Here's an example scenario to illustrate the problem:

Suppose we have a paint shop that produces toy cars, and we need to paint the cars using four different colors: red (R), green (G), blue (B), and yellow (Y). The shop can use any combination of these colors, but it wants to use the minimum number of colors possible while satisfying certain requirements.

We are given a list of N cars to be painted, and for each car, we are given a list of K colors that are acceptable for that car. Our goal is to determine which colors to use for each car in order to minimize the number of different colors used.

Here's an example input:

N = 3
K1 = 3 R G B
K2 = 2 R G
K3 = 2 B Y

This input specifies that we have three cars to paint. The first car can be painted in any of the three colors (R, G, or B), the second car can be painted in either R or G, and the third car can be painted in either B or Y.

To solve the Paint Shop Problem, we can use a search algorithm that tries all possible combinations of colors for the cars, and checks if each combination satisfies the constraints. One algorithm that can be used is a backtracking algorithm.

Here's how the algorithm works:

Start with an empty list of colors for each car.
For the first car, try all possible colors that are acceptable for that car. For each color tried, add it to the list of colors for that car and recursively solve the problem for the remaining cars.
If a solution is found, return it.
If no solution is found for the first car, backtrack and try a different color.
If a solution is found for the first car, continue trying different colors for the remaining cars.
If a solution is found for all cars, return it.
If no solution is found for any car, backtrack and try a different color for the previous car.
If no solution is found for any color for the first car, return "No solution".
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