merge sort in scheme

merge sort的思想很简单，首先将表均匀分成2份，然后每份都是递归使用merge sort来排序，最后使用一个线性合并的方法来合并两个有序表。

为此我们首先定义的是split-evenly，用来切分一个list

(define (split-evenly lst)

  (if (null? lst) (list '() '()) ;空表的话返回两个空表

    (let* ((h (car lst)) (rest (cdr lst)) (len (length lst)) (sp (split-evenly rest)) (first (car sp)) (second (cadr sp)))

           (if (= (remainder len 2) 0)

               (list (cons h first) second)

               (list first (cons h second))))))

 

这个历程就是讲一个表拆分成为两个表，下一个历程是将两个有序表合并成为一个表

(define (merge-sorted-list p lst-1 lst-2)

 (cond ((null? lst-1) lst-2)

          ((null? lst-2) lst-1)

          ((p (car lst-1) (car lst-2)) (cons (car lst-1) (merge-sorted-list p (cdr lst-1) lst-2)))

          (else (cons (car lst-2) (merge-sorted-list p ls-1 (cdr lst-2))))))

有了这两个辅助函数以后，merge sort就是水到渠成了

(define (merge-sort p lst)

  (if (or (null? lst) (= (length lst) 1)) lst

      (let* ((sp (split-evenly lst))

               (first (car sp))

               (second (cadr sp))

               (merge-sorted-list p (merge-sort p first) (merge-sort p second)))))

简单测试都是可以通过的。