Data and File Structures
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Data Structures: Queues and Graphs, Study notes of Data Structures and Algorithms
An overview of two essential data structures: queues and graphs. Queues are a linear data structure that follows the first-in-first-out (fifo) principle, with properties such as elements removed in order of insertion. Graphs, on the other hand, are non-linear data structures consisting of vertices and edges, representing connections between different entities. Various topics related to graphs, including paths, simple graphs, connected components, cycles, and acyclic graphs. It also discusses different graph representations like adjacency matrices and linked lists.
Typology: Study notes
2010/2011
1 / 32
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Data Structures: Queues and Graphs and more Study notes Data Structures and Algorithms in PDF only on Docsity!
Data and File Structures
Queue
- (^) Properties
- (^) Elements removed in order of insertion
- (^) First-in, First-out (FIFO)
- (^) Must track Front (first in) and Back (last in)
- (^) Queue operations
- (^) Enqueue = add element (to back)
- (^) Dequeue = remove element (from front)
Queue Implementations
- (^) Linked list
- (^) Add to tail (Back) of list
- (^) Remove from head (Front) of list
- (^) Array
- (^) Circular array
Circular Queue
- (^) Circular array (ring)
- (^) q[ 0 ] follows q[ MAX – 1 ]
- (^) Index using q[ i % MAX ]
- (^) Problem
- (^) Detecting difference between empty and nonempty queue
Circular Queue
- (^) Approach 2
- (^) Keep Front at first in
- (^) Keep Back at last in – 1
- (^) Problem
- (^) Empty queue identical to full queue
Circular Queue
- (^) Inherent problem for queue of size N
- (^) Only N possible (Front – Back) pointer locations
- (^) N+1 possible queue configurations
- (^) Queue with 0, 1, … N elements
- (^) Solutions
- (^) Maintain additional state information
- (^) Use state to recognize empty / full queue
- (^) Examples
- (^) Record Size
- (^) Record QueueEmpty flag
- (^) Leave empty element in queue
- (^) Store marker in queue
- (^) Maintain additional state information
Data Structures - Graph
THESE ARE ALL GRAPHS.
Graph Terms
- (^) Path –
- (^) A path from vertex u and v of a graph G exists if there exists a set adjacent edges that starts with u and ends with v
- (^) Simple Graph –
- (^) A graph without loops and with at most one edge between any two vertices is called a simple graph
- (^) Length of a path –
- (^) The number of edges in the aforementioned set
Examples
0
1 2
3
0
1
2
0
1 2
G 1^3 4 5
G 2
G 3
V(G 1 )={0,1,2,3} E(G 1 )={(0,1),(0,2),(0,3),(1,2),(1,3),(2, V(G 2 )={0,1,2,3,4,5,6} E(G 2 )={(0,1),(0,2),(1,3),(1,4),(2,5),(2, V(G 3 )={0,1,2} E(G 3 )={<0,1>,<1,0>,<1,2>}
complete undirected graph: n ( n –1)/2 edges complete directed graph: n ( n –1) edges
complete graph incomplete graph
Representing Graphs
- (^) Graphs –
- (^) Inherently abstract
- (^) Directed or Undirected
- (^) Two common representations:
- (^) Adjacency matrix
- (^) Adjacency linked list
A B C
A 0 1 1
B 1 1 0
C 0 0 1
{ (A,B),(A,C),(B,A),(B,B),(C,C)
- (^) Adjacency Lists
[0]
[1]
[2]
0
1
2
NULL
NULL
NULL
Weighted Graphs
• Weighted Graph –
- (^) A graph G, with the added property that the
edges between nodes is assigned a
“weight”
- (^) Edge weight may represent: cost, distance,
time…
A B C
A 0 1.5 2.
B 1.3 2.0 0
C 0 0 1.
(A,B,1.5),(A,C,2.3),
(B,A,1.3),
(B,B,2.0),(C,C,1.1)
Rooted Trees
- (^) Rooted Tree
- (^) A tree, with a “root” node
- (^) Root nodes are selected arbitrarily (any vertex)
- (^) Tree genealogy
- (^) Ancestors
- (^) Children
- (^) Siblings
- (^) Parents
- (^) Descendents
- (^) Leaf nodes