator_category = forward_iterator_tag;
			using value_type =
			typename ::akantu::iterators::ZipIterator<Its...>::value_type;
			using difference_type =
			typename ::akantu::iterators::ZipIterator<Its...>::difference_type;
			using pointer = typename ::akantu::iterators::ZipIterator<Its...>::pointer;
			using reference =
			typename ::akantu::iterators::ZipIterator<Its...>::reference;
			};

			} // namespace std

			#endif /* AKANTU_AKA_ITERATORS_HH */

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