Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Question
Chapter 24.2, Problem 3E
Program Plan Intro
To modify the DAG-SHORTEST-PATHS
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Students have asked these similar questions
When we learn about Graph Traversals, one question that I'm sometimes asked by students is why we need them at all. Consider the two implementation strategies for graphs that we learned about previously: an adjacency matrix and adjacency lists. Both of them include a separate array-based structure in which information about every vertex is stored. So if our only goal is to visit every vertex, we can do that by just iterating through that array-based structure.
If visiting every vertex is as easy as iterating through them, then why do we need graph traversal algorithms such as depth-first and breadth-first? What purpose do they serve that just iterating through the vertices one at a time, without regard for the presence of edges, wouldn't?
JAVA PROGRAMMING
The Graph Data Structure is made up of nodes and edges. (A Tree Data Structure is a special kind of a
Graph Data Structure). A Graph may be represented by an Adjacency Matrix or an Adjacency List. Through
this exercise, you should be able to have a better grasp the Adjacency Matrix concept. You are expected to
read about the Adjacency Matrix concept as well as the Adjacency List concept.
Suppose the vertices A, B, C, D, E, F, G and H of a Graph are mapped to row and column
indices(0,1,2,3,4,5,6,and 7) of a matrix (i.e. 2-dimensional array) as shown in the following table.
Vertex of Graph
Index in the 2-D Array Adjacency Matrix
Representation of Graph
A
B
2
F
6.
H
7
Suppose further, that the following is an Adjacency Matrix representing the Graph.
3
4
5.
6.
7
0.
1
1
1
1
01
1
01
1.
3
14
1
1
1
6.
1
Exercise:
Show/Draw the Graph that is represented by the above Adjacency matrix. Upload the document that contains
your result. (Filename: AdjacencyMatrixExercise.pdf)
Notes:
-The nodes of the…
Please Answer this in Python language:
You're given a simple undirected graph G with N vertices and M edges. You have to assign, to each
vertex i, a number C; such that 1 ≤ C; ≤ N and Vi‡j, C; ‡ Cj.
For any such assignment, we define D; to be the number of neighbours j of i such that C; < C₁.
You want to minimise maai[1..N) Di - mini[1..N) Di.
Output the minimum possible value of this expression for a valid assignment as described above,
and also print the corresponding assignment.
Note:
The given graph need not be connected.
• If there are multiple possible assignments, output anyone.
• Since the input is large, prefer using fast input-output methods.
Input
1
57
12
13
14
23
24
25
35
Output
2
43251
Q
Chapter 24 Solutions
Introduction to Algorithms
Ch. 24.1 - Prob. 1ECh. 24.1 - Prob. 2ECh. 24.1 - Prob. 3ECh. 24.1 - Prob. 4ECh. 24.1 - Prob. 5ECh. 24.1 - Prob. 6ECh. 24.2 - Prob. 1ECh. 24.2 - Prob. 2ECh. 24.2 - Prob. 3ECh. 24.2 - Prob. 4E
Ch. 24.3 - Prob. 1ECh. 24.3 - Prob. 2ECh. 24.3 - Prob. 3ECh. 24.3 - Prob. 4ECh. 24.3 - Prob. 5ECh. 24.3 - Prob. 6ECh. 24.3 - Prob. 7ECh. 24.3 - Prob. 8ECh. 24.3 - Prob. 9ECh. 24.3 - Prob. 10ECh. 24.4 - Prob. 1ECh. 24.4 - Prob. 2ECh. 24.4 - Prob. 3ECh. 24.4 - Prob. 4ECh. 24.4 - Prob. 5ECh. 24.4 - Prob. 6ECh. 24.4 - Prob. 7ECh. 24.4 - Prob. 8ECh. 24.4 - Prob. 9ECh. 24.4 - Prob. 10ECh. 24.4 - Prob. 11ECh. 24.4 - Prob. 12ECh. 24.5 - Prob. 1ECh. 24.5 - Prob. 2ECh. 24.5 - Prob. 3ECh. 24.5 - Prob. 4ECh. 24.5 - Prob. 5ECh. 24.5 - Prob. 6ECh. 24.5 - Prob. 7ECh. 24.5 - Prob. 8ECh. 24 - Prob. 1PCh. 24 - Prob. 2PCh. 24 - Prob. 3PCh. 24 - Prob. 4PCh. 24 - Prob. 5PCh. 24 - Prob. 6P
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