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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

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DSA - Graphs and Hashing -Q15


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+2 votes

Consider the following statements about computing out-degree of every vertex in a Graph G: 

1. Given an adjacency-list representation of a directed graph G = (V, E), it takes \Theta(V + E) time to compute the out-degree of every vertex without any additional storage. 

2. Given an adjacency-list representation of a directed graph G = (V , E), it takes \Theta(V ) time to compute the out-degree of every vertex with \Theta(V ) additional storage.

Which of the above is correct? 

A. 1 Only 

B. 2 Only 

C. Both 1,2 

D. None 

asked Aug 3, 2020 by gbeditor-2 (72,840 points)
reshown Aug 6, 2020 by gbeditor-2

1 Answer

0 votes
 
Best answer
Given an adjacency-list representation Adj of a directed graph, the outdegree of a vertex u is equal to the length of Adj[u], and the sum of the lengths of all the adjacency lists in Adj is |E|. Thus the time to compute the out-degree of one vertex v is (|Adj(v)|) and for all vertices is (V + E).
answered Aug 14, 2020 by deepak-gatebook (226,240 points)
Answer:

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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

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