Podcast
Questions and Answers
Iterative deepening search guarantees completeness and optimality for unit step costs while keeping space complexity ___
Iterative deepening search guarantees completeness and optimality for unit step costs while keeping space complexity ___
linear
Bidirectional search terminates when the two ___ meet.
Bidirectional search terminates when the two ___ meet.
frontiers
Uniform-cost search is a specific instance of ___-first search where the evaluation function f(n) is equal to g(n).
Uniform-cost search is a specific instance of ___-first search where the evaluation function f(n) is equal to g(n).
best
The ___ factor represents the maximum number of successor nodes for any given node in the search tree.
The ___ factor represents the maximum number of successor nodes for any given node in the search tree.
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The ___ set keeps track of all the states that have been visited during the search process.
The ___ set keeps track of all the states that have been visited during the search process.
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Search algorithms like breadth-first and depth-first differ in terms of ___ and optimality.
Search algorithms like breadth-first and depth-first differ in terms of ___ and optimality.
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Heuristic functions differ from uninformed search methods by using an estimate of the cost or ___ from a given state to a goal state.
Heuristic functions differ from uninformed search methods by using an estimate of the cost or ___ from a given state to a goal state.
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Depth-limited search is a variation of depth-first search that introduces a depth ___ to avoid infinite loops.
Depth-limited search is a variation of depth-first search that introduces a depth ___ to avoid infinite loops.
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Time complexity is the amount of ___ it takes for a search algorithm to find a solution.
Time complexity is the amount of ___ it takes for a search algorithm to find a solution.
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A higher branching factor generally leads to a larger search space and increased computational ___ .
A higher branching factor generally leads to a larger search space and increased computational ___ .
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A well-defined search problem consists of: states, the initial state, actions, a transition model, a goal test, and an action cost function for determining the cost of each ______.
A well-defined search problem consists of: states, the initial state, actions, a transition model, a goal test, and an action cost function for determining the cost of each ______.
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Tree-like search explores all possible paths without considering if a state has been ______ before.
Tree-like search explores all possible paths without considering if a state has been ______ before.
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Breadth-first search expands nodes ______ by level, ensuring that all nodes at a shallower depth are explored before those at a deeper level.
Breadth-first search expands nodes ______ by level, ensuring that all nodes at a shallower depth are explored before those at a deeper level.
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The primary advantage of depth-first search is its low space complexity, as it only needs to store the current ______ and unexplored siblings.
The primary advantage of depth-first search is its low space complexity, as it only needs to store the current ______ and unexplored siblings.
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Depth-limited search modifies depth-first search by introducing a ______ limit, preventing exploration beyond a certain depth.
Depth-limited search modifies depth-first search by introducing a ______ limit, preventing exploration beyond a certain depth.
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Iterative deepening search combines the benefits of depth-first and breadth-first search by ______ the depth limit incrementally until a solution is found.
Iterative deepening search combines the benefits of depth-first and breadth-first search by ______ the depth limit incrementally until a solution is found.
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Bidirectional search employs a strategy that involves searching from both the initial state and the ______ state simultaneously.
Bidirectional search employs a strategy that involves searching from both the initial state and the ______ state simultaneously.
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Uniform-cost search is considered a special case of ______-first search, as it selects the node with the lowest path cost for exploration.
Uniform-cost search is considered a special case of ______-first search, as it selects the node with the lowest path cost for exploration.
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Graph search keeps track of visited states using a ______ set to avoid revisiting them.
Graph search keeps track of visited states using a ______ set to avoid revisiting them.
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Depth-limited search modifies depth-first search by introducing a depth ______, preventing exploration beyond a certain depth.
Depth-limited search modifies depth-first search by introducing a depth ______, preventing exploration beyond a certain depth.
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The strategy employed in iterative deepening search involves gradually ______ the depth limit until a solution is found.
The strategy employed in iterative deepening search involves gradually ______ the depth limit until a solution is found.
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Uniform-cost search is considered a special case of best-______ search, as it selects the node with the lowest path cost for exploration.
Uniform-cost search is considered a special case of best-______ search, as it selects the node with the lowest path cost for exploration.
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The concept of bidirectional search involves searching from both the initial state and the ______ state simultaneously.
The concept of bidirectional search involves searching from both the initial state and the ______ state simultaneously.
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If heuristic h2(n) is always greater than or equal to h1(n) for all nodes, then h2 dominates h1 during ______ search.
If heuristic h2(n) is always greater than or equal to h1(n) for all nodes, then h2 dominates h1 during ______ search.
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A ______ problem is a simplified version of the original problem obtained by removing constraints.
A ______ problem is a simplified version of the original problem obtained by removing constraints.
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A ______ database contains precomputed solution costs for subproblems, enhancing heuristic performance.
A ______ database contains precomputed solution costs for subproblems, enhancing heuristic performance.
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In A* search, nodes are expanded based on the function ______ = g(n) + h(n).
In A* search, nodes are expanded based on the function ______ = g(n) + h(n).
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A consistent heuristic ensures that the estimated cost does not exceed the actual cost, thus it is always considered ______.
A consistent heuristic ensures that the estimated cost does not exceed the actual cost, thus it is always considered ______.
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Greedy Best-First Search expands the node closest to the goal based on the heuristic ______(n).
Greedy Best-First Search expands the node closest to the goal based on the heuristic ______(n).
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In reachability analysis, a method is used to compute the set of ______ reachable from a given initial state.
In reachability analysis, a method is used to compute the set of ______ reachable from a given initial state.
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The time and space complexity of A* search is ______ in the easiest case.
The time and space complexity of A* search is ______ in the easiest case.
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Pruning in A* search refers to the process of eliminating subtrees with ______(n) greater than a certain optimal path cost.
Pruning in A* search refers to the process of eliminating subtrees with ______(n) greater than a certain optimal path cost.
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A higher branching factor generally leads to a larger search ______ and increased computational complexity.
A higher branching factor generally leads to a larger search ______ and increased computational complexity.
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Bidirectional search performs two simultaneous searches, one forward from the initial state and another backward from the ___ state.
Bidirectional search performs two simultaneous searches, one forward from the initial state and another backward from the ___ state.
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Best-first search provides a general framework for prioritizing nodes based on different ___ functions.
Best-first search provides a general framework for prioritizing nodes based on different ___ functions.
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The 'reached' set in graph search algorithms stores the states that have already been ___ during the search.
The 'reached' set in graph search algorithms stores the states that have already been ___ during the search.
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The branching factor (b) represents the maximum number of ___ nodes for any given node in the search tree.
The branching factor (b) represents the maximum number of ___ nodes for any given node in the search tree.
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Depth is defined as the number of edges along the path from the root node to a given ___ in the search tree.
Depth is defined as the number of edges along the path from the root node to a given ___ in the search tree.
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Uniform-cost search is a specific instance of best-first search where the evaluation function f(n) is equal to ___(n), the path cost from the initial state to node n.
Uniform-cost search is a specific instance of best-first search where the evaluation function f(n) is equal to ___(n), the path cost from the initial state to node n.
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Heuristic functions in informed search provide estimates of the cost or distance from a given state to a ___ state.
Heuristic functions in informed search provide estimates of the cost or distance from a given state to a ___ state.
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Greedy best-first search expands the node with the lowest estimated cost to the ___, without considering the cost to reach that node.
Greedy best-first search expands the node with the lowest estimated cost to the ___, without considering the cost to reach that node.
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Completeness is the property of a search algorithm that guarantees finding a ___ if one exists.
Completeness is the property of a search algorithm that guarantees finding a ___ if one exists.
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Heuristic functions must be ____ in order to ensure they do not overestimate the cost to reach the goal.
Heuristic functions must be ____ in order to ensure they do not overestimate the cost to reach the goal.
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When using heuristics in search problems, there are potential benefits, but also limitations such as ___ and admissibility issues.
When using heuristics in search problems, there are potential benefits, but also limitations such as ___ and admissibility issues.
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A* search expands the node with the lowest sum of the cost to reach that node (g(n)) and the estimated cost to the ___ (h(n)).
A* search expands the node with the lowest sum of the cost to reach that node (g(n)) and the estimated cost to the ___ (h(n)).
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Bidirectional search might not be beneficial when the search space is too ___ or the initial state and goal are too far apart.
Bidirectional search might not be beneficial when the search space is too ___ or the initial state and goal are too far apart.
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Study Notes
Uninformed Search Components
- A well-defined search problem comprises states (possible configurations), an initial state, actions (agent's steps), a transition model (action outcomes), a goal test (checking for desired goal), and an action cost function (determining action costs).
Tree vs. Graph Search
- Tree search explores all paths without tracking visited states, potentially revisiting them and resulting in redundant effort.
- Graph search utilizes a "reached" set to track visited states, thus preventing cycles and redundant exploration for efficiency.
Breadth-First Search Optimality
- Breadth-first search expands nodes level by level, ensuring the shortest paths are found when step costs are equal. This is because it explores all paths of equal lengths before moving on to longer paths.
Depth-First Search Advantages & Drawbacks
- Depth-first search has low memory usage (stores current path and unexplored siblings).
- It's incomplete (may not find solutions in infinite spaces) and not optimal (may not find the shortest path).
Depth-Limited Search
- Depth-limited search addresses the non-termination issue of depth-first search by introducing a depth limit. This prevents exploring beyond a certain depth, though it might miss solutions beyond that limit.
Iterative Deepening Search
- Iterative deepening combines breadth-first and depth-first advantages.
- It repeatedly performs depth-limited searches with increasing depth limits, guaranteeing completeness and optimality for unit costs while maintaining linear space complexity.
Bidirectional Search
- Bidirectional search simultaneously searches forward from the initial state and backward from the goal state.
- Termination occurs when the search frontiers meet, potentially reducing time complexity, especially with large branching factors.
Uniform-Cost Search & Best-First Search
- Uniform-cost search is a best-first search variation where the evaluation function is solely the path cost.
- Best-first search uses an evaluation function to prioritize node expansion.
"Reached" Set Function
- The "reached" set in graph search stores visited states. This prevents revisiting, eliminating cycles and redundant exploration.
Branching Factor Impact
- The branching factor (maximum successor nodes per node) significantly impacts search complexity.
- Larger branching factors create exponentially larger search spaces and increased computational cost.
Informed Search Components
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Informed Search: Uses domain-specific knowledge (heuristics) to guide search more efficiently.
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Heuristic Function (h(n)): Estimates the cost of the cheapest path from node n to a goal state.
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Admissible Heuristic: Never overestimates the actual cost to reach the goal.
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Consistent Heuristic: Satisfies the triangle inequality (estimated cost from n to goal ≤ cost to n' + estimated cost from n' to goal).
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Greedy Best-First Search: Expands node with lowest estimated cost to goal (f(n) = h(n)).
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A* Search: Expands node with lowest f(n) = g(n) + h(n) (cost to reach + estimated cost to goal).
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Dominating Heuristic: If h2(n) ≥ h1(n) for all nodes, h2 dominates h1; using h2 results in fewer node expansions in A*.
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Relaxed Problem: A simplified version of the original problem (with loosened constraints); relaxed problem's optimal solution cost can be an admissible heuristic.
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Pattern Database: Precomputed solution costs for subproblems, providing heuristics.
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Reachability Analysis: Computes reachable states from the initial state, useful in continuous state spaces.
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Greedy Best-First Search: Time/space complexity: O(bm), where b is branching factor, m is maximum path length.
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A* Search: Time/space complexity: O(bεd), where ε is relative heuristic error, d is depth.
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Heuristic Functions Examples (e.g., 8-puzzle):
- h1: Number of misplaced tiles.
- h2: Sum of Manhattan distances of tiles.
- h2 dominates h1.
Informed Search Quiz Answers
- Question 1 (Multiple Choice): The answer is It always provides the exact cost to reach the goal.
- Question 2 (Multiple Choice): The answer is All of the above.
- Question 3 (Multiple Choice): The answer is Greedy best-first search.
- Question 4 (Multiple Choice): The answer is h2 is always greater than or equal to h1.
- Question 1 (True/False): False
- Question 2 (True/False): True
- Question 3 (True/False): True
- Question 4 (True/False): True
Short Answer Question 1
- A relaxed problem is a simplified version of the original problem where some constraints are removed. This simplification makes it possible to calculate a solution cost. A relaxed problem's solution cost can generate a heuristic that never overestimates the true cost because there are fewer restrictions on what the optimal solution can be.
Short Answer Questions 2 & 3
- (These require more context and details than can be provided in a concise bullet point format.)
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