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We have discussed a detailed example on Alpha Beta Pruning in the lectures.
S is the initial state and D is the goal state. The values on the links are the distances between the cities. Hence the right most branch of the tree will be pruned and handoute be evaluated for static evaluation. We convert the map to a tree as shown below. Hence both have different goals. 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 select H which is the best of them. Both have their advantages and disadvantages. We handoute focus on board games for simplicity The rode is a game tree represent board configuration and the branches indicate how moves can connect them. We see that C is a leaf node so we bind C too as shown in the next diagram. 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.
The number of branches in an exhaustive survey would be on the order of 10 We proceed in a Best First Search manner. Given the following tree, use the hill climbing handoutx to climb up the tree. Support your answer with small examples of a few trees.
K is the goal state and numbers written on each node is the estimate of remaining distance to the goal. 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. The maximizer has to keep in view that what choices will be available to the minimizer on the next step. The static evaluation scores for each leaf node are written under it.
Hence using dynamic programming we will ignore the whole sub-tree beneath D the child of A as shown in the next diagram. The readers are required to go though the last portion of Lecture 10 for the explanation of this example, if required.
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A problem habdouts is that if we go with an overestimate hxndouts the remaining distance then we might loose a solution that is somewhere nearby. Its early in the morning and assume that no other person is awake in the town who can guide him on the way. We yandouts F and finally we reach G as shown in the subsequent diagrams. Many games can be modeled as trees 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 Suggest solutions to the commonly encountered problems that are local maxima, plateau problem and ridge problem.
Suppose we start of with a game tree in the diagram below. Search the history of over billion web pages on the Internet. This approach is analogous to the brute force method and is also called the British museum sc607. Try to model the problem in a graphical representation.
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Hence maximizer will end up with a score of 2 if he goes to C from A. So we ignore any further paths ahead of the path S D A B. In many applications there might be multiple agents or persons searching for solutions in the same solution space. Q6 Discuss how best first search works in a tree. Only two leaf nodes have been evaluated so handoutw. This procedure is called Alpha Beta pruning which “prunes” the tree branches thus reducing the number of static evaluations.
Q3 Given the following tree. Their goals are usually contrary to each other. So traveling further from S D A B to some other node will make the path longer. The simple idea of branch and bound is the following: Negative numbers indicate favor to the other player.
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Such scenarios usually occur in game playing where two opponents also called adversaries are searching for a goal. By using “guesses” about remaining distance as well as facts about distance already accumulated we will be able to travel in the solution space more efficiently.
For example, in a game of tic-tac-toe player one might want that he should complete a line with crosses while at the same time player two wants to complete a line of zeros. Next we visit E, then we visit B the child of E, we bound the sub-tree below B. To develop this stance he uses a look ahead thinking strategy. Run the MiniMax procedure on the given tree.
Positive numbers, by convention indicate favor to one player. The other player is called minimizing player or minimizer.
We start with a tree with goodness of every node mentioned on it. The handouuts has to keep in view that what choices will be available to the maximizer on the next step. Now A and E are equally good nodes so we arbitrarily choose amongst them, and we move to A. Support your answer with examples of a few trees.
The numbers on the nodes are the estimated distance on the node from the goal state.