a.Given the steps of Kruskal’s algorithm, analyze each loop and find its running time cost in terms of V and E.   MST-KRUSKAL(G,w) A ←  for each vertex v  V MAKE-SET(v) sort E into non-decreasing order by w for each (u, v) taken from the sorted list if FIND-SET(u)  FIND-SET(v) then A ← A  {(u, v)} UNION(u, v) return A

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
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a.Given the steps of Kruskal’s algorithm, analyze each loop and find its running time cost in terms of V and E.

 

MST-KRUSKAL(G,w)

  1. A ← 
  2. for each vertex v  V
  3. MAKE-SET(v)
  4. sort E into non-decreasing order by w
  5. for each (u, v) taken from the sorted list
  6. if FIND-SET(u)  FIND-SET(v)
  7. then A ← A  {(u, v)}
  8. UNION(u, v)
  9. return A

b. What is the total asymptotic running time of Kruskal’s algorithm

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