Consider the following algorithm to check connectivity of a graph defined by its adjacency matrix. C++ v Algorithm Connected (A[0..n-1, 0..n-1]) { //Input: Adjacency matrix A of an undirected graph G //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; Co ption ... 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.

Consider the following algorithm to check connectivity of a graph defined by its adjacency matrix. C++ v Algorithm Connected (A[0..n-1, 0..n-1]) { //Input: Adjacency matrix A of an undirected graph G //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; Co ption ... 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.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Consider the following algorithm to check connectivity of a graph defined by its adjacency matrix.
C++ v
Algorithm Connected (A[0..n-1, 0..n-1]) {
//Input: Adjacency matrix A of an undirected graph G
}
//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;
Co
ption
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.

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