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Louis Reasoner is having a terrible time doing exercise 2.42. His
queens procedure seems to work, but it runs extremely slowly. (Louis never does manage to wait long enough for it to solve even the 6 × 6 case.) When Louis asks Eva Lu Ator for help, she points
out that he has interchanged the order of the nested mappings in the
flatmap, writing it as
(flatmap (lambda (new-row) (map (lambda (rest-of-queens) (adjoin-position new-row k rest-of-queens)) (queen-cols (- k 1)))) (enumerate-interval 1 board-size))
Explain why this interchange makes the program run slowly. Estimate how long it will take Louis’s program to solve the eight-queens puzzle, assuming that the program in exercise 2.42 solves the puzzle in time T.