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Questions and Answers
What is the term used to describe a node with no children in the search tree?
Which algorithm avoids consideration of redundant paths in the search process?
What is the term used to describe choosing one option now and putting the others aside for later?
What is the term used to describe a state that is generated in the search tree by a loopy path?
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Which criteria refers to the question: 'Is the algorithm guaranteed to find a solution when there is one?'
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What does the 'frontier' refer to in the context of search algorithms?
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What is the main goal of the 8-queens problem?
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What kind of formulation for the 8-queens problem involves operators that add a queen to the state description?
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Which type of formulation starts with all 8 queens on the board and moves them around?
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What is the transition model in the incremental formulation of the 8-queens problem?
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Which of the following is NOT a requirement for a goal test in solving the 8-queens problem?
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What is considered of no interest in path cost when solving the 8-queens problem?
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Study Notes
The 8-Queens Problem
- The goal is to place 8 queens on a chessboard so that no queen attacks another.
- The problem remains a useful test for search algorithms despite efficient special-purpose algorithms existing for it.
Formulation of the 8-Queens Problem
- There are two main formulations: incremental and complete-state.
- Incremental formulation involves adding queens to an empty state, while complete-state formulation starts with all 8 queens on the board and moves them around.
Incremental Formulation
- States: Any arrangement of 0 to 8 queens on the board.
- Initial state: No queens on the board.
- Actions: Add a queen to any empty square.
- Transition model: Returns the board with a queen added to the specified square.
- Goal test: 8 queens are on the board, none attacked.
Searching for Solutions
- A solution is an action sequence, and search algorithms work by considering possible action sequences.
- The search tree has the initial state at the root, with branches representing actions and nodes representing states in the state space.
- A general tree-search algorithm considers all possible paths, whereas a graph-search algorithm avoids redundant paths.
Expanding the Search Tree
- Expanding the current state generates new states by applying legal actions.
- The search algorithm chooses which branch to consider further, following up one option and putting others aside for later.
The Frontier
- The set of all leaf nodes available for expansion at any given point is called the frontier.
- The process of expanding nodes on the frontier continues until a solution is found or there are no more states to expand.
Measuring Problem-Solving Performance
- Evaluating an algorithm's performance involves four criteria:
- Completeness: Guaranteed to find a solution when there is one?
- Optimality: Does the strategy find the optimal solution?
- Time complexity: How long does it take?
- Other criteria may also be considered.
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Description
Learn about the classic 8-queens problem where the goal is to place eight queens on a chessboard without attacking each other. Discover different formulations and algorithms used to solve this popular test problem for search algorithms.
