Initial data commit

Task/Sorting-algorithms-Heapsort/00-TASK.txt

@@ -0,0 +1,64 @@
+{{Sorting Algorithm}} 
+[[Category:Sorting]]
+{{wikipedia|Heapsort}}
+{{omit from|GUISS}}
+
+<br>
+[[wp:Heapsort|Heapsort]] is an in-place sorting algorithm with worst case and average complexity of &nbsp; <span style="font-family: serif">O(''n'' log''n'')</span>. 
+
+The basic idea is to turn the array into a binary heap structure, which has the property that it allows efficient retrieval and removal of the maximal element. 
+
+We repeatedly "remove" the maximal element from the heap, thus building the sorted list from back to front. 
+
+A heap sort requires random access, so can only be used on an array-like data structure.
+
+Pseudocode:
+ '''function''' heapSort(a, count) '''is'''
+    '''input:''' an unordered array ''a'' of length ''count''
+  
+    <span style="color: grey">''(first place a in max-heap order)''</span>
+    heapify(a, count)
+  
+    end := count - 1
+    '''while''' end > 0 '''do'''
+       <span style="color: grey">''(swap the root(maximum value) of the heap with the''
+        ''last element of the heap)''</span>
+       swap(a[end], a[0])
+       <span style="color: grey">''(decrement the size of the heap so that the previous''
+        ''max value will stay in its proper place)''</span>
+       end := end - 1
+       <span style="color: grey">''(put the heap back in max-heap order)''</span>
+       siftDown(a, 0, end)
+
+  
+ '''function''' heapify(a,count) '''is'''
+    <span style="color: grey">''(start is assigned the index in ''a'' of the last parent node)''</span>
+    start := (count - 2) / 2
+    
+    '''while''' start ≥ 0 '''do'''
+       <span style="color: grey">''(sift down the node at index start to the proper place''
+        ''such that all nodes below the start index are in heap''
+        ''order)''</span>
+       siftDown(a, start, count-1)
+       start := start - 1
+    <span style="color: grey">''(after sifting down the root all nodes/elements are in heap order)''</span>
+  
+ '''function''' siftDown(a, start, end) '''is'''
+    <span style="color: grey">''(''end'' represents the limit of how far down the heap to sift)''</span>
+    root := start
+ 
+    '''while''' root * 2 + 1 ≤ end '''do'''       <span style="color: grey">''(While the root has at least one child)''</span>
+       child := root * 2 + 1           <span style="color: grey">''(root*2+1 points to the left child)''</span>
+       <span style="color: grey">''(If the child has a sibling and the child's value is less than its sibling's...)''</span>
+       '''if''' child + 1 ≤ end '''and''' a[child] < a[child + 1] '''then'''
+          child := child + 1           <span style="color: grey">''(... then point to the right child instead)''</span>
+       '''if''' a[root] < a[child] '''then'''     <span style="color: grey">''(out of max-heap order)''</span>
+          swap(a[root], a[child])
+          root := child                <span style="color: grey">''(repeat to continue sifting down the child now)''</span>
+       '''else'''
+          '''return'''
+
+<br>
+Write a function to sort a collection of integers using heapsort.
+<br><br>
+