Created
January 22, 2017 12:46
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My solution to SICP exercise 2.42 - Eight-queens puzzle
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;;; Exercise 2.42 | |
;;; ============= | |
(define (enumerate-interval low high) | |
(if (> low high) | |
'() | |
(cons low (enumerate-interval (+ low 1) high)))) | |
(define (accumulate op initial sequence) | |
(if (null? sequence) | |
initial | |
(op (car sequence) | |
(accumulate op initial (cdr sequence))))) | |
(define (flatmap proc seq) | |
(accumulate append '() (map proc seq))) | |
(define (queens board-size) | |
(define (queen-cols k) | |
(if (= k 0) | |
(list empty-board) | |
(filter | |
(lambda (positions) (safe? k positions)) | |
(flatmap | |
(lambda (rest-of-queens) | |
(map (lambda (new-row) | |
(adjoin-position new-row k rest-of-queens)) | |
(enumerate-interval 1 board-size))) | |
(queen-cols (- k 1)))))) | |
(queen-cols board-size)) | |
(define empty-board '()) | |
; You don't really need `k` | |
(define (safe? k positions) | |
(define (safe-iter i pos result) | |
(if (null? pos) | |
result | |
(let ((last (car positions)) | |
(this (car pos)) | |
(rest (cdr pos))) | |
(safe-iter (+ i 1) | |
rest | |
(or (= last (+ this i)) | |
(= last (- this i)) | |
(= last this) | |
result))))) | |
(not (safe-iter 1 (cdr positions) #f))) | |
; `new-row` is attached to the beginning of `rest-of-queens` | |
(define (adjoin-position new-row k rest-of-queens) | |
(cons new-row rest-of-queens)) | |
(length (queens 8)) | |
;Value: 92 | |
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