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Task/Sorting-algorithms-Merge-sort/00-TASK.txt

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+{{Sorting Algorithm}}
+[[Category:Sorting]]
+[[Category:Recursion]]
+
+The &nbsp; '''merge sort''' &nbsp; is a recursive sort of order &nbsp; <big> n*log(n). </big>
+
+It is notable for having a worst case and average complexity of &nbsp; <big> ''O(n*log(n))'', </big> &nbsp; and a best case complexity of &nbsp; <big> ''O(n)'' &nbsp; </big> (for pre-sorted input). 
+
+The basic idea is to split the collection into smaller groups by halving it until the groups only have one element or no elements &nbsp; (which are both entirely sorted groups). 
+
+Then merge the groups back together so that their elements are in order.
+ 
+This is how the algorithm gets its &nbsp; ''divide and conquer'' &nbsp; description.
+
+
+;Task:
+Write a function to sort a collection of integers using the merge sort. 
+
+
+The merge sort algorithm comes in two parts: 
+    a sort function     and 
+    a merge function 
+
+The functions in pseudocode look like this:
+ '''function''' ''mergesort''(m)
+    '''var''' list left, right, result
+    '''if''' length(m) ≤ 1
+        '''return''' m
+    '''else'''
+        '''var''' middle = length(m) / 2
+        '''for each''' x '''in''' m '''up to''' middle - 1
+            '''add''' x '''to''' left
+        '''for each''' x '''in''' m '''at and after''' middle
+            '''add''' x '''to''' right
+        left = mergesort(left)
+        right = mergesort(right)
+        '''if''' last(left) ≤ first(right) 
+           '''append''' right '''to''' left
+           '''return''' left
+        result = merge(left, right)
+        '''return''' result
+ 
+ '''function''' ''merge''(left,right)
+    '''var''' list result
+    '''while''' length(left) > 0 and length(right) > 0
+        '''if''' first(left) ≤ first(right)
+            '''append''' first(left) '''to''' result
+            left = rest(left)
+        '''else'''
+            '''append''' first(right) '''to''' result
+            right = rest(right)
+    '''if''' length(left) > 0 
+        '''append''' rest(left) '''to''' result
+    '''if''' length(right) > 0 
+        '''append''' rest(right) '''to''' result
+    '''return''' result
+
+
+;See also:
+* &nbsp; the Wikipedia entry: &nbsp; [[wp:Merge_sort| merge sort]]
+
+
+Note: &nbsp; better performance can be expected if, rather than recursing until &nbsp; <big> length(m) ≤ 1, </big> &nbsp; an insertion sort is used for &nbsp; <big> length(m) </big> &nbsp; smaller than some threshold larger than &nbsp; '''1'''. &nbsp; However, this complicates the example code, so it is not shown here.
+<br><br>
+