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Differences between Prim's and Kruskal's algorithms?

I've read the Edexcel D1 textbook over and over, and I can't get it clear in my head what the difference is between Kruskal's and Prim's algorithms for finding minimum spanning trees.

Can anyone clarify?

Reply 1

CalculusMan

10

Kruska's builds a minimum spanning tree by adding one edge at a time. The next line is always the shortest (minimum weight) ONLY if it does NOT create a cycle.

Prims builds a mimimum spanning tree by adding one vertex at a time. The next vertex to be added is always the one nearest to a vertex already on the graph.

Reply 2

edmundwillis

5

The attachments are from an OCR (MEI) cheatsheet but I am sure Edexcel will tackle these questions in the same way.

Hopefully, they make the different methods simple enough. :smile:

Reply 3

Prim always joins a "new" vertex to an "old" vertex, so that every stage is a tree. Kruskal's allows both "new" to "new" and "old" to "old" to get connected, so it risks creating a circuit and must check for them every time. So Kruskal's has a larger complexity than Prim.

Reply 4

declique

1

Original post by James

I've read the Edexcel D1 textbook over and over, and I can't get it clear in my head what the difference is between Kruskal's and Prim's algorithms for finding minimum spanning trees.

Can anyone clarify?

Here you find the best answer: http://stackoverflow.com/questions/1195872/kruskal-vs-prim

However, try and understand each algorithm - wikipedia is a good start.

Reply 5

tehforum

20

Original post by declique

Here you find the best answer: http://stackoverflow.com/questions/1195872/kruskal-vs-prim

However, try and understand each algorithm - wikipedia is a good start.

Sorry, you're a bit late.

5 years late.

Reply 6

declique

1

Original post by tehforum

Sorry, you're a bit late.

5 years late.

Are you from the late police? This is the 3rd result in Google for "prim kruskal" so I didn't do it for the OP but for the people who get here from Google results.
But, yes... assume I don't know to read when this was posted.

Reply 7

tehforum

20

Original post by declique

Are you from the late police? This is the 3rd result in Google for "prim kruskal" so I didn't do it for the OP but for the people who get here from Google results.
But, yes... assume I don't know to read when this was posted.

Oh sorry, my mind reading machine wasn't working at that precise moment.

My bad.

Reply 8

Bobifier

13

Prim's is easier to draw.

Aside from that, Prim's selects edges only from the set of edges that are adjacent to those you have already put in your tree. Kruskal's selects edges from the set of all possible edges.

Reply 9

mattys851

Original post by edmundwillis

The attachments are from an OCR (MEI) cheatsheet but I am sure Edexcel will tackle these questions in the same way.

Hopefully, they make the different methods simple enough. :smile:

you sir may have just got me the B I need in maths!

Reply 10

the bear

20

i like Prim's... i used not to like the matrix method but it is OK now

one of my textbooks says you should also check that Prim's does not form a cycle but i guess that is just a mistake.

Prim's reminds me of Pimms...