{"id":2419,"date":"2024-04-12T07:54:47","date_gmt":"2024-04-12T07:54:47","guid":{"rendered":"https:\/\/jita-au.com\/?p=2419"},"modified":"2024-04-29T12:59:12","modified_gmt":"2024-04-29T12:59:12","slug":"enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors","status":"publish","type":"post","link":"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/","title":{"rendered":"Enumeration, Ranking and Generation of Binary Trees Based on Level-Order Traversal Using Catalan Cipher Vectors"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"2419\" class=\"elementor elementor-2419\" data-elementor-settings=\"{&quot;ha_cmc_init_switcher&quot;:&quot;no&quot;}\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e232701 elementor-section-height-min-height elementor-section-full_width elementor-hidden-tablet elementor-hidden-mobile elementor-section-height-default elementor-section-items-middle wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no\" data-id=\"e232701\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;_ha_eqh_enable&quot;:false}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cb97594\" data-id=\"cb97594\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a18c791 elementor-widget__width-inherit ha-has-bg-overlay elementor-widget elementor-widget-heading\" data-id=\"a18c791\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Vol. 3 No. 2 (2013): JITA - APEIRON<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b2fff26 elementor-widget elementor-widget-heading\" data-id=\"b2fff26\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><b>Adrijan Bo\u017einovski, Biljana Stoj\u010devska, Veno Pa\u010dovski<b><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-52044bb elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"52044bb\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1c82606 elementor-widget elementor-widget-heading\" data-id=\"1c82606\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Enumeration, Ranking and Generation of Binary Trees Based on Level-Order Traversal Using Catalan Cipher Vectors<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c297c9e elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"c297c9e\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-503a970 e-grid e-con-full wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no e-con e-parent\" data-id=\"503a970\" data-element_type=\"container\" data-settings=\"{&quot;_ha_eqh_enable&quot;:false}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-acb26ac elementor-widget__width-initial elementor-widget elementor-widget-heading\" data-id=\"acb26ac\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Original scientific paper<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-265ed1c elementor-widget__width-initial elementor-widget elementor-widget-heading\" data-id=\"265ed1c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">DOI: https:\/\/doi.org\/10.7251\/JIT1302078B<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cb7c4cb elementor-widget__width-inherit elementor-widget elementor-widget-heading\" data-id=\"cb7c4cb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2f3b63f elementor-align-center elementor-widget elementor-widget-button\" data-id=\"2f3b63f\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/04\/970-Article-Text-2113-2-10-20140128.pdf\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Download Article PDF<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-61aebe3 elementor-widget__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"61aebe3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In this paper, a new representation of a binary tree is introduced, called the Catalan Cipher Vector, which is a vector of\u00a0 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.<br \/>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\u2019s 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.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5c5f19e elementor-widget elementor-widget-heading\" data-id=\"5c5f19e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Keywords: Enumeration,  Rank,  Generation,  Binary  tree,  Level-order  traversal,  Catalan  Cipher  Vector,  Canonical  State-Space Tableau.<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6dd494a wpr-logo-position-center elementor-widget elementor-widget-wpr-logo\" data-id=\"6dd494a\" data-element_type=\"widget\" data-widget_type=\"wpr-logo.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\n\t\t\t<div class=\"wpr-logo elementor-clearfix\">\n\n\t\t\t\t\t\t\t\t<picture class=\"wpr-logo-image\">\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/03\/cc-by-1.png\" alt=\"\">\n\n\t\t\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\t\t\t\t\t<\/picture>\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\n\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cb049d1 elementor-widget elementor-widget-shortcode\" data-id=\"cb049d1\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\"><div class=\"post-views content-post post-2419 entry-meta load-static\">\r\n\t\t\t\t<span class=\"post-views-icon dashicons dashicons-chart-bar\"><\/span> <span class=\"post-views-label\">Post Views:<\/span> <span class=\"post-views-count\">675<\/span>\r\n\t\t\t<\/div><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-511d0df elementor-section-height-min-height elementor-section-full_width elementor-hidden-mobile elementor-hidden-desktop elementor-hidden-laptop elementor-section-height-default elementor-section-items-middle wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no\" data-id=\"511d0df\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;_ha_eqh_enable&quot;:false}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0acee9c\" data-id=\"0acee9c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c0e98b3 elementor-widget__width-inherit ha-has-bg-overlay elementor-widget elementor-widget-heading\" data-id=\"c0e98b3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Vol. 26 No. 2 (2023): JITA - APEIRON<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e6b43c5 elementor-widget elementor-widget-heading\" data-id=\"e6b43c5\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><strong>Igor Shubinsky, <\/strong>\n<strong> Alexey Ozerov<\/strong><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-68f1849 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"68f1849\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-186a6b2 elementor-widget elementor-widget-heading\" data-id=\"186a6b2\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Application of Artificial Intelligence Methods for the Prediction of Hazardous Failures<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7b2f501 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"7b2f501\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5027126 elementor-widget__width-initial elementor-widget elementor-widget-heading\" data-id=\"5027126\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Original scientific paper<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4a5312c elementor-widget__width-initial elementor-widget elementor-widget-heading\" data-id=\"4a5312c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">DOI: <a href=\"http:\/\/localhost\/mytestingsite\/wp-content\/uploads\/2024\/02\/PVTC-Technical-Requirements.pdf\" target=\"_blank\" rel=\"noopener\">https:\/\/doi.org\/10.7251\/JIT2302061S<\/a><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8d7a912 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"8d7a912\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/03\/10430-Article-Text-23890-1-10-20240103.pdf\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Download Article PDF<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-580ffd3 elementor-widget__width-inherit elementor-widget elementor-widget-heading\" data-id=\"580ffd3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-211717e elementor-widget__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"211717e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>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\u2019 expenditures.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-62b72c3 elementor-widget elementor-widget-heading\" data-id=\"62b72c3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Keywords: predictive analysis, maintenance, functional safety, Big Data, Data Science, risk indicators.<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f4dcd16 wpr-logo-position-center elementor-widget elementor-widget-wpr-logo\" data-id=\"f4dcd16\" data-element_type=\"widget\" data-widget_type=\"wpr-logo.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\n\t\t\t<div class=\"wpr-logo elementor-clearfix\">\n\n\t\t\t\t\t\t\t\t<picture class=\"wpr-logo-image\">\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/03\/cc-by-1.png\" alt=\"\">\n\n\t\t\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\t\t\t\t\t<\/picture>\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\n\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0f73093 elementor-widget elementor-widget-shortcode\" data-id=\"0f73093\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\"><div class=\"post-views content-post post-2419 entry-meta load-static\">\r\n\t\t\t\t<span class=\"post-views-icon dashicons dashicons-chart-bar\"><\/span> <span class=\"post-views-label\">Post Views:<\/span> <span class=\"post-views-count\">675<\/span>\r\n\t\t\t<\/div><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2d980b8 elementor-section-height-min-height elementor-section-full_width elementor-hidden-tablet elementor-hidden-desktop elementor-hidden-laptop elementor-section-height-default elementor-section-items-middle wpr-particle-no wpr-jarallax-no wpr-parallax-no wpr-sticky-section-no\" data-id=\"2d980b8\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;_ha_eqh_enable&quot;:false}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d772afa\" data-id=\"d772afa\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5597455 elementor-widget__width-inherit elementor-widget-mobile__width-inherit ha-has-bg-overlay elementor-widget elementor-widget-heading\" data-id=\"5597455\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Vol. 26 No. 2 (2023): JITA - APEIRON<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f3e70ee elementor-widget elementor-widget-heading\" data-id=\"f3e70ee\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><strong>Igor Shubinsky, <\/strong>\n<strong> Alexey Ozerov<\/strong><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b0a72e2 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"b0a72e2\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-87a3678 elementor-widget elementor-widget-heading\" data-id=\"87a3678\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Application of Artificial Intelligence Methods for the Prediction of Hazardous Failures<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-96936f4 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"96936f4\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f04febc elementor-widget__width-initial elementor-widget-mobile__width-inherit elementor-widget elementor-widget-heading\" data-id=\"f04febc\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Original scientific paper<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-389228b elementor-widget__width-initial elementor-widget-mobile__width-inherit elementor-widget elementor-widget-heading\" data-id=\"389228b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">DOI: <a href=\"http:\/\/localhost\/mytestingsite\/wp-content\/uploads\/2024\/02\/PVTC-Technical-Requirements.pdf\" target=\"_blank\" rel=\"noopener\">https:\/\/doi.org\/10.7251\/JIT2302061S<\/a><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-73b8917 elementor-align-center elementor-widget elementor-widget-button\" data-id=\"73b8917\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/03\/10430-Article-Text-23890-1-10-20240103.pdf\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Download Article PDF<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-80faf79 elementor-widget__width-inherit elementor-widget elementor-widget-heading\" data-id=\"80faf79\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8cefffd elementor-widget__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"8cefffd\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>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\u2019 expenditures.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0c5e44b elementor-widget elementor-widget-heading\" data-id=\"0c5e44b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Keywords: predictive analysis, maintenance, functional safety, Big Data, Data Science, risk indicators.<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dee52ab wpr-logo-position-center elementor-widget elementor-widget-wpr-logo\" data-id=\"dee52ab\" data-element_type=\"widget\" data-widget_type=\"wpr-logo.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\n\t\t\t<div class=\"wpr-logo elementor-clearfix\">\n\n\t\t\t\t\t\t\t\t<picture class=\"wpr-logo-image\">\n\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/03\/cc-by-1.png\" alt=\"\">\n\n\t\t\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\t\t\t\t\t<\/picture>\n\t\t\t\t\n\t\t\t\t\n\t\t\t\t\t\t\t\t\t<a class=\"wpr-logo-url\" rel=\"home\" aria-label=\"\" href=\"https:\/\/jita-au.com\/\"><\/a>\n\t\t\t\t\n\t\t\t<\/div>\n\t\t\t\t\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5cb9871 elementor-widget elementor-widget-shortcode\" data-id=\"5cb9871\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-shortcode\"><div class=\"post-views content-post post-2419 entry-meta load-static\">\r\n\t\t\t\t<span class=\"post-views-icon dashicons dashicons-chart-bar\"><\/span> <span class=\"post-views-label\">Post Views:<\/span> <span class=\"post-views-count\">675<\/span>\r\n\t\t\t<\/div><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Vol. 3 No. 2 (2013): JITA &#8211; APEIRON Adrijan Bo\u017einovski, Biljana Stoj\u010devska, Veno Pa\u010dovski Enumeration, Ranking and Generation of Binary Trees Based on Level-Order Traversal Using Catalan Cipher Vectors Original scientific paper DOI: https:\/\/doi.org\/10.7251\/JIT1302078B Abstract Download Article PDF In this paper, a new representation of a binary tree is introduced, called the Catalan Cipher Vector, which is a vector of\u00a0 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\u2019s 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. Keywords: Enumeration, Rank, Generation, Binary tree, Level-order traversal, Catalan Cipher Vector, Canonical State-Space Tableau. Vol. 26 No. 2 (2023): JITA &#8211; APEIRON Igor Shubinsky, Alexey Ozerov Application of Artificial Intelligence Methods for the Prediction of Hazardous Failures Original scientific paper DOI: https:\/\/doi.org\/10.7251\/JIT2302061S Download Article PDF Abstract 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\u2019 expenditures. Keywords: predictive analysis, maintenance, functional safety, Big Data, Data Science, risk indicators. Vol. 26 No. 2 (2023): JITA &#8211; APEIRON Igor Shubinsky, Alexey Ozerov Application of Artificial Intelligence Methods for the Prediction of Hazardous Failures Original scientific paper DOI: https:\/\/doi.org\/10.7251\/JIT2302061S Download Article PDF Abstract 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\u2019 expenditures. Keywords: predictive analysis, maintenance, functional safety, Big Data, Data Science, risk indicators.<\/p>\n","protected":false},"author":1,"featured_media":534,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2419","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Enumeration, Ranking and Generation of Binary Trees Based on Level-Order Traversal Using Catalan Cipher Vectors - JITA -Journal of Information Technology and Application<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Enumeration, Ranking and Generation of Binary Trees Based on Level-Order Traversal Using Catalan Cipher Vectors - JITA -Journal of Information Technology and Application\" \/>\n<meta property=\"og:description\" content=\"Vol. 3 No. 2 (2013): JITA &#8211; APEIRON Adrijan Bo\u017einovski, Biljana Stoj\u010devska, Veno Pa\u010dovski Enumeration, Ranking and Generation of Binary Trees Based on Level-Order Traversal Using Catalan Cipher Vectors Original scientific paper DOI: https:\/\/doi.org\/10.7251\/JIT1302078B Abstract Download Article PDF In this paper, a new representation of a binary tree is introduced, called the Catalan Cipher Vector, which is a vector of\u00a0 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\u2019s 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. Keywords: Enumeration, Rank, Generation, Binary tree, Level-order traversal, Catalan Cipher Vector, Canonical State-Space Tableau. Vol. 26 No. 2 (2023): JITA &#8211; APEIRON Igor Shubinsky, Alexey Ozerov Application of Artificial Intelligence Methods for the Prediction of Hazardous Failures Original scientific paper DOI: https:\/\/doi.org\/10.7251\/JIT2302061S Download Article PDF Abstract 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\u2019 expenditures. Keywords: predictive analysis, maintenance, functional safety, Big Data, Data Science, risk indicators. Vol. 26 No. 2 (2023): JITA &#8211; APEIRON Igor Shubinsky, Alexey Ozerov Application of Artificial Intelligence Methods for the Prediction of Hazardous Failures Original scientific paper DOI: https:\/\/doi.org\/10.7251\/JIT2302061S Download Article PDF Abstract 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\u2019 expenditures. Keywords: predictive analysis, maintenance, functional safety, Big Data, Data Science, risk indicators.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/\" \/>\n<meta property=\"og:site_name\" content=\"JITA -Journal of Information Technology and Application\" \/>\n<meta property=\"article:published_time\" content=\"2024-04-12T07:54:47+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-04-29T12:59:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/03\/cover_issue_949_en_US.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"595\" \/>\n\t<meta property=\"og:image:height\" content=\"793\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\/\/jita-au.com\/#\/schema\/person\/d4becda53cfcbc99c449927eabf3877f\"},\"headline\":\"Enumeration, Ranking and Generation of Binary Trees Based on Level-Order Traversal Using Catalan Cipher Vectors\",\"datePublished\":\"2024-04-12T07:54:47+00:00\",\"dateModified\":\"2024-04-29T12:59:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/\"},\"wordCount\":534,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/jita-au.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/jita-au.com\/wp-content\/uploads\/2024\/03\/cover_issue_949_en_US.jpg\",\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/\",\"url\":\"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/\",\"name\":\"Enumeration, Ranking and Generation of Binary Trees Based on Level-Order Traversal Using Catalan Cipher Vectors - 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JITA -Journal of Information Technology and Application","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/jita-au.com\/index.php\/2024\/04\/12\/enumeration-ranking-and-generation-of-binary-trees-based-on-level-order-traversal-using-catalan-cipher-vectors\/","og_locale":"en_US","og_type":"article","og_title":"Enumeration, Ranking and Generation of Binary Trees Based on Level-Order Traversal Using Catalan Cipher Vectors - JITA -Journal of Information Technology and Application","og_description":"Vol. 3 No. 2 (2013): JITA &#8211; APEIRON Adrijan Bo\u017einovski, Biljana Stoj\u010devska, Veno Pa\u010dovski Enumeration, Ranking and Generation of Binary Trees Based on Level-Order Traversal Using Catalan Cipher Vectors Original scientific paper DOI: https:\/\/doi.org\/10.7251\/JIT1302078B Abstract Download Article PDF In this paper, a new representation of a binary tree is introduced, called the Catalan Cipher Vector, which is a vector of\u00a0 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\u2019s 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. Keywords: Enumeration, Rank, Generation, Binary tree, Level-order traversal, Catalan Cipher Vector, Canonical State-Space Tableau. Vol. 26 No. 2 (2023): JITA &#8211; APEIRON Igor Shubinsky, Alexey Ozerov Application of Artificial Intelligence Methods for the Prediction of Hazardous Failures Original scientific paper DOI: https:\/\/doi.org\/10.7251\/JIT2302061S Download Article PDF Abstract 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\u2019 expenditures. Keywords: predictive analysis, maintenance, functional safety, Big Data, Data Science, risk indicators. Vol. 26 No. 2 (2023): JITA &#8211; APEIRON Igor Shubinsky, Alexey Ozerov Application of Artificial Intelligence Methods for the Prediction of Hazardous Failures Original scientific paper DOI: https:\/\/doi.org\/10.7251\/JIT2302061S Download Article PDF Abstract 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\u2019 expenditures. 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