Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove that given the preorder and postorder traversals of a binary tree, the leaf (leaves) of a bi...

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...

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...

We present new links between some remarkable martingales found in the study of the Binary Search Tree or of the bisection problem, looking at them on the probability space of a continuous time binary branching process.

Limit laws for several quantities in random binary search trees that are related to the local shape of a tree around each node can be obtained very simply by applying central limit theorems for rn-dependent random variables . Examples include : the number of leaves (La ), the number of nodes with k descendants (k fixed), the number of nodes with no left child, the number of nodes with k left de...

2 Binary search trees 2 2.1 Definition of a binary search tree . . . . . . . . . . . . . . . . . . 2 2.2 Profile of a binary search tree . . . . . . . . . . . . . . . . . . . . 3 2.2.1 Level polynomial. BST martingale . . . . . . . . . . . . . 3 2.2.2 Embedding in continuous time. Yule tree . . . . . . . . . . 6 2.2.3 Connection Yule tree binary search tree . . . . . . . . . . 7 2.2.4 Asymptoti...

Graphs have enormous usage in software engineering, network and electrical engineering. In fact graphs drawing is a geometrically representation of information. Among graphs, trees are concentrated because of their ability in hierarchical extension as well as processing VLSI circuit. Many algorithms have been proposed for drawing binary trees within polygons. However these algorithms generate b...

The purpose of this paper is to settle two conjectures by Flajolet, Gourdon and Martinez ( 1996). We confirm that in a random binary tree on n nodes, the expected number of different subtrees grows indeed as 0 (n/ log n). Secondly, if K is the largest integer such that all possible shapes of subtrees of cardinality less than or equal to K occur in a random binary search tree, then we show that ...