Exercise 2.43: 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
.