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 Incoming links: Kruskal's algorithm

Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Functional programming, design and analysis of algorithms / 7 / b / Solution 2026-10-25

Write each undirected edge with its smaller endpoint first. Kruskal's algorithm orders candidates first by weight and then lexicographically:

edge (4, 6) (1, 3) (3, 4) (1, 4) (4, 5) (5, 6) (1, 2) weight 1223334 action add add add reject: closes a cycle add reject: closes a cycle add and finish

Thus the requested addition order is

(4, 6), (1, 3), (3, 4), (4, 5), (1, 2),

and the minimum spanning tree has total weight $12$ . Five accepted edges connect all six vertices, so the remaining weight-four edges need not be scanned.

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