Initial data commit

Task/Sorting-algorithms-Heapsort/Icon/sorting-algorithms-heapsort.icon

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+procedure main()                     #: demonstrate various ways to sort a list and string
+   demosort(heapsort,[3, 14, 1, 5, 9, 2, 6, 3],"qwerty")
+end
+
+procedure heapsort(X,op)                            #: return sorted list ascending(or descending)
+local head,tail
+
+   op := sortop(op,X)                               # select how and what we sort
+
+   every head := (tail := *X) / 2  to 1 by -1 do    # work back from from last parent node
+      X := siftdown(X,op,head,tail)                 # sift down from head to make the heap
+
+   every tail := *X to 2 by -1 do {                 # work between the beginning and the tail to final positions
+      X[1] :=: X[tail]
+      X := siftdown(X,op,1,tail-1)                  # re-sift next (previous) branch after shortening the heap
+      }
+
+   return X
+end
+
+procedure siftdown(X,op,root,tail)                  #: the value @root is moved "down" the path of max(min) value to its level
+local child
+
+   while (child :=  root * 2) <= tail do {          # move down the branch from root to tail
+
+      if op(X[child],X[tail >= child + 1]) then     # choose the larger(smaller)
+         child +:= 1                                # ... child
+
+      if op(X[root],X[child]) then  {               # root out of order?
+         X[child] :=: X[root]
+         root := child                              # follow max(min) branch
+         }
+      else
+         return X
+      }
+   return X
+end