Solved: Try to prove that your algorithms work in the sense that, Mathematics

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Try to prove that your algorithms work in the sense that

Question: 1. Try to prove that your algorithms work, in the sense that

(a) they produce trees and

(b) they produce a total weight that is smallest. (This is pretty challenging, so do not be surprised if you can only come up with part of a proof.)

2. An un-weighted graph could be considered an edge-weighted graph with all edges of the same weight (perhaps 1). What happens if you run Prim's algorithm on it?

3. What happens if you run one of the spanning tree algorithms for unweighted graphs on an edge-weighted graph?

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