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Problem formulation Suppose that the agent's sensors give it enough information to tell exactly which state it is in (i.e., the world is accessible); Suppose that it knows exactly what each of its actions does. Then it can calculate exactly which state it will be in after any sequence of actions.
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Types of problems When the environment is completely accessible and the agent can calculate its state after any sequence of action, we call it aÂ single-state problem. When the world is not fully accessible, the agent must reason about sets of states that it might get to, rather than single states. We call this aÂ multiple-state problem.
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Components of a Well defined problems and solutions Data type Components: AÂ ProblemÂ An OperatorÂ TheÂ Goal Test functionÂ AÂ Path CostÂ function
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Measuring problem solving Performance The effectiveness of a search technique can be measured in at least three ways.1) Does it find a solution?2) Is it a good solution/low cost ?3) What is the search cost associated with the time and memory required to find a solution?
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Problem formulation for 8-Queens Problem Goal test:Â 8 queens on board: placing 8 queens on chess board so that no queen attacks each other.Path cost:Â zero.States:Â Any arrangement of 0 to 8 queens on board.Operators:Â Add a queen to any square.Route finding:Â It is used in a variety of applications, such as routing in computer networks, automated travel advisory systems, and airline travel planning systems.
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Searching for solutions Solution to an AI problems involves performing an action to go to one proper state among possible numerous possible states of agent. Thus the processes of finding solution can be boiled down to searching of that best state among all the possible states.
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Data structures for search trees Data typeÂ node Components: STATE, PARENT-NODE, OPERATOR, DEPTH, PATH-COST TheÂ StateÂ in the state space to which the node corresponds. TheÂ NodeÂ in the search tree that generated this node. TheÂ OperatorÂ that was applied to generate the node. TheÂ NumberÂ of nodes on the path from the root to this node (the depth of the node). TheÂ path costÂ of the path from the initial state to the node.
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Optimality of search algorithm's is based on following factors Completeness:Â is the strategy guaranteed to find a solution when there is one? Time complexity:Â how long does it take to find a solution? Space complexity:Â how much memory does it need to perform the search? Optimality:Â does the strategy find the highest-quality solution when there are several different solutions?
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What is Breadth-first search? One simple search strategy is a breadth-first search. In this strategy, the root node is expanded first, then all the nodes generated by the root node are expanded next, and then their successors, and so on.
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What is Uniform cost search? Breadth-first search finds the shallowest goal state, but this may not always be the least-cost solution for a general path cost function. Uniform cost search modifies the breadth-first strategy by always expanding the lowest-cost node on the fringe (as measured by the path cost g(n)), rather than the lowest-depth node.
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What is Depth-first search? Depth-first search always expands one of the nodes at the deepest level of the tree. Only when the search hits a dead end (a non goal node with no expansion) does the search go back and expand nodes at shallower levels.
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What is Depth-limited search? Its basically similar to depth first search with following modification. Depth-limited search avoids the pitfalls of depth-first search by imposing a cutoff on the maximum depth of a path.
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What is Iterative deepening search? Iterative deepening search is a strategy that sidesteps the issue of choosing the best depth limit by trying all possible depth limits: first depth 0, then depth 1, then depth 2, and so on.
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What is Bidirectional search? The idea behind bidirectional search is to simultaneously search both forward from the initial state and backward from the goal, and stop when the two searches meet in the middle .
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