Section 1 Worksheet Solutions: CSPs
2 min read
6 months ago
Published on Jun 30, 2024
This response is partially generated with the help of AI. It may contain inaccuracies.
Table of Contents
Step-by-Step Tutorial: Section 1 Worksheet Solutions: CSPs
Formulating a CSP for Scheduling Professors to Classes:
- Identify the entities involved: classes and professors.
- Determine the variables and values: Classes are the variables and Professors are the values.
- Define unary constraints: Professors cannot teach every class.
- Establish binary constraints: Classes cannot overlap in scheduling.
Creating a Constraint Graph for the CSP:
- Draw a node for each variable (class).
- Connect nodes with edges representing constraints between classes.
- Ensure all constraints are included in the graph.
Trapped Pac-Man Description:
- Identify the variables (corridors) and values (pit, ghost, exit).
- Establish constraints:
- Pac-Man can feel a breeze between corridors.
- Neighboring corridors cannot both be exits.
Implementing Forward Checking:
- Start with unary constraints.
- Assign a value to a variable and check neighboring variables for consistency.
- Prune values that violate constraints.
- Repeat for all variables until a solution is found or backtrack if needed.
Applying MRV (Minimum Remaining Values) Heuristic:
- Choose the variable with the fewest remaining values to assign next.
- Consider constraints to eliminate invalid assignments.
- Deduce possible solutions based on constraints.
Solving CSP Using Tree Structure:
- Linearize the tree from any node as the root.
- Perform a backward pass to check consistency of parent-child arcs.
- If a variable has an empty domain, backtrack to the cut-set variable.
- Conduct a forward pass to reach a solution without backtracking.
Backtracking Behavior in CSP:
- Backtrack only on assigning values to the cut-set variable (x1).
- Explore all branches efficiently using the tree CSP algorithm.
- Enforce consistency to ensure valid solutions without unnecessary backtracking.
By following these steps, you can effectively solve CSPs and tackle complex scheduling and logical problems efficiently.