Add file for non-recursive merge sort

sorting-algorithms/bottom_up_merge_sort.cpp

@@ -0,0 +1,100 @@
+#include <cstddef>//for size_t
+#include <utility>//for std::move & std::remove_reference_t
+template<class Iterator>
+void merge(Iterator, Iterator, const Iterator, char[]);
+///bottom-up merge sort which sorts elements in a non-decreasing order
+/**
+ * sorts elements non-recursively by breaking them into small segments, merging
+ * adjacent segments into larger sorted segments, then increasing the sizes of
+ * segments by factors of 2.
+ * best-case = worst-case = O(n)
+ * @param first points to the first element
+ * @param last points to 1-step past the last element
+ * @param the number of elements
+*/
+template<class Iterator>
+void nonrecursiveMergeSort(const Iterator first, const Iterator last,
+						   const size_t n)
+{
+	//create a buffer large enough to store all elements
+	char buffer[n * sizeof(*first)];
+	//buffer size can be optimized to largest power of 2 less than n elements
+	//divide the container into equally-sized segments whose length start at 1
+	// and keeps increasing by factors of 2
+	for (size_t length(1); length < n; length <<= 1)
+	{
+		//merge adjacent segments whose number is n / (length * 2)
+		Iterator left(first);
+		for (size_t counter(n / (length << 1)); counter; --counter)
+		{
+			Iterator right(left + length), end(right + length);
+			merge(left, right, end, buffer);
+			left = end;
+		}
+		//if the number of remaining elements (n * 2 % length) is longer
+		//than a segment, merge the remaining elements
+		if ((n & ((length << 1) - 1)) > length)
+			merge(left, left + length, last, buffer);
+	}
+}
+///merges 2 sorted adjacent segments into a larger sorted segment
+/**
+ * best-case = worst-case = O(n)
+ * @param l points to the left part
+ * @param r points to the right part, end of left part
+ * @param e points to end of right part
+ * @param b points at the buffer
+*/
+template<class Iterator>
+void merge(Iterator l, Iterator r, const Iterator e, char b[])
+{
+	//create 2 pointers to point at the buffer
+	auto p(reinterpret_cast<std::remove_reference_t<decltype(*l)>*>(b)), c(p);
+	//move the left part of the segment
+	for (Iterator t(l); r != t; ++t)
+		*p++ = std::move(*t);
+	//while neither the buffer nor the right part has been exhausted
+	//move the smallest element of the two back to the container
+	while (e != r && c != p)
+		*l++ = std::move(*r < *c ? *r++ : *c++);
+	//notice only one of the two following loops will be executed
+	//while the right part hasn't bee exhausted, move it back
+	while (e != r)
+		*l++ = std::move(*r++);
+	//while the buffer hasn't bee exhausted, move it back
+	while (c != p)
+		*l++ = std::move(*c++);
+}
+template<class Iterator>
+void nonrecursiveMergeSort(const Iterator first, const size_t n)
+{
+	nonrecursiveMergeSort(first, first + n, n);
+}
+template<class Iterator>
+void nonrecursiveMergeSort(const Iterator first, const Iterator last)
+{
+	nonrecursiveMergeSort(first, last, last - first);
+}
+//the rest of this is file is only for testing, it can be removed to convert it
+//into a header file
+#include <iostream>
+#include <random>
+using namespace std;
+int main(int argc, char ** argv)
+{
+	size_t n;
+	cout << "enter the number of elements\n";
+	cin >> n;
+	unsigned a[n];
+	default_random_engine e;
+	for (size_t i(0); i != n; ++i)
+		a[i] = e() % 10;
+	cout << "presorting\n";
+	for (size_t i(0); i != n; ++i)
+		cout << "a[" << i << "] = " << a[i] << '\n';
+	nonrecursiveMergeSort(a, n);
+	cout << "after sorting\n";
+	for (size_t i(0); i != n; ++i)
+		cout << "a[" << i << "] = " << a[i] << '\n';
+	return 0;
+}