CSC 172 DATA STRUCTURES.

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Presentation transcript:

CSC 172 DATA STRUCTURES

Kruskal’s Algorithm An example of a “greedy” algorithm “do what seems best at the moment” Use the merge/find MWST algorithm on the edges in ascending order O(m log m) Since m <= n2, log m <= 2 log n, so O(m log n) time

Find the MWST A 10 1 F B 8 7 9 5 2 6 11 12 E C 3 4 D

Find the MWST 1 + 2 + 3 + 4 + 5 == 15 A 10 1 F B 8 7 9 5 2 6 11 12 E C 1 + 2 + 3 + 4 + 5 == 15 A 10 1 F B 8 7 9 5 2 6 11 12 E C 3 4 D

GREED IS NOT ALWAYS GOOD

Find the minimum cycle A 10 1 F B 8 7 9 5 2 6 11 12 E C 3 4 D

Find the minimum cycle 1 + 2 + 3 + 4 + 5 +10 == 25 A 10 1 F B 8 7 9 5 6 11 12 E C 3 4 D

Find the minimum cycle 1 + 2 + 3 + 6 + 5 + 7 = 24 A 10 1 F B 8 7 9 5 2 11 12 E C 3 4 D