Consider the problem of constructing (not solving) crossword puzzles:5 fitting words into a rectangular grid. The grid, which is given as part of the problem, specifics which square are blank 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 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, if you think one is needed. Is it better to fill in 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?