Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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### Problem 1
Consider the following algorithm to check
connectivity of a graph defined by its adjacency
matrix.
срр
Algorithm Connected (A[0..n-1, 0..n-1]) {
//Input: Adjacency matrix A of an undirected
graph G
7/Output: 1 (true) if G is connected and 0
(false) if it is not
if n
1 return 1; // //one-vertex graph is
==
connected by definition
else {
if not Connected (A[0..n-2, 0..n-2]) return 0;
else {
for j = 0 to n - 2 do {
if A[n-1, j] return 1;
}
return 0;
}
Does this algorithm work correctly for every
undirected graph with `n` vertices? If you answer
YES, indicate the algorithm's efficiency class in
the worst case.
If you answer NO, provide a counter
example.
#### Answer:
Here
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Transcribed Image Text:### Problem 1 Consider the following algorithm to check connectivity of a graph defined by its adjacency matrix. срр Algorithm Connected (A[0..n-1, 0..n-1]) { //Input: Adjacency matrix A of an undirected graph G 7/Output: 1 (true) if G is connected and 0 (false) if it is not if n 1 return 1; // //one-vertex graph is == connected by definition else { if not Connected (A[0..n-2, 0..n-2]) return 0; else { for j = 0 to n - 2 do { if A[n-1, j] return 1; } return 0; } Does this algorithm work correctly for every undirected graph with `n` vertices? If you answer YES, indicate the algorithm's efficiency class in the worst case. If you answer NO, provide a counter example. #### Answer: Here
Algorithms in pseudo code **MUST** be placed in
code blocks/fences, and use `cpp` as the syntax
highlighter.
Algorithms should follow the pseudo code standard
described in *Pseudocode Handout*.
- Do NOT change the template except the answer
portion.
- Formulas and equations should be in math mode
using Latex math symbols.
Markdown math tutorial:
http://tug.ctan.org/info/undergradmath/undergradmat
h.pdf
Two ways to enter math mode:
Insert a pair of dollar signs: \$your
equations go here\$. This is the inline math mode.
*Notice that there is no space between the \$ and
the letter*.
Insert a pair of double-dollar signs: \$\$
your equations go here \$\$, which produces a
standalone equation/formula set.
expand button
Transcribed Image Text:Algorithms in pseudo code **MUST** be placed in code blocks/fences, and use `cpp` as the syntax highlighter. Algorithms should follow the pseudo code standard described in *Pseudocode Handout*. - Do NOT change the template except the answer portion. - Formulas and equations should be in math mode using Latex math symbols. Markdown math tutorial: http://tug.ctan.org/info/undergradmath/undergradmat h.pdf Two ways to enter math mode: Insert a pair of dollar signs: \$your equations go here\$. This is the inline math mode. *Notice that there is no space between the \$ and the letter*. Insert a pair of double-dollar signs: \$\$ your equations go here \$\$, which produces a standalone equation/formula set.
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