Computer Science: A Structured Programming Approach Using C1 15-6 Graphs A graph is a collection of...

Computer Science: A Structured Programming Approach Using C 1

15-6 Graphs

A graph is a collection of nodes, called vertices, and a A graph is a collection of nodes, called vertices, and a collection of segments, called lines, connecting pairs collection of segments, called lines, connecting pairs of vertices. In other words, a graph consists of two of vertices. In other words, a graph consists of two sets, a set of vertices and a set of lines.sets, a set of vertices and a set of lines.

Graph TraversalTopics discussed in this section:Topics discussed in this section:

FIGURE 15-45 Directed and Undirected Graphs

Graphs may be directed or undirected. In a directed graph, each line, called an arc, has a direction indicatinghow it may be traversed. In an undirected graph,

the line is known as an edge, and it may be traversed in either direction.

NoteNote

A file is an external collection of related data treated as a unit.

NoteNote

FIGURE 15-46 Cycles and Loops

FIGURE 15-47 Connected and Disjoint Graphs

FIGURE 15-48 Depth-first Traversal of a Tree

In the depth-first traversal, all of a node’s descendents are processed before moving to an adjacent node.

NoteNote

FIGURE 15-49 Depth-first Traversal of a Graph

FIGURE 15-50 Breadth-first Traversal of a Tree

FIGURE 15-51 Breadth-first Traversal of a Graph

In the breadth-first traversal, all adjacentvertices are processed before processing

the descendents of a vertex.

NoteNote

15-7 Software Engineering

Because lists are useful structures, programmers use Because lists are useful structures, programmers use them in many applications. Rather than rewrite their them in many applications. Rather than rewrite their functions each time we need them, we can write functions each time we need them, we can write functions once and put them in a library. The name functions once and put them in a library. The name given to a complete set of these functions is abstract given to a complete set of these functions is abstract data type (ADT). data type (ADT).

Atomic and Composite DataData Structure and Abstract Data TypeA Model for an Abstract Data TypeADT Data Structure

Topics discussed in this section:Topics discussed in this section:

Atomic Data Type1. A set of values.2. A set of operations on the values.

NoteNote

Data Structure1. A combination of elements, each of which is either a data type or another data structure.2. A set of associations or relationships (structure) involving the combined elements.

NoteNote

Table 15-2 Two Structures

In the concept of abstractionWe know what a data type can do.How it is done is hidden.

NoteNote

FIGURE 15-52 Structures for Holding a List

Abstract Data Type1. Declaration of data.2. Declaration of operations.

NoteNote

FIGURE 15-53 Abstract Data Type Model

Computer Science: A Structured Programming Approach Using C1 15-6 Graphs A graph is a collection of...

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