DSW algorithm

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DSW algorithm
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DSW algorithm

• To avoid sorting, it required deconstructing and
  then reconstructing the tree, which is
  inefficient except for relatively small trees
• DSW algorithm require little additional storage
  for intermediate variables and use no sorting
  procedure
• Devised by Colin Day and improved by Quentin F.
  Stout and Bette L. Warren

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• First phase The DSW algorithm transfigures an
  arbitrary BST into a link listlike tree called a
  backbone (or a vine).
• Second phase This elongated tree is transformed
  in a series of passes into a perfected tree by
  repeatedly rotating every second node of the
  backbone about its parent

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First phase

• Createbackbone(root,n)
• tmproot
• while (tmp!null)
• if (tmp has a left child)
• rotate this child about tmp
• //hence the left child became parent of
  tmp
• set tmp to the child which just became
  parent
• else set tmp to the right child

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Transforming a BST into a backbone
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• The building block for the tranformations is the
  rotation. (rotate right, left)
• Rotateright(gr,par, ch)
• if par is not the root of the tree //i.e., if
  gr isnt null
• grandparent gr of child ch becomes chs
  parent by replacing par
• right subtree of ch becomes left subtree of
  chs parent par
• node ch acquires par as its right child

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the second phase

• Createperfecttree(n)
• m2 lg(n1) -1
• Make n-m rotations starting from the top of
  backbone//first pass
• while (mgt1)
• mm/2
• Make m rotations starting from the top
  of backbone

In the second phase, the backbone is transformed
into a tree, but this time, the tree is perfectly
balanced by having leaves only on two adjacent
levels. In each pass down the backbone, every
second node is rotated about its parent. On such
pass decreases the size of the backbone by
one-half. But the first pass
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M3/2 Make 1 rotation
M7/2 Make 3 rotations
First pass make 9-7 rotations
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Exercise-1

• Transfigure this tree into backbone
• Then, create a perfect balanced binary search tree

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Exercise-2

• Transfigure the backbone to create a perfect
  balanced binary search tree