The number b, of binary trees with n nodes is well known. Two ways to determine b, are presented in [3]. One, based on constructing them, leads to recurrence relations solved by generating functions. The other recognizes that b, is the same as the number of stack permutations and counts these permutations. In [l], a method based on well-formed sequences of parentheses is given, and the result i...

A binary tree is a common data structure used in many branches of computer science. It is often used for solving various types of searching problems. In complexity analysis we usually abstract from the real implementation and derive easily the time complexity of traversal from the root of a balanced tree to any leaf in asymptotic time O(log(m)), where m is the number of leaves. In this paper we...

Let H~ be the height of a random binary search tree on n nodes. We show that there exists constants a = 4.31107.. . and/3 = 1.95.. . such that E(H~) = c~logn / 3 1 o g l o g n + O(1), We also show that Var(H~) = O(1).

A visual pests diagnosis system development tools based on binary tree (abbreviation: knowledge system development tools) was developed by techniques of computer visualization, binary tree, XML database and reasoning. This tool combined tree knowledge expression with rule-based reasoning machine, proposed the knowledge acquisition and the reasoning technique based on binary tree, and solved the...

In this study, the focus was on the use of ternary tree over binary tree. Here, a new one pass Algorithm for Decoding adaptive Huffman ternary tree codes was implemented. To reduce the memory size and fasten the process of searching for a symbol in a Huffman tree, we exploited the property of the encoded symbols and proposed a memory efficient data structure to represent the codeword length of ...

In this paper, we study two diverse problems from a random matrix perspective. The first one is the problem of binary testing (or object/entity identification) that arises in applications such as active learning, fault diagnosis and computer vision, and the second is the problem of zero or bounded skew clock tree construction which arises in applications such as VLSI circuit design and network ...

Through block cipher method, this paper demonstrates using preorder and post traversal sequence of a binary tree with 64 nodes to implement symmetric encryption/decryption. The different traversal sequences may determine a binary tree, so the method is vulnerable to be attacked. The paper’s further deduction involves improvement using multiple binary trees, so that more secure and efficient sym...

Network structures and models have been widely adopted, e.g., for Internet of Things, wireless sensor networks, smart grids, transportation communication social computer grid systems. reliability is an effective popular technique to estimate the probability that network still functioning. Networks composed binary-state (e.g., working or failed) components (arcs and/or nodes) are called networks...