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Negative numbers indicate favor to the other handoits. As all the sub-trees emerging from B make our path length more than 9 units so we bound this path, as shown in the next diagram. Also note that while traveling from S to B we have already covered a distance of 9 units. Try to model the problem in a graphical representation.

### Artificial Intelligence – CS VU Lecture Handouts

The second improvement is dynamic programming. Hxndouts minimizer has to keep in view that what choices will be available to the maximizer on the next step. The maximizer has to keep in view that what choices will be available to the minimizer on the next step.

Many games can be modeled as trees as shown below. Dynamic Programming The idea of estimates is that we can travel in the solution space using a heuristic estimate. Now A and E are equally good nodes so we arbitrarily choose amongst them, and we move to A.

For example the static evaluation scores for the left most leaf node is Given the following tree, use the hill climbing procedure to climb up the tree. So we explore D. The readers are required to go though the last portion of Lecture 10 for the explanation of this example, if required.

Their goals are usually contrary to each other. Now after gandouts the other side of the tree, this score will either increase or will remain the same as this level is for the maximizer. Next we visit E, then we visit B the child of E, we bound the sub-tree below B.

## Artificial Intelligence – CS607 VU Video Lectures

Q6 Discuss how best first search works in a tree. Q5 Discuss the problems in Hill Climbing. The player hoping for positive numbers is called maximizing player or maximizer.

Should he follow blind or heuristic search strategy? Hence best first search is a greedy approach will handputs for the best amongst the available options and hence can sometimes reduce the searching time.

We construct the tree corresponding to the graph above. The basic idea was to reduce the search space by binding the paths that gandouts the path length from S to G. The maximizer wishes to maximize the score so apparently 7 being the maximum score, the maximizer should go to C and then to G.

We will discuss the two most famous ways to improve it.

## CS607 Artificial Intelligence

Notice further that if player one puts a cross in any box, player-two will intelligently try to make a move that would leave player-one with minimum chance to win, that is, he will try to stop player- one from completing a line of crosses and at the same time will try to complete his line of zeros.

Hence maximizer will end up with a score of 2 if he goes to Handoits from A.

A problem here is that if we go with an overestimate of the remaining distance then we might loose a solution that is somewhere nearby. We then move to F as that is the best option at this point with a value 7. We use the following example to explain the notion of Alpha Beta Pruning. We convert the map to a tree as shown below. But in reality, exploring the entire search space is never feasible and at times is not even possible, for instance, if we just consider the tree corresponding to a game of chess we will learn about game trees laterthe effective branching factor is 16 and the effective depth is We have shown the sequence of steps in the diagrams below.

Among these, D the child of S is the best option. All these heuristically informed procedures are considered better but they do not guarantee the optimal solution, as they are dependent on the quality of heuristic being used. Now, since the choice is between scores of 3 or 2, the maximizer will go to node B from A. On the other hand, if the maximizer goes to B from A the worst which the minimizer can do is that he will force the maximizer to a score of 3. Clearly identify the four components of problem solving in the above statement, i.

### CS – Artificial Intelligence

When he evaluates the first leaf node on the other side of the tree, he will see that the minimizer can force him to a score of less than 3 hence there is no need to fully explore the tree from that side. This approach is analogous to the brute force method and is also called the British museum procedure. We have discussed a detailed example handoute Alpha Beta Pruning in the lectures.

Only two leaf nodes have been evaluated so far. Will it handokts guarantee the best solution? We proceed in this manner. Is best first search always the best strategy?

The static evaluation scores for each leaf node are written under it. So we ignore hancouts further paths ahead of the path S D A B.

The number of branches hanfouts an exhaustive survey would be on the order of 10 We will demonstrate this improvement with an example. Both have their advantages and disadvantages.

Hence the right most branch of the tree will be pruned and won’t be evaluated for static evaluation. Its early in the morning and assume that no other person is awake in the town who can guide him on the way.