... letting V
1
be the
cluster containing v and letting V
2
contain the rest of the vertices in V. This clearly
defines a disjoint partitioning of the vertices of V and, more importantly, since ... switching centers, and whose edges represent communication lines
joining pairs of centers. Edges are marked by their bandwidth, and the
bandwidth of a path is the bandwidth of its lowest...
... finding such a tree are the focus of this section.
Problem Definition
Given a weighted undirected graph G, we are interested in finding a tree T that
contains all the vertices in G and minimizes ... Rather than computing a shortest
path tree from some particular vertex v, we are interested instead in finding a (free)
tree T that contains all the vertices of G and has the minimu...
...
as an instance variable, an integer, and it provides several operations for accessing
this data, including methods for converting it into other number types, for
converting it to a string of ... implementations of data structures and algorithms. These
design patterns fall into two groups—patterns for solving algorithm design
problems and patterns for solving software engineer...
... for inserting an element at the beginning of a singly linked
list. Assume that the list does not have a sentinel header node, and instead uses
a variable head to reference the first node in ... space in memory).
Example 3.2: Much of the syntax in modern programming languages is defined
in a recursive way. For example, we can define an argument list in Java using the
followin...
... because finding the index
of an element in a linked list requires searching through the list incrementally from
its beginning or end, counting elements as we go.
For instance, we could define a ... by their indices is called an array list
(or vector, using an older term). Since our index definition is more consistent with the
way arrays are indexed in Java and other programming l...
... data structures in
computing—trees. Tree structures are indeed a breakthrough in data organization, for
they allow us to implement a host of algorithms much faster than when using linear
data ...
empty binary tree. Starting from this empty tree, we can build any binary tree by
creating the first node with method addRoot and repeatedly applying the
insertLeft and inser...
... example, if we insert a
series of entries with keys in increasing or decreasing order. (See Figure 10. 6.)
Figure 10. 6: Example of a binary search tree with
linear height, obtained by inserting entries ... expanded
into a new internal node accommodating the new entry. An example of insertion
into a binary search tree is shown in Figure 10. 3.
Figure 10. 3: Insertion of an entry...
... Figure 10. 10b
.
R -10. 10
Draw the AVL tree resulting from the removal of the entry with key 62 from the
AVL tree of Figure 10. 10b
.
R -10. 11
Explain why performing a rotation in an n-node binary ... 9.5.2) using a (2,4) tree.
673
Are the rotations in Figures 10. 8 and 10. 10 single or double rotations?
R -10. 9
Draw the AVL tree resulting from the insertion of an entry...
... operation involves being given a string X, and looking for all the
strings in S that contain X as a prefix.
12.3.1 Standard Tries
Let S be a set of s strings from alphabet σ such that no string in ... Since most document
processing algorithms are used in applications where the underlying character set is
744
Return and update S to be the string obtained by inserting Q insid...
... concatenating two doubly linked lists L and M, with
header and trailer sentinel nodes, into a single list L ′.
C-3.9
Describe in detail how to swap two nodes x and y in a singly linked list ... algorithm for finding the penultimate node in a singly linked list where
the last element is indicated by a null next reference.
R-3.9
Describe a nonrecursive method for finding, by l...