BAN: Move heap functions to Heap.h

This also adds push_heap and pop_heap, similar to what C++ standard
library provides

BAN/include/BAN/Heap.h

@@ -0,0 +1,90 @@
+#pragma once
+
+#include <BAN/Iteration.h>
+#include <BAN/Swap.h>
+#include <BAN/Traits.h>
+#include <cstddef>
+
+namespace BAN
+{
+
+	namespace detail
+	{
+
+		template<typename It, typename Comp>
+		void heapify_up(It begin, size_t index, Comp comp)
+		{
+			size_t parent = (index - 1) / 2;
+			while (parent < index)
+			{
+				if (comp(*(begin + index), *(begin + parent)))
+					break;
+				swap(*(begin + parent), *(begin + index));
+				index = parent;
+				parent = (index - 1) / 2;
+			}
+		}
+
+		template<typename It, typename Comp>
+		void heapify_down(It begin, size_t index, size_t len, Comp comp)
+		{
+			for (;;)
+			{
+				const size_t lchild = 2 * index + 1;
+				const size_t rchild = 2 * index + 2;
+
+				size_t child = 0;
+				if (lchild < len && !comp(*(begin + lchild), *(begin + index)))
+				{
+					if (rchild < len && !comp(*(begin + rchild), *(begin + lchild)))
+						child = rchild;
+					else
+						child = lchild;
+				}
+				else if (rchild < len && !comp(*(begin + rchild), *(begin + index)))
+					child = rchild;
+				else
+					break;
+
+				swap(*(begin + child), *(begin + index));
+				index = child;
+			}
+		}
+
+	}
+
+	template<typename It, typename Comp = less<it_value_type_t<It>>>
+	void make_heap(It begin, It end, Comp comp = {})
+	{
+		const size_t len = distance(begin, end);
+		if (len <= 1)
+			return;
+
+		size_t index = (len - 2) / 2;
+		while (index < len)
+			detail::heapify_down(begin, index--, len, comp);
+	}
+
+	template<typename It, typename Comp = less<it_value_type_t<It>>>
+	void push_heap(It begin, It end, Comp comp = {})
+	{
+		const size_t len = distance(begin, end);
+		detail::heapify_up(begin, len - 1, comp);
+	}
+
+	template<typename It, typename Comp = less<it_value_type_t<It>>>
+	void pop_heap(It begin, It end, Comp comp = {})
+	{
+		const size_t len = distance(begin, end);
+		swap(*begin, *(begin + len - 1));
+		detail::heapify_down(begin, 0, len - 1, comp);
+	}
+
+	template<typename It, typename Comp = less<it_value_type_t<It>>>
+	void sort_heap(It begin, It end, Comp comp = {})
+	{
+		while (begin != end)
+			pop_heap(begin, end--, comp);
+	}
+
+}

BAN/include/BAN/Sort.h

@@ -1,5 +1,6 @@
 #pragma once
 
+#include <BAN/Heap.h>
 #include <BAN/Math.h>
 #include <BAN/Swap.h>
 #include <BAN/Traits.h>
@@ -67,82 +68,6 @@ namespace BAN::sort
 		}
 	}
 
-	namespace detail
-	{
-
-		template<typename It, typename Comp>
-		void push_heap(It begin, size_t hole_index, size_t top_index, it_value_type_t<It> value, Comp comp)
-		{
-			size_t parent = (hole_index - 1) / 2;
-			while (hole_index > top_index && comp(*next(begin, parent), value))
-			{
-				*next(begin, hole_index) = move(*next(begin, parent));
-				hole_index = parent;
-				parent = (hole_index - 1) / 2;
-			}
-			*next(begin, hole_index) = move(value);
-		}
-
-		template<typename It, typename Comp>
-		void adjust_heap(It begin, size_t hole_index, size_t len, it_value_type_t<It> value, Comp comp)
-		{
-			const size_t top_index = hole_index;
-			size_t child = hole_index;
-			while (child < (len - 1) / 2)
-			{
-				child = 2 * (child + 1);
-				if (comp(*next(begin, child), *next(begin, child - 1)))
-					child--;
-				*next(begin, hole_index) = move(*next(begin, child));
-				hole_index = child;
-			}
-			if (len % 2 == 0 && child == (len - 2) / 2)
-			{
-				child = 2 * (child + 1);
-				*next(begin, hole_index) = move(*next(begin, child - 1));
-				hole_index = child - 1;
-			}
-			push_heap(begin, hole_index, top_index, move(value), comp);
-		}
-
-	}
-
-	template<typename It, typename Comp = less<it_value_type_t<It>>
-	void make_heap(It begin, It end, Comp comp = {})
-	{
-		const size_t len = distance(begin, end);
-		if (len <= 1)
-			return;
-
-		size_t parent = (len - 2) / 2;
-		while (true)
-		{
-			detail::adjust_heap(begin, parent, len, move(*next(begin, parent)), comp);
-
-			if (parent == 0)
-				break;
-
-			parent--;
-		}
-	}
-
-	template<typename It, typename Comp = less<it_value_type_t<It>>>
-	void sort_heap(It begin, It end, Comp comp = {})
-	{
-		const size_t len = distance(begin, end);
-		if (len <= 1)
-			return;
-
-		size_t last = len;
-		while (last > 1)
-		{
-			last--;
-			typename It::value_type x = move(*next(begin, last));
-			*next(begin, last) = move(*begin);
-			detail::adjust_heap(begin, 0, last, move(x), comp);
-		}
-	}
-
 	template<typename It, typename Comp = less<it_value_type_t<It>>>
 	void heap_sort(It begin, It end, Comp comp = {})
 	{