Merge pull request #39 from kariya-mitsuru/is_permutation

[algorithm.is_permutation] Reduce complexity

sprout/algorithm/is_permutation.hpp

@@ -17,27 +17,38 @@
 #include <sprout/functional/equal_to.hpp>
 #include <sprout/functional/bind2nd.hpp>
 #include <sprout/algorithm/count_if.hpp>
+#include <sprout/algorithm/find_if.hpp>
+#include <sprout/algorithm/mismatch.hpp>
 
 namespace sprout {
 	namespace detail {
+		template<typename Difference, typename ForwardIterator, typename BinaryPredicate>
+		inline SPROUT_CONSTEXPR bool
+		is_permutation_impl_check(Difference count, ForwardIterator first, ForwardIterator last, BinaryPredicate pred)
+		{
+			return count != 0 && sprout::count_if(sprout::next(first), last, sprout::bind2nd(pred, *first)) + 1 == count;
+		}
 		template<typename RandomAccessIterator1, typename RandomAccessIterator2, typename BinaryPredicate>
 		inline SPROUT_CONSTEXPR bool
 		is_permutation_impl_ra(
 			RandomAccessIterator1 first1, RandomAccessIterator1 last1,
 			RandomAccessIterator2 first2, RandomAccessIterator2 last2,
-			BinaryPredicate pred,
+			BinaryPredicate pred, RandomAccessIterator1 current,
-			typename std::iterator_traits<RandomAccessIterator1>::difference_type pivot
+			typename std::iterator_traits<RandomAccessIterator1>::difference_type size
 			)
 		{
-			return pivot == 0 ? sprout::count_if(first1, last1, sprout::bind2nd(pred, *first1))
+			return size == 1 ? sprout::find_if(first1, current, sprout::bind2nd(pred, *current)) != current
-					<= sprout::count_if(first2, last2, sprout::bind2nd(pred, *first1))
+					|| sprout::detail::is_permutation_impl_check(
+						sprout::count_if(first2, last2, sprout::bind2nd(pred, *current)),
+						current, last1, pred
+						)
 				: sprout::detail::is_permutation_impl_ra(
 					first1, last1, first2, last2,
-					pred, pivot / 2
+					pred, current, size / 2
 					)
 					&& sprout::detail::is_permutation_impl_ra(
-						sprout::next(first1, pivot), last1, first2, last2,
+						first1, last1, first2, last2,
-						pred, (sprout::distance(first1, last1) - pivot) / 2
+						pred, sprout::next(current, size / 2), size - size / 2
 						)
 				;
 		}
@@ -47,68 +58,70 @@ namespace sprout {
 			bool
 		>::type
 		is_permutation(
-			RandomAccessIterator1 first1, RandomAccessIterator1 last1, RandomAccessIterator2 first2, BinaryPredicate pred,
+			sprout::pair<RandomAccessIterator1, RandomAccessIterator2> first, RandomAccessIterator1 last1, BinaryPredicate pred,
 			std::random_access_iterator_tag*
 			)
 		{
-			return first1 == last1 ? true
+			return first.first == last1
-				: sprout::detail::is_permutation_impl_ra(
+				|| sprout::detail::is_permutation_impl_ra(
-					first1, last1, first2, sprout::next(first2, sprout::distance(first1, last1)),
+					first.first, last1, first.second, sprout::next(first.second, sprout::distance(first.first, last1)),
-					pred, sprout::distance(first1, last1) / 2
+					pred, first.first, sprout::distance(first.first, last1)
 					)
 				;
 		}
-
 		template<typename ForwardIterator1, typename ForwardIterator2, typename BinaryPredicate>
 		inline SPROUT_CONSTEXPR sprout::pair<ForwardIterator1, bool>
 		is_permutation_impl_1(
 			sprout::pair<ForwardIterator1, bool> const& current,
-			ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2,
+			ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2,
 			BinaryPredicate pred, typename std::iterator_traits<ForwardIterator1>::difference_type n
 			)
 		{
 			typedef sprout::pair<ForwardIterator1, bool> type;
 			return !current.second || current.first == last1 ? current
-				: n == 1 ? sprout::count_if(current.first, last1, sprout::bind2nd(pred, *current.first))
+				: n == 1 ? sprout::find_if(first1, current.first, sprout::bind2nd(pred, *current.first)) != current.first
-					<= sprout::count_if(first2, last2, sprout::bind2nd(pred, *current.first))
+					|| sprout::detail::is_permutation_impl_check(
+						sprout::count_if(first2, last2, sprout::bind2nd(pred, *current.first)),
+						current.first, last1, pred
+						)
 					? type(sprout::next(current.first), true)
 					: type(current.first, false)
 				: sprout::detail::is_permutation_impl_1(
 					sprout::detail::is_permutation_impl_1(
 						current,
-						last1, first2, last2, pred, n / 2
+						first1, last1, first2, last2, pred, n / 2
 						),
-					last1, first2, last2, pred, n - n / 2
+					first1, last1, first2, last2, pred, n - n / 2
-					)
-				;
-		}
-		template<typename ForwardIterator1, typename ForwardIterator2, typename BinaryPredicate>
-		inline SPROUT_CONSTEXPR sprout::pair<ForwardIterator1, bool>
-		is_permutation_impl(
-			sprout::pair<ForwardIterator1, bool> const& current,
-			ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2,
-			BinaryPredicate pred, typename std::iterator_traits<ForwardIterator1>::difference_type n
-			)
-		{
-			return !current.second || current.first == last1 ? current
-				: sprout::detail::is_permutation_impl(
-					sprout::detail::is_permutation_impl_1(
-						current,
-						last1, first2, last2, pred, n
-						),
-					last1, first2, last2, pred, n * 2
 					)
 				;
 		}
 		template<typename ForwardIterator1, typename ForwardIterator2, typename BinaryPredicate>
 		inline SPROUT_CONSTEXPR bool
-		is_permutation(
+		is_permutation_impl(
-			ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, BinaryPredicate pred,
+			ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2,
-			std::forward_iterator_tag*
+			BinaryPredicate pred, typename std::iterator_traits<ForwardIterator1>::difference_type size
 			)
 		{
 			typedef sprout::pair<ForwardIterator1, bool> type;
-			return sprout::detail::is_permutation_impl(type(first1, true), last1, first2, sprout::next(first2, sprout::distance(first1, last1)), pred, 1).second;
+			return sprout::detail::is_permutation_impl_1(
+					type(first1, true),
+					first1, last1, first2, sprout::next(first2, size),
+					pred, size
+					).second
+				;
+		}
+		template<typename ForwardIterator1, typename ForwardIterator2, typename BinaryPredicate>
+		inline SPROUT_CONSTEXPR bool
+		is_permutation(
+			sprout::pair<ForwardIterator1, ForwardIterator2> first, ForwardIterator1 last1, BinaryPredicate pred,
+			std::forward_iterator_tag*
+			)
+		{
+			return first.first == last1
+				|| sprout::detail::is_permutation_impl(
+					first.first, last1, first.second, pred, sprout::distance(first.first, last1)
+					)
+				;
 		}
 	}	// namespace detail
 
@@ -121,7 +134,7 @@ namespace sprout {
 	inline SPROUT_CONSTEXPR bool
 	is_permutation(ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, BinaryPredicate pred) {
 		typedef typename sprout::common_iterator_category<ForwardIterator1, ForwardIterator2>::type* category;
-		return sprout::detail::is_permutation(first1, last1, first2, pred, category());
+		return sprout::detail::is_permutation(sprout::mismatch(first1, last1, first2, pred), last1, pred, category());
 	}
 	template<typename ForwardIterator1, typename ForwardIterator2>
 	inline SPROUT_CONSTEXPR bool
@@ -130,6 +143,20 @@ namespace sprout {
 	}
 
 	namespace detail {
+		template<typename RandomAccessIterator1, typename RandomAccessIterator2, typename BinaryPredicate>
+		inline SPROUT_CONSTEXPR bool
+		is_permutation_impl_ra_1(
+			sprout::pair<RandomAccessIterator1, RandomAccessIterator2> first,
+			RandomAccessIterator1 last1, RandomAccessIterator2 last2, BinaryPredicate pred
+			)
+		{
+			return first.first == last1
+				|| sprout::detail::is_permutation_impl_ra(
+					first.first, last1, first.second, last2,
+					pred, first.first, sprout::distance(first.first, last1)
+					)
+				;
+		}
 		template<typename RandomAccessIterator1, typename RandomAccessIterator2, typename BinaryPredicate>
 		inline SPROUT_CONSTEXPR typename std::enable_if<
 			sprout::is_constant_distance_iterator<RandomAccessIterator1>::value && sprout::is_constant_distance_iterator<RandomAccessIterator2>::value,
@@ -141,13 +168,40 @@ namespace sprout {
 			)
 		{
 			return sprout::distance(first1, last1) == sprout::distance(first2, last2)
-				&& sprout::detail::is_permutation_impl_ra(
+				&& sprout::detail::is_permutation_impl_ra_1(
-					first1, last1, first2, last2,
+					sprout::mismatch(first1, last1, first2, last2, pred),
-					pred, sprout::distance(first1, last1) / 2
+					last1, last2, pred)
+				;
+		}
+		template<typename ForwardIterator1, typename ForwardIterator2, typename BinaryPredicate, typename Difference1, typename Difference2>
+		inline SPROUT_CONSTEXPR bool
+		is_permutation_impl_3(
+			ForwardIterator1 first1, ForwardIterator1 last1,
+			ForwardIterator2 first2, ForwardIterator2 last2, BinaryPredicate pred,
+			Difference1 size1, Difference2 size2
+			)
+		{
+			typedef sprout::pair<ForwardIterator1, bool> type;
+			return size1 == size2
+				&& sprout::detail::is_permutation_impl_1(
+					type(first1, true), first1, last1, first2, last2,
+					pred, size1
+					).second
+				;
+		}
+		template<typename ForwardIterator1, typename ForwardIterator2, typename BinaryPredicate>
+		inline SPROUT_CONSTEXPR bool
+		is_permutation_impl_2(
+			sprout::pair<ForwardIterator1, ForwardIterator2> first,
+			ForwardIterator1 last1, ForwardIterator2 last2, BinaryPredicate pred
+			)
+		{
+			return sprout::detail::is_permutation_impl_3(
+				first.first, last1, first.second, last2, pred,
+				sprout::distance(first.first, last1), sprout::distance(first.second, last2)
 				)
 				;
 		}
-
 		template<typename ForwardIterator1, typename ForwardIterator2, typename BinaryPredicate>
 		inline SPROUT_CONSTEXPR bool
 		is_permutation(
@@ -155,10 +209,9 @@ namespace sprout {
 			std::forward_iterator_tag*
 			)
 		{
-			typedef sprout::pair<ForwardIterator1, bool> type;
+			return sprout::detail::is_permutation_impl_2(
-			return sprout::distance(first1, last1) == sprout::distance(first2, last2)
+				sprout::mismatch(first1, last1, first2, last2, pred),
-				&& sprout::detail::is_permutation_impl(type(first1, true), last1, first2, last2, pred, 1).second
+				last1, last2, pred);
-				;
 		}
 	}	// namespace detail