csp problem set
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6.1 how many solutions are there for the mapcoloring problem in figure 6.1? how many solutions if four colors are allowed? two colors?
6.2 consider the problem of placing k knights on an n x n chessboard such that no two knights are attacking each other, where k is given and k ≤n^2
a. choose a csp formulation. in your formulation, what are the variables?
b. what are the possible values of each variable?
c. what sets of variables are constrained, and how?
d. now consider the problem of putting as many knights as possible on the board without any attacks. explain how to solve this with local search by defining appropriate actions and result functions and a sensible objective function.
6.3 consider the problem of construction (not solving) crossword puzzles: fitting words into a rectangular grid. the grid, which is given as part of the problem, specifies which squares are black and which are shaded. assume that a list of words (i.e., a dictionary) is provided and that the task is to fill in the blank squares by using any subset of the list. formulate this problem precisely in two ways:
a. as a general search problem. choose an appropriate search algorithm and specify a heuristic function. is it better to fill in the blanks one letter at a time or one word at a time?
b. as a constraint satisfaction problem. should the variables be words or letters?
which formulation do you think will be better? why?
6.4 give precise formulations for each of the following as constraint satisfaction problems:
a. rectilinear floorplanning: find nonoverlapping places in a large rectangle for a number of smaller rectangles.
b. class scheduling: there is a fixed number of professors and classrooms, a list of classes to be offered, and a list of possible time slots for classes. each professor has a set of classes that he or she can teach.
c. hamiltonian tour: given a network of cities connected by roads, choose an order to visit all cities in a country without repeating any.
6.2 consider the problem of placing k knights on an n x n chessboard such that no two knights are attacking each other, where k is given and k ≤n^2
a. choose a csp formulation. in your formulation, what are the variables?
b. what are the possible values of each variable?
c. what sets of variables are constrained, and how?
d. now consider the problem of putting as many knights as possible on the board without any attacks. explain how to solve this with local search by defining appropriate actions and result functions and a sensible objective function.
6.3 consider the problem of construction (not solving) crossword puzzles: fitting words into a rectangular grid. the grid, which is given as part of the problem, specifies which squares are black and which are shaded. assume that a list of words (i.e., a dictionary) is provided and that the task is to fill in the blank squares by using any subset of the list. formulate this problem precisely in two ways:
a. as a general search problem. choose an appropriate search algorithm and specify a heuristic function. is it better to fill in the blanks one letter at a time or one word at a time?
b. as a constraint satisfaction problem. should the variables be words or letters?
which formulation do you think will be better? why?
6.4 give precise formulations for each of the following as constraint satisfaction problems:
a. rectilinear floorplanning: find nonoverlapping places in a large rectangle for a number of smaller rectangles.
b. class scheduling: there is a fixed number of professors and classrooms, a list of classes to be offered, and a list of possible time slots for classes. each professor has a set of classes that he or she can teach.
c. hamiltonian tour: given a network of cities connected by roads, choose an order to visit all cities in a country without repeating any.
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