DOCSLIB.ORG

B-Tree Algorithm Complexity Analysis to Evaluate The

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
B-Tree Algorithm Complexity Analysis to Evaluate The Samira Arabgol, Hoo Sang Ko JAISCR, 2013, Vol. 3, No. 3, pp. 251 – 263 DOI 10.2478/jaiscr-2014-0018 [20] D. E. Goldberg, Genetic Algorithms in Search, Waste Management, vol. 29, no. 11, 2009, pp. Optimization, and Machine Learning, Addison- 2874–2879,. Wesley, 1989. [21] S. Jahandideh, S. Jahandideh, E. Barzegari Asad- [22] D. Venkatesan, K. Kannan, and R. Saravanan, ”A B-TREE ALGORITHM COMPLEXITY ANALYSIS TO abadi, M. Askarian, M. M. Movahedi, S. Hos- Genetic Algorithm-based Artificial Neural Net- seini, and M. Jahandideh, ”The Use of Artificial work Model for the Optimization of Machining EVALUATE THE FEASIBILITY OF ITS APPLICATION IN Neural Networks and Multiple Linear Regression Processes,” Neural Computing and Applications, to Predict Rate of Medical Waste Generation,” vol. 18, no. 2, 2009, pp. 135–140. THE UNIVERSITY COURSE TIMETABLING PROBLEM Marco Antonio Cruz Chvez, Alina Martnez Oropeza CIICAp, Universidad Autnoma del Estado de Morelos Av. Universidad 1001. Col. Chamilpa, C.P. 62209. Cuernavaca, Morelos, Mxico [email protected] Abstract This paper presents a comparative analysis of complexity between the B-TREE and the Binary Search Algorithms, both theoretically and experimentally, to evaluate their effi- ciency in finding overlap of classes for students and teachers in the University Course Timetabling Problem (UCTP). According to the theory, B-TREE Search complexity is lower than Binary Search. The performed experimental tests showed the B-TREE Search Algorithm is more efficient than Binary Search, but only using a dataset larger than 75 students per classroom. 1 Introduction sity where there are many constraints to be consid- ered in order to obtain a feasible solution. Resource Scheduling is a very important area To treat the problem of scheduling at a univer- within computer sciences due to its wide applica- sity level, there is a proposed mathematical model tion in different areas, such as manufacturing, the and some benchmarks which are used as a paradigm academic environment, and vehicle routing, among to try to obtain feasible and better solutions. The others. One of the typical problems in this area name of the problem in combinatorial optimiza- is the scheduling in an academic environment [6], tion is the University Course Timetabling Problem where school schedules must be established. Their (UCTP), which has been classified within the set development requires long periods of time due to of NP-Complete problems due to its complexity [1, the number of variables to assess. Also on occasion, 2]. This means that there is no known deterministic unfeasible solutions are obtained because overlaps algorithm bound by a polynomial temporal func- could occur. An overlap is the timeslot in which the tion to solve this kind of problem [3]. Therefore, same event or activity happens simultaneously; in the scientific community has focused its research this context, when scheduling classes, teachers and on the treatment of NP-Complete problems through students cannot give or take different classes during non-deterministic algorithms, which are bound by the same timeslot. polynomial time. These algorithms (better known Designing school schedules is not an easy task, as Heuristics) need to be constantly improved in but its complexity depends on the level. For exam- attempt to obtain better solutions or reduce the ex- ple in an elementary school the complexity is re- ecution time [4]. There are several techniques that duced due to the smaller quantity of teachers, class- have been used to find feasible solutions to this rooms, and the fixed student groups, so they do not problem, but the most common are metaheuristics. have to take into account so many variables. The complexity increases for a high school or a univer- 252 Cruz Chvez M. A., Martnez Oropeza A. To find a good solution to UCTP using any the efficiency of the search algorithms applied to metaheuristic, local search application is necessary. this specific case. The heart of a local search is the application of a The contribution of this work is to find the most neighborhood structure, which generates exchanges efficient search algorithm to detect overlap of events of elements. Iterative local search, guided by an for students and teachers in the UCTP. objective function, can improve the solution of a problem as UCTP, but every swap generated by the The present research is divided as follows. Sec- neighborhood structure through local search could tion one provides a general introduction to the generate an unfeasible solution. To detect a move- problem, and emphasizes the importance of having ment of the neighborhood structure that can gener- an efficient method which can obtain good solu- ate an unfeasible solution in UCTP, it is necessary tions in a reasonable computational time. Section to use a search algorithm. For example, in a UCTP, two presents the formal definition of the Univer- moving a student e to take a class on day i, at a sity Course Timetabling Problem, focusing on the specific hour j, in classroom k, (i, j, k), may cre- explanation of the set of constraints, which define ate schedule conflicts (overlap) for the student and the specific case. Section three discusses the theo- other classes that he takes. To determine if there retical complexity managed in the literature for the is overlap, it is necessary to perform a search in all principal search methods. An explanation is given classrooms (k = 1,..., n) to verify that the student e for the methods of both Binary Search and B-TREE is not taking another class in the same timeslot (i, Search. The fourth section presents the temporal j). functions specified to each algorithm. Section five shows the experimental results, and the compara- According to theory, the search algorithms with tive analysis of both methods, taking into account the least theoretical complexity are B-TREE and their theoretical and experimental complexity. Fi- Binary search. The B-TREE complexity, in the nally, the conclusions of this research are presented worst case, is lower than the Binary search com- in section six. plexity. For this reason, in this work, these two search algorithms were tested for UCTP. A set of hard constraints were accounted for, which ensured 2 University Course Timetabling non-overlapping classes for both teachers and stu- Problem dents [5]. The fulfillment of these constraints must be verified; it is necessary to check that students do The University Course Timetabling Problem not take more than one subject per timeslot (i, j), (UCTP) has been classified within the Complexity and in one classroom k. If a student e takes more Theory as NP-Complete [1]. This problem could be than one subject in the same timeslot (i, j), the stu- solved by deterministic or non-deterministic meth- dent is overlapping; therefore, the obtained solution ods. Using a deterministic method, it is only fea- is unfeasible. sible to obtain the optimal solution for a small in- In this research, the two most efficient search al- stance, because if the instance size grows, the com- gorithms, according to their theoretical complexity, putation time of a deterministic algorithm increases were used to conduct an experimental comparison. exponentially. As a result, most researchers have focused on heuristics, which get approximated so- Application of a search method allows for re- lutions in a reasonable time; although, there is no vision of each student e assigned to an event in a guarantee of their optimality. timeslot in a CR classroom. It also allows for revi- sion of possible overlaps with other events the stu- The features of the components that are consid- dent takes, where an event is a class taken by the ered in this problem, such as students, classrooms, student e. According to this reasoning, the meth- facilities, teachers, and classes, when considered in ods applied to UCTP require a very efficient search combination with the features of limited resources, algorithm within their structure due to the iterative time considerations and the available spaces for as- nature which is required for this problem. Accord- signing the events, make it difficult to get feasible ing to theoretical and experimental results, a con- solutions in a reasonable computing time. clusion was reached as to the best option, based on Cruz Chvez M. A., Martnez Oropeza A. B-TREE ALGORITHM COMPLEXITY ANALYSIS TO . 253 To find a good solution to UCTP using any the efficiency of the search algorithms applied to The goal of finding solutions to the UCTP is all the students assigned to attend the event. metaheuristic, local search application is necessary. this specific case. to obtain a scheduling such that both students and H3. The assigned classroom must have the required The heart of a local search is the application of a The contribution of this work is to find the most teachers can attend all their programmed classes facilities to carry out the assigned event. neighborhood structure, which generates exchanges without time difficulties. The UCTP has some spe- efficient search algorithm to detect overlap of events H4. No classroom can have more than one event in of elements. Iterative local search, guided by an for students and teachers in the UCTP. cific features that must be respected to obtaining a objective function, can improve the solution of a feasible solution. These features are known as con- the same timeslot. problem as UCTP, but every swap generated by the The present research is divided as follows. Sec- straints, and are classified into two kinds of con- H5. No teacher attends more than one event in the neighborhood structure through local search could tion one provides a general introduction to the straints. same timeslot. generate an unfeasible solution. To detect a move- problem, and emphasizes the importance of having an efficient method which can obtain good solu- Hard Constraints: They must be fulfilled com- Set of Soft Constraints ment of the neighborhood structure that can gener- pletely, and must not be violated.
Load more

Recommended publications
  • Binary Search Tree
    ADT Binary Search Tree! Ellen Walker! CPSC 201 Data Structures! Hiram College! Binary Search Tree! •" Value-based storage of information! –" Data is stored in order! –" Data can be retrieved by value efficiently! •" Is a binary tree! –" Everything in left subtree is < root! –" Everything in right subtree is >root! –" Both left and right subtrees are also BST#s! Operations on BST! •" Some can be inherited from binary tree! –" Constructor (for empty tree)! –" Inorder, Preorder, and Postorder traversal! •" Some must be defined ! –" Insert item! –" Delete item! –" Retrieve item! The Node<E> Class! •" Just as for a linked list, a node consists of a data part and links to successor nodes! •" The data part is a reference to type E! •" A binary tree node must have links to both its left and right subtrees! The BinaryTree<E> Class! The BinaryTree<E> Class (continued)! Overview of a Binary Search Tree! •" Binary search tree definition! –" A set of nodes T is a binary search tree if either of the following is true! •" T is empty! •" Its root has two subtrees such that each is a binary search tree and the value in the root is greater than all values of the left subtree but less than all values in the right subtree! Overview of a Binary Search Tree (continued)! Searching a Binary Tree! Class TreeSet and Interface Search Tree! BinarySearchTree Class! BST Algorithms! •" Search! •" Insert! •" Delete! •" Print values in order! –" We already know this, it#s inorder traversal! –" That#s why it#s called “in order”! Searching the Binary Tree! •" If the tree is
    [Show full text]
  • Binary Search Trees (BST)
    CSCI-UA 102 Joanna Klukowska Lecture 7: Binary Search Trees [email protected] Lecture 7: Binary Search Trees (BST) Reading materials Goodrich, Tamassia, Goldwasser: Chapter 8 OpenDSA: Chapter 18 and 12 Binary search trees visualizations: http://visualgo.net/bst.html http://www.cs.usfca.edu/~galles/visualization/BST.html Topics Covered 1 Binary Search Trees (BST) 2 2 Binary Search Tree Node 3 3 Searching for an Item in a Binary Search Tree3 3.1 Binary Search Algorithm..............................................4 3.1.1 Recursive Approach............................................4 3.1.2 Iterative Approach.............................................4 3.2 contains() Method for a Binary Search Tree..................................5 4 Inserting a Node into a Binary Search Tree5 4.1 Order of Insertions.................................................6 5 Removing a Node from a Binary Search Tree6 5.1 Removing a Leaf Node...............................................7 5.2 Removing a Node with One Child.........................................7 5.3 Removing a Node with Two Children.......................................8 5.4 Recursive Implementation.............................................9 6 Balanced Binary Search Trees 10 6.1 Adding a balance() Method........................................... 10 7 Self-Balancing Binary Search Trees 11 7.1 AVL Tree...................................................... 11 7.1.1 When balancing is necessary........................................ 12 7.2 Red-Black Trees.................................................. 15 1 CSCI-UA 102 Joanna Klukowska Lecture 7: Binary Search Trees [email protected] 1 Binary Search Trees (BST) A binary search tree is a binary tree with additional properties: • the value stored in a node is greater than or equal to the value stored in its left child and all its descendants (or left subtree), and • the value stored in a node is smaller than the value stored in its right child and all its descendants (or its right subtree).
    [Show full text]
  • A Set Intersection Algorithm Via X-Fast Trie
    Journal of Computers A Set Intersection Algorithm Via x-Fast Trie Bangyu Ye* National Engineering Laboratory for Information Security Technologies, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100091, China. * Corresponding author. Tel.:+86-10-82546714; email: [email protected] Manuscript submitted February 9, 2015; accepted May 10, 2015. doi: 10.17706/jcp.11.2.91-98 Abstract: This paper proposes a simple intersection algorithm for two sorted integer sequences . Our algorithm is designed based on x-fast trie since it provides efficient find and successor operators. We present that our algorithm outperforms skip list based algorithm when one of the sets to be intersected is relatively ‘dense’ while the other one is (relatively) ‘sparse’. Finally, we propose some possible approaches which may optimize our algorithm further. Key words: Set intersection, algorithm, x-fast trie. 1. Introduction Fast set intersection is a key operation in the context of several fields when it comes to big data era [1], [2]. For example, modern search engines use the set intersection for inverted posting list which is a standard data structure in information retrieval to return relevant documents. So it has been studied in many domains and fields [3]-[8]. One of the most typical situations is Boolean query which is required to retrieval the documents that contains all the terms in the query. Besides, set intersection is naturally a key component of calculating the Jaccard coefficient of two sets, which is defined by the fraction of size of intersection and union. In this paper, we propose a new algorithm via x-fast trie which is a kind of advanced data structure.
    [Show full text]
  • Objectives Objectives Searching a Simple Searching Problem A
    Python Programming: Objectives An Introduction to To understand the basic techniques for Computer Science analyzing the efficiency of algorithms. To know what searching is and understand the algorithms for linear and binary Chapter 13 search. Algorithm Design and Recursion To understand the basic principles of recursive definitions and functions and be able to write simple recursive functions. Python Programming, 1/e 1 Python Programming, 1/e 2 Objectives Searching To understand sorting in depth and Searching is the process of looking for a know the algorithms for selection sort particular value in a collection. and merge sort. For example, a program that maintains To appreciate how the analysis of a membership list for a club might need algorithms can demonstrate that some to look up information for a particular problems are intractable and others are member œ this involves some sort of unsolvable. search process. Python Programming, 1/e 3 Python Programming, 1/e 4 A simple Searching Problem A Simple Searching Problem Here is the specification of a simple In the first example, the function searching function: returns the index where 4 appears in def search(x, nums): the list. # nums is a list of numbers and x is a number # Returns the position in the list where x occurs # or -1 if x is not in the list. In the second example, the return value -1 indicates that 7 is not in the list. Here are some sample interactions: >>> search(4, [3, 1, 4, 2, 5]) 2 Python includes a number of built-in >>> search(7, [3, 1, 4, 2, 5]) -1 search-related methods! Python Programming, 1/e 5 Python Programming, 1/e 6 Python Programming, 1/e 1 A Simple Searching Problem A Simple Searching Problem We can test to see if a value appears in The only difference between our a sequence using in.
    [Show full text]
  • Prefix Hash Tree an Indexing Data Structure Over Distributed Hash
    Prefix Hash Tree An Indexing Data Structure over Distributed Hash Tables Sriram Ramabhadran ∗ Sylvia Ratnasamy University of California, San Diego Intel Research, Berkeley Joseph M. Hellerstein Scott Shenker University of California, Berkeley International Comp. Science Institute, Berkeley and and Intel Research, Berkeley University of California, Berkeley ABSTRACT this lookup interface has allowed a wide variety of Distributed Hash Tables are scalable, robust, and system to be built on top DHTs, including file sys- self-organizing peer-to-peer systems that support tems [9, 27], indirection services [30], event notifi- exact match lookups. This paper describes the de- cation [6], content distribution networks [10] and sign and implementation of a Prefix Hash Tree - many others. a distributed data structure that enables more so- phisticated queries over a DHT. The Prefix Hash DHTs were designed in the Internet style: scala- Tree uses the lookup interface of a DHT to con- bility and ease of deployment triumph over strict struct a trie-based structure that is both efficient semantics. In particular, DHTs are self-organizing, (updates are doubly logarithmic in the size of the requiring no centralized authority or manual con- domain being indexed), and resilient (the failure figuration. They are robust against node failures of any given node in the Prefix Hash Tree does and easily accommodate new nodes. Most impor- not affect the availability of data stored at other tantly, they are scalable in the sense that both la- nodes). tency (in terms of the number of hops per lookup) and the local state required typically grow loga- Categories and Subject Descriptors rithmically in the number of nodes; this is crucial since many of the envisioned scenarios for DHTs C.2.4 [Comp.
    [Show full text]
  • Chapter 13 Sorting & Searching
    13-1 Java Au Naturel by William C. Jones 13-1 13 Sorting and Searching Overview This chapter discusses several standard algorithms for sorting, i.e., putting a number of values in order. It also discusses the binary search algorithm for finding a particular value quickly in an array of sorted values. The algorithms described here can be useful in various situations. They should also help you become more comfortable with logic involving arrays. These methods would go in a utilities class of methods for Comparable objects, such as the CompOp class of Listing 7.2. For this chapter you need a solid understanding of arrays (Chapter Seven). · Sections 13.1-13.2 discuss two basic elementary algorithms for sorting, the SelectionSort and the InsertionSort. · Section 13.3 presents the binary search algorithm and big-oh analysis, which provides a way of comparing the speed of two algorithms. · Sections 13.4-13.5 introduce two recursive algorithms for sorting, the QuickSort and the MergeSort, which execute much faster than the elementary algorithms when you have more than a few hundred values to sort. · Sections 13.6 goes further with big-oh analysis. · Section 13.7 presents several additional sorting algorithms -- the bucket sort, the radix sort, and the shell sort. 13.1 The SelectionSort Algorithm For Comparable Objects When you have hundreds of Comparable values stored in an array, you will often find it useful to keep them in sorted order from lowest to highest, which is ascending order. To be precise, ascending order means that there is no case in which one element is larger than the one after it -- if y is listed after x, then x.CompareTo(y) <= 0.
    [Show full text]
  • P4 Sec 4.1.1, 4.1.2, 4.1.3) Abstraction, Algorithms and ADT's
    Computer Science 9608 P4 Sec 4.1.1, 4.1.2, 4.1.3) Abstraction, Algorithms and ADT’s with Majid Tahir Syllabus Content: 4.1.1 Abstraction show understanding of how to model a complex system by only including essential details, using: functions and procedures with suitable parameters (as in procedural programming, see Section 2.3) ADTs (see Section 4.1.3) classes (as used in object-oriented programming, see Section 4.3.1) facts, rules (as in declarative programming, see Section 4.3.1) 4.1.2 Algorithms write a binary search algorithm to solve a particular problem show understanding of the conditions necessary for the use of a binary search show understanding of how the performance of a binary search varies according to the number of data items write an algorithm to implement an insertion sort write an algorithm to implement a bubble sort show understanding that performance of a sort routine may depend on the initial order of the data and the number of data items write algorithms to find an item in each of the following: linked list, binary tree, hash table write algorithms to insert an item into each of the following: stack, queue, linked list, binary tree, hash table write algorithms to delete an item from each of the following: stack, queue, linked list show understanding that different algorithms which perform the same task can be compared by using criteria such as time taken to complete the task and memory used 4.1.3 Abstract Data Types (ADT) show understanding that an ADT is a collection of data and a set of operations on those data
    [Show full text]
  • Binary Search Algorithm This Article Is About Searching a Finite Sorted Array
    Binary search algorithm This article is about searching a finite sorted array. For searching continuous function values, see bisection method. This article may require cleanup to meet Wikipedia's quality standards. No cleanup reason has been specified. Please help improve this article if you can. (April 2011) Binary search algorithm Class Search algorithm Data structure Array Worst case performance O (log n ) Best case performance O (1) Average case performance O (log n ) Worst case space complexity O (1) In computer science, a binary search or half-interval search algorithm finds the position of a specified input value (the search "key") within an array sorted by key value.[1][2] For binary search, the array should be arranged in ascending or descending order. In each step, the algorithm compares the search key value with the key value of the middle element of the array. If the keys match, then a matching element has been found and its index, or position, is returned. Otherwise, if the search key is less than the middle element's key, then the algorithm repeats its action on the sub-array to the left of the middle element or, if the search key is greater, on the sub-array to the right. If the remaining array to be searched is empty, then the key cannot be found in the array and a special "not found" indication is returned. A binary search halves the number of items to check with each iteration, so locating an item (or determining its absence) takes logarithmic time. A binary search is a dichotomic divide and conquer search algorithm.
    [Show full text]
  • Binary Search Algorithm
    Binary search algorithm Definition Search a sorted array by repeatedly dividing the search interval in half. Begin with an interval covering the whole array. If the value of the search key is less than the item in the middle of the interval, narrow the interval to the lower half. Otherwise narrow it to the upper half. Repeatedly check until the value is found or the interval is empty. Generally, to find a value in unsorted array, we should look through elements of an array one by one, until searched value is found. In case of searched value is absent from array, we go through all elements. In average, complexity of such an algorithm is proportional to the length of the array. Divide in half A fast way to search a sorted array is to use a binary search. The idea is to look at the element in the middle. If the key is equal to that, the search is finished. If the key is less than the middle element, do a binary search on the first half. If it's greater, do a binary search of the second half. Performance The advantage of a binary search over a linear search is astounding for large numbers. For an array of a million elements, binary search, O(log N), will find the target element with a worst case of only 20 comparisons. Linear search, O(N), on average will take 500,000 comparisons to find the element. Algorithm Algorithm is quite simple. It can be done either recursively or iteratively: 1. get the middle element; 2.
    [Show full text]
  • Algorithm for Character Recognition Based on the Trie Structure
    University of Montana ScholarWorks at University of Montana Graduate Student Theses, Dissertations, & Professional Papers Graduate School 1987 Algorithm for character recognition based on the trie structure Mohammad N. Paryavi The University of Montana Follow this and additional works at: https://scholarworks.umt.edu/etd Let us know how access to this document benefits ou.y Recommended Citation Paryavi, Mohammad N., "Algorithm for character recognition based on the trie structure" (1987). Graduate Student Theses, Dissertations, & Professional Papers. 5091. https://scholarworks.umt.edu/etd/5091 This Thesis is brought to you for free and open access by the Graduate School at ScholarWorks at University of Montana. It has been accepted for inclusion in Graduate Student Theses, Dissertations, & Professional Papers by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact [email protected]. COPYRIGHT ACT OF 1 9 7 6 Th is is an unpublished manuscript in which copyright sub ­ s i s t s , Any further r e p r in t in g of its contents must be approved BY THE AUTHOR, Ma n sfield L ibrary U n iv e r s it y of Montana Date : 1 987__ AN ALGORITHM FOR CHARACTER RECOGNITION BASED ON THE TRIE STRUCTURE By Mohammad N. Paryavi B. A., University of Washington, 1983 Presented in partial fulfillment of the requirements for the degree of Master of Science University of Montana 1987 Approved by lairman, Board of Examiners iean, Graduate School UMI Number: EP40555 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted.
    [Show full text]
  • Binary Search Algorithm Anthony Lin¹* Et Al
    WikiJournal of Science, 2019, 2(1):5 doi: 10.15347/wjs/2019.005 Encyclopedic Review Article Binary search algorithm Anthony Lin¹* et al. Abstract In In computer science, binary search, also known as half-interval search,[1] logarithmic search,[2] or binary chop,[3] is a search algorithm that finds a position of a target value within a sorted array.[4] Binary search compares the target value to an element in the middle of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. Binary search runs in logarithmic time in the worst case, making 푂(log 푛) comparisons, where 푛 is the number of elements in the array, the 푂 is ‘Big O’ notation, and 푙표푔 is the logarithm.[5] Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary search. There are spe- cialized data structures designed for fast searching, such as hash tables, that can be searched more efficiently than binary search. However, binary search can be used to solve a wider range of problems, such as finding the next- smallest or next-largest element in the array relative to the target even if it is absent from the array. There are numerous variations of binary search.
    [Show full text]
  • ECE 2574 Introduction to Data Structures and Algorithms 31
    ECE 2574 Introduction to Data Structures and Algorithms 31: Binary Search Trees Chris Wyatt Electrical and Computer Engineering Recall the binary search algorithm using a sorted list. We can represent the sorted list using a binary tree with a specific relationship among the nodes. This leads to the Binary Search Tree ADT. We can map the sorted list operations onto the binary search tree. Because the insert and delete can use the binary structure, they are more efficient. Better than binary search on a pointer-based (linked) list. Binary Search Tree (BST) Operations Consider the items of type TreeItemType to have an associated key of keyType. // create an empty BST +createBST() // destroy a BST +destroyBST() // check if a BST is empty +isEmpty(): bool Binary Search Tree (BST) Operations // insert newItem into the BST based on its // key value, fails if key exists or node // cannot be created +insert(in newItem:TreeItemType): bool // delete item with searchKey from the BST // fails if no such key exists +delete(in searchKey:KeyItemType): bool // get item corresponding to searchKey from // the BST, fails if no such key exists +retrieve(in searchKey:KeyItemType, out treeItem:TreeItemType): bool Binary Search Tree (BST) Operations // call function visit passing each node data //as the argument, using a preorder //traversal +preorderTraverse(in visit:FunctionType) // call function visit passing each node data // as the argument, using an inorder //traversal +inorderTraverse(in visit:FunctionType) // call function visit passing each node dat a // as the argument, using a postorder // traversal +postorderTraverse(in visit:FunctionType) An interface for Binary Search Trees Template over the key type and the value type.
    [Show full text]