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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

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

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

DSA - Graphs and Hashing -Q6


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+1 vote

Suppose we run Prim's algorithm and Kruskal's algorithm on a graph G and the two algorithms produce minimum-cost spanning trees TP and TQ respectively, and TP is different from TK. Which of the following must be true?

(A). If e is a minimum cost edge in G, e belongs to both TP and TQ.

(B). If e is a maximum cost edge in G, e belongs to neither TP nor TQ.

(C). All edges in G have the same weight.

(D). Some pair of edges in G have the same weight

asked Aug 3, 2020 by gbeditor-2 (72,840 points)
edited Oct 7, 2020 by gbeditor-2

1 Answer

0 votes
 
Best answer
Some pair of edges in G have the same weight.

If edge weights are distinct, the spanning tree is unique.

As a counterexample for the first two options, consider a triangle with all edge weights equal.

For the third option, consider a square with opposite edges having equal weights, but adjacent edges not equal
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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