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my sudject :Artificial Inttelegence Question 2: a. Show that breadth-first search given constant cost for all...

my sudject :Artificial Inttelegence

Question 2:

a. Show that breadth-first search given constant cost for all actions is guaranteedto find the shortest solution.

b. Show that this is not the case for varying costs.

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Answer #1

a) BFS guarantees finding shortest path from a source to all other nodes when all edges are of the same cost. This is because BFS traverses the graph level by level. That is all nodes at distance 0 are visited first and then distance 1 and then those at distance 2...and so on.

For a more detailed proof see here : http://www.cs.toronto.edu/~krueger/csc263h/lectures/BFS.pdf

b) Example to prove that bfs doesn't work for varying cost edges.

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