Consider the following algorithm to check whether a graph defined by itsadjacency matrix is complete.ALGORITHM GraphComplete(A[0..n − 1, 0..n − 1])//Input: Adjacency matrix A[0..n − 1, 0..n − 1]) of an undirected graph G//Output: 1 (true) if G is complete and 0 (false) otherwiseif n = 1 return 1 //one-vertex graph is complete by definitionelseif not GraphComplete(A[0..n − 2, 0..n − 2]) return 0else for j ← 0 to n − 2 doif A[n − 1, j ] = 0 return 0return 1What is the algorithm’s efficiency class in the worst case?
Question
Consider the following algorithm to check whether a graph defined by itsadjacency matrix is complete.ALGORITHM GraphComplete(A[0..n − 1, 0..n − 1])//Input: Adjacency matrix A[0..n − 1, 0..n − 1]) of an undirected graph G//Output: 1 (true) if G is complete and 0 (false) otherwiseif n = 1 return 1 //one-vertex graph is complete by definitionelseif not GraphComplete(A[0..n − 2, 0..n − 2]) return 0else for j ← 0 to n − 2 doif A[n − 1, j ] = 0 return 0return 1What is the algorithm’s efficiency class in the worst case?
Solution
The efficiency class of the given algorithm in the worst case is O(n^2). This is because the algorithm checks each element in the adjacency matrix once, and the adjacency matrix has n^2 elements (where n is the number of vertices in the graph). Therefore, the time complexity of the algorithm is proportional to the square of the size of the input, which is characteristic of the O(n^2) complexity class.
Similar Questions
What is a complete graph?a.A graph in which every vertex is connected to every other vertexb.A graph with no edgesc.A graph with only one vertexd.A graph with parallel edges
If every node u in G adjacent to every other node v in G, A graph is said to be Complete Options true false
A graph that is both bipartite and complete is:A. PlanarB. TreeC. CycleD. Complete bipartite graph
Which of the following statements about Adjacency Matrices are true? Note: You may select multiple answers. Group of answer choices Adjacency matrices are symmetric for both directed and undirected graphs. An adjacency matrix for a graph with V vertices requires O(V2) space, irrespective of the number of edges in the graph. Finding the existence of an edge in a graph given an adjacency matrix representation is an O(1) operation. Finding the neighbours of a vertex v, in a graph of V vertices, given its adjacency matrix representation is a Ө(V2) operation.
An Algorithm is said as Complete algorithm if____________
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.