Solving Puzzles with AI

Have you ever solved a Sudoku puzzle or tried to create a school schedule where no classes conflict? If so, you've already dealt with Constraint Satisfaction Problems (CSPs) without even knowing it! Let's explore what CSPs are and how computers can solve them.

What are Constraint Satisfaction Problems?

A Constraint Satisfaction Problem is a type of puzzle where:

1. We have a set of variables (things we need to assign values to)
2. Each variable has a domain (possible values it can take)
3. There are constraints (rules that limit which combinations of values are allowed)

The goal is to assign a value to each variable so that all constraints are satisfied.

A Simple Example: Map Coloring

Imagine we need to color a map of the Western United States so that no neighboring states share the same color. We only have three colors: red, green, and blue.

• Variables: The states of the Western US (WA, OR, CA, ID, NV, UT)
• Domain: {red, green, blue} for each state
• Constraints: Adjacent states must have different colors

This is a CSP! And one solution might be:

• WA = red
• OR = green
• CA = blue
• ID = blue
• NV = red
• UT = green

Why CSPs are Special

CSPs are different from regular search problems:

• In regular search problems, we're often looking for a sequence of actions to reach a goal
• In CSPs, we only care about the final state – the assignment of values to variables

This special structure allows us to use specialized techniques to solve CSPs efficiently.