In this paper, a new representation of a binary tree is introduced, called the Catalan Cipher Vector, which is a vector of elements with certain properties. It can be ranked using a special form of the Catalan Triangle designed for this purpose. It is shown that the vector coincides with the level-order traversal of the binary tree and how it can be used to generate a binary tree from it. Streamlined algorithms for directly obtaining the rank from a binary tree and vice versa, using the Catalan Cipher Vector during the processes, are given. The algorithms are analyzed for time and space complexity and shown to be linear for both.
The Catalan Cipher Vector enables a straightforward determination of the position and linking for every node of the binary tree, since it contains information for both every node’s ancestor and the direction of linking from the ancestor to that node. Thus, it is especially well suited for binary tree generation. Using another structure, called a canonical state-space tableau, the relationship between the Catalan Cipher Vector and the level-order traversal of the binary tree is explained.
The availability of real-time data on the state of railway facilities and the state-of-the art technologies for data collection and analysis allow transition to the fourth generation maintenance. It is based on the prediction of the facility functional safety and dependability and the risk-oriented facility management. The article describes an approach to assessing the risks of hazardous facility failures using the latest digital data processing methods. The implementation of this approach will help set maintenance objectives and contribute to the efficient use of resources and the reduction of railway facility managers’ expenditures.
The availability of real-time data on the state of railway facilities and the state-of-the art technologies for data collection and analysis allow transition to the fourth generation maintenance. It is based on the prediction of the facility functional safety and dependability and the risk-oriented facility management. The article describes an approach to assessing the risks of hazardous facility failures using the latest digital data processing methods. The implementation of this approach will help set maintenance objectives and contribute to the efficient use of resources and the reduction of railway facility managers’ expenditures.
