An improved algorithm to reconstruct a binary tree from its inorder and postorder traversals

نویسندگان

  • Henk Koppelaar Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands.
  • Niloofar Aghaieabiane Department of Engineering, School of Computer Science, New Jersey Institute of Technology, Newark, New Jersey, the USA.
  • Peyman Nasehpour Golpayegan University of Technology, Department of Engineering Science, Golpayegan, Iran.
چکیده مقاله:

It is well-known that, given inorder traversal along with one of the preorder or postorder traversals of a binary tree, the tree can be determined uniquely. Several algorithms have been proposed to reconstruct a binary tree from its inorder and preorder traversals. There is one study to reconstruct a binary tree from its inorder and postorder traversals, and this algorithm takes running time of  $ BigO{emph{n}^2} $. In this paper, we present $ proc{InPos} $ an improved algorithm to reconstruct a binary tree from its inorder and postorder traversals. The running time and space complexity of the algorithm are an order of $ BigTheta{emph{n}} $ and $ BigTheta{emph{n}} $ respectively, which we prove to be optimal.  The $ proc{InPos} $ algorithm not only reconstructs the binary tree, but also it determines different types of the nodes in a binary tree; nodes with two children, nodes with one child, and nodes with no child. At the end, the $ proc{InPos} $ returns a matrix-based structure to represent the binary tree, and enabling  access to any structural information of the reconstructed tree in linear time with any given tree traversals.  

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عنوان ژورنال

دوره 49  شماره 1

صفحات  93- 113

تاریخ انتشار 2017-06-01

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