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2 . 4 . 4 . Sometimes the number of decisions is not the appropriate measure to use in looking for a goal. For example,
Sometimes the number of decisions is not the appropriate measure to use in looking for a goal. For example, suppose we have a map of highways with mileages between highway intersections. The goal is to find the shortest route between intersections A and Ba Explain how a search graph can be constructed where the vertices are intersections and each edge has a "cost" equal to the number of miles.b Show how this leads to a search tree with a the root labeled Ab all goals labeled Bc a cost for each edge equal to mileage, and d the aim of finding that path from the root to a B for which the sum of the edge weights is a minimum. We can associate with each vertex v a cost Cv that equals the sum of the edge weights on the path from the root to vThe path is unique since we are in a tree.c We can generalize the previous part to a search tree in which each vertex v has an associated cost Cv and costs increase as we move downward. Modify the breadthfirst algorithm to produce a "bestfirst" algorithm that finds the leastcost goal.Hint. Always remove the vertex with the least cost from and do not check whether a vertex is a goal until you remove it from d Prove that the algorithm you have given does in fact find the least cost goal.
Sometimes the number of decisions is not the appropriate measure to use in looking for a goal. For example, suppose we have a map of highways with mileages between highway intersections. The goal is to find the shortest route between intersections A and Ba Explain how a search graph can be constructed where the vertices are intersections and each edge has a "cost" equal to the number of miles.b Show how this leads to a search tree with a the root labeled Ab all goals labeled Bc a cost for each edge equal to mileage, and d the aim of finding that path from the root to a B for which the sum of the edge weights is a minimum. We can associate with each vertex v a cost Cv that equals the sum of the edge weights on the path from the root to vThe path is unique since we are in a tree.c We can generalize the previous part to a search tree in which each vertex v has an associated cost Cv and costs increase as we move downward. Modify the breadthfirst algorithm to produce a "bestfirst" algorithm that finds the leastcost goal.Hint. Always remove the vertex with the least cost from and do not check whether a vertex is a goal until you remove it from d Prove that the algorithm you have given does in fact find the least cost goal.
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