data structures and algorithms alfred v aho pdf

... Insertion28 <ErrorCode> recursiveInsert (val subroot <pointer>, val newData <DataType>,ref median <DataType>,ref rightBranch <pointer>) Return overflow, duplicate_error, success ... 29<ErrorCode> recursiveInsert (val subroot <pointer>, val newData <DataType>, ref median <DataType>, ref rightBranch <pointer>) (cont.) 2 // else, local variables: extraEntry, ... subroot , newData , position) = success) Trang 30Push In30 Trang 3131 <void> push_in (val subroot <pointer>, val entry <DataType>,val rightBranch <pointer>, val position

Ngày tải lên: 15/03/2014, 17:20

... Depth-First Traverse: <void> preOrderTraverse (ref<void>Operation(ref Data <DataType>)) <void> inOrderTraverse (ref<void>Operation(ref Data <DataType>)) <void> ... Search (ref DataOut <DataType>) <ErrorCode> Insert (val DataIn <DataType>) <ErrorCode> Remove (val key <KeyType>) <ErrorCode> Retrieve (ref DataOut <DataType>) ... <void> postOrderTraverse (ref<void>Operation(ref Data <DataType>)) • Breadth-First Traverse: <void> BreadthFirstTraverse (ref<void>Operation(ref Data <DataType>)) 16

Ngày tải lên: 15/03/2014, 17:20

... whereas lower values float to the left This behavior is caused by moving through the list many times, comparingadjacent values, and swapping them if the value to the left is greater than thevalue to ... algorithm works In the following tests, however, the ar-ray sizes are varied to demonstrate how the three algorithms perform withboth smaller data sets and larger data sets The timing tests are run for ... can handle large data sets more efficiently We’ll examinetheir design and use in Chapter16 In this chapter we discussed three algorithms for sorting data: the Selectionsort, the Bubble sort, and

Ngày tải lên: 12/08/2014, 16:21

... Not (data(hash_value).Contains(item)) Then data(hash_value).Add(item) End If End Sub Public Sub Remove(ByVal item As String) Dim hash_value As Integer hash_value = Hash(item) If (data(hash_value).Contains(item)) ... an Add method to add new data, an Item method to retrieve a value, a Remove method to remove a key–value pair, and a Clear method to clear the data structure of all data Let’s begin the discussion ... provide fast insertion, deletion, and retrieval, they perform poorly for operations that involve searching, such asfinding the minimum or maximum value For these types of operations, otherdata structures

Ngày tải lên: 12/08/2014, 16:21

... data structure considered In VB.NET, however, it is possible to use one of the built-in data structures, such as the ArrayList, and achieve the same result as implementing a linked list However, ... method and the other two traversalmethods is where the recursive calls and the call to displayNode are placed In a postorder traversal, the method first recurses over the left subtrees and then over ... chosen over more fundamental structures, such as arrays and linked lists, because you can search a binary tree quickly (as opposed to a linked list) and you can quickly insert data and delete data

Ngày tải lên: 12/08/2014, 16:21

... difference occurs? Trang 15AVL TREESNamed for the two computer scientists who discovered this data structure— G M Adelson-Velskii and E M Landis—in 1962, AVL trees provide anothersolution to maintaining ... node and above a smaller node Applying this algorithm continually removes the data from the heap in sorted order Here is the code for the Remove and TrickleDown methods: Public Function Remove() ... algorithm exemplifies a recursive algorithm This algorithm works by breaking up the data set into two halves and recursively sorting each half When the two halves are sorted, they are brought

Ngày tải lên: 12/08/2014, 16:21

... Implements IComparable Private item As String Private val As Single Private unit As Integer Public Sub New(ByVal i As String, ByVal v As _ Single, ByVal u As Integer) item = i val = v unit = u End Sub ... O’Reilly and Associates, 1997 Knuth, Donald E., The Art of Computer Programming, Volume 1, Fundamental Algorithms Reading, Massachusetts: Addison Wesley, 1998. LaFore, Robert Data Structures and Algorithms ... Rivest, Ronald L., and CliffordStein Introduction to Algorithms Cambridge, Massachusetts: The MIT Press, 2001 Ford, William and William Topp Data Structures with C++ Upper Saddle River, New Jersey:

Ngày tải lên: 12/08/2014, 16:21

... sense that it does not return any value, whereas the methods firstValue and nextValue both return long-integer values That is, firstValue and nextValue are functions, and printProgression is a procedure ... first value of the progression; • cur: current value of the progression; and the following three methods: firstValue(): Reset the progression to the first value, and return that value nextValue(): ... quickly, and there is no provision for handling the inevitable overflow of the long integers involved For example, since 340 > 263, a geometric progression with base b = 3 will overflow a

Ngày tải lên: 14/08/2014, 01:21

... last, and so on We can solve this problem using linear recursion, by observing that the reversal of an array can be achieved by swapping the first and last elements and then recursively reversing ... and again in the analysis of data structures and algorithms is the summation, which is defined as follows: , Trang 35where a and b are integers and a ≤ b Summations arise in data structure and ... a value to some variable, or comparing two numbers Trang 304.1.2 The Logarithm function One of the interesting and sometimes even surprising aspects of the analysis of data structures and algorithms

Ngày tải lên: 14/08/2014, 01:21

... respectively refer to p and q, and then have p's next link refer to t, and have q's prev link refer to t Likewise, to remove an element stored at a node t, we can access the nodes p and q on ... remainder after an integral division For example, 14 divided by 4 is 3 with remainder 2, so 14 mod 4 = 2 Specifically, given integers x and y such that x ≥ 0 and y > 0, we have x mod y = x − x/y y ... array and it also includes two instance variables, f and r, which index the front of the queue and first empty cell after the rear of the queue respectively Trang 15The implementation above contains

Ngày tải lên: 14/08/2014, 01:21

... iterators are pervasive concepts in the Java Collections Framework. Our node list ADT is derived from the "position" abstraction introduced by Aho, Hopcroft, and Ullman [5], and the list ... linear data structures, such as list. Trees also provide a natural organization for data, and consequently have become ubiquitous structures in file systems, graphical user interfaces, databases, ... Abstract Data Type 373 270 7.1.3 Implementing a Tree 271 7.2 Tree Traversal Algorithms 273 7.2.1 Depth and Height 273 7.2.2 Preorder Traversal 276 7.2.3 Postorder Traversal

Ngày tải lên: 14/08/2014, 01:21

... additional update operation: removeExternal(v): Remove an external node v and its parent, replacing v's parent with v's sibling; an error occurs if v is not external Given this operation, we begin ... class with a private location variable and protected methods, location() and setLocation(p), which return and set this variable respectively We then require that the location variable for an ... Insert an entry with key k and value x • remove(e): Remove an entry e, and return it • removeAll(k): Remove all entries with key k, returning an iterator of their values Method find returns

Ngày tải lên: 14/08/2014, 01:21

... the data structures discussed in this chapter are extensively covered by Knuth in his Sorting and Searching book [63], and by Mehlhorn in [74] AVL trees are due to Adel'son-Vel'skii and Landis ... performing a split at a node v in a (2,4) tree is to partition v into v ′ and v ′′, with v ′ being a 2-node and v ′′ a 3-node Which of the keys k1, k2, k3, or k4 do we store at v's parent in this case? ... not have an external child, we find the internal node v following u in the inorder traversal of T, move the entry at v to u, and perform the removal at v Thus, we may consider only the removal

Ngày tải lên: 14/08/2014, 01:22

... Let us also say that a chain of k ≥ 2 edges, (v0,v1)(v1,v2)…(v k−1 ,v k), ith the is redundant if: • v i is redundant for i = 1, …, k−1 1 • v0 and vk are not redundant We can transform T into ... by replacing each redundant chain (v0,v1) … (vk−1,v k) of k ≥ 2 edges into a single edge (v0, vk ), relabeling vk w concatenation of the labels of nodes v1,…, v k Figure 12.8: Compressed trie ... in the appendix and the book by Motwani and Raghavan [79] The quick-sort analysis given in this chapter is a combination of an analysis given in a previous edition of this book and the analysis

Ngày tải lên: 14/08/2014, 01:22

... last, and so on We can solve this problem using linear recursion, by observing that the reversal of an array can be achieved by swapping the first and last elements and then recursively reversing ... and again in the analysis of data structures and algorithms is the summation, which is defined as follows: , Trang 35where a and b are integers and a ≤ b Summations arise in data structure and ... a value to some variable, or comparing two numbers Trang 304.1.2 The Logarithm function One of the interesting and sometimes even surprising aspects of the analysis of data structures and algorithms

Ngày tải lên: 14/08/2014, 06:22

... additional update operation: removeExternal(v): Remove an external node v and its parent, replacing v's parent with v's sibling; an error occurs if v is not external Given this operation, we begin ... class with a private location variable and protected methods, location() and setLocation(p), which return and set this variable respectively We then require that the location variable for an ... Insert an entry with key k and value x • remove(e): Remove an entry e, and return it • removeAll(k): Remove all entries with key k, returning an iterator of their values Method find returns

Ngày tải lên: 14/08/2014, 06:22

... the data structures discussed in this chapter are extensively covered by Knuth in his Sorting and Searching book [63], and by Mehlhorn in [74] AVL trees are due to Adel'son-Vel'skii and Landis ... performing a split at a node v in a (2,4) tree is to partition v into v ′ and v ′′, with v ′ being a 2-node and v ′′ a 3-node Which of the keys k1, k2, k3, or k4 do we store at v's parent in this case? ... not have an external child, we find the internal node v following u in the inorder traversal of T, move the entry at v to u, and perform the removal at v Thus, we may consider only the removal

Ngày tải lên: 14/08/2014, 06:22

... Let us also say that a chain of k ≥ 2 edges, (v0,v1)(v1,v2)…(v k−1 ,v k), ith the is redundant if: • v i is redundant for i = 1, …, k−1 1 • v0 and vk are not redundant We can transform T into ... by replacing each redundant chain (v0,v1) … (vk−1,v k) of k ≥ 2 edges into a single edge (v0, vk ), relabeling vk w concatenation of the labels of nodes v1,…, v k Figure 12.8: Compressed trie ... in the appendix and the book by Motwani and Raghavan [79] The quick-sort analysis given in this chapter is a combination of an analysis given in a previous edition of this book and the analysis

Ngày tải lên: 14/08/2014, 06:22

... the outgoing edges of u, and thus must reach also vertex v via edge (u,v) Hence, v should be in Vs, and we have obtained a contradiction Therefore, Vs must contain every vertex reachable from s ... an ordering v1, ,vn of the vertices of Because of the construction above, if ( ,vj) is an edge of vi , then vi must be deleted before vj can be deleted, and thus i<j Thus, v1, , vn is a topological ... of the edges of P That is, if P = ((v0,v1),(v1,v2), , (vk−1,vk)), then the length of P, Trang 13The distance from a vertex v to a vertex U in G, denoted d(v, U), is the length of a minimum length

Ngày tải lên: 14/08/2014, 06:22