Sort and Shuffle functions

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Sort and Shuffle functions

Permanent link to this post Posted by steve » Thu Aug 10, 2017 5:19 pm

This came up in another topic recently, and I thought that it could be of interest to others.

Nyquist includes a function for sorting lists (http://www.audacity-forum.de/download/e ... ef-242.htm)
For example, to sort a list of numbers in ascending order:
Code: Select all
(setf data (list 5 1 9 2 0 4 3 8 6 7))
(format nil "~a" (sort data '<))
;; returns (0 1 2 3 4 5 6 7 8 9)


Caution:

"SORT" is a destructive list function. The function destroys the list data.
For example, if you run as Debug:
Code: Select all
(setf data (list 5 1 9 2 0 4 3 8 6 7))
(format t "Sorted data: ~a~%" (sort data '<))
(format t "data = ~a" data)

the debug output is:
Code: Select all
Sorted data: (0 1 2 3 4 5 6 7 8 9)
data = (5 6 7 8 9)

Part of the list has been destroyed!

If we wish to keep the list intact, we must recreate it from the returned value. For example:
Code: Select all
(setf data (list 5 1 9 2 0 4 3 8 6 7))
(format t "Sorted data: ~a~%" (setf data (sort data '<)))
(format t "data = ~a" data)

the debug output is:
Code: Select all
Sorted data: (0 1 2 3 4 5 6 7 8 9)
data = (0 1 2 3 4 5 6 7 8 9)


======================

Swapping values:

Here's a neat little macro for swapping (exchanging) the values of two variables.
Code: Select all
(defmacro swap (x y)
  `(let ((temp ,x))
      (setf ,x ,y)
      (setf ,y temp)))


It's quite versatile as it can not only be used for variables, but for elements of a list, or elements of an array.

Example: swapping values of a variables:
Code: Select all
(defmacro swap (x y)
  `(let ((temp ,x))
      (setf ,x ,y)
      (setf ,y temp)))

(setq a "swans a swimming") ; a string value
(setq b 15) ; an integer value
(swap a b)
(format nil "~a ~a" (/ a 2) b)
;; prints: 7 swans a swimming


Example: Swap left and right channels of the selected track:
Code: Select all
;version 4

(defmacro swap (x y)
  `(let ((temp ,x))
      (setf ,x ,y)
      (setf ,y temp)))

(swap (aref *track* 0)(aref *track* 1))
*track*


======================

Back to the original issue:

Randomizing the order of elements in a list
In other words, shuffling the elements of a list to produce a random permutation.

A well known algorithm for this is the "Fisher–Yates shuffle"
This implementation is based on the "modern algorithm" and uses the "swap" macro (above) for exchanging the elements:

Code: Select all
;; Fisher-Yates_shuffle (modern algorithm)
;; From: https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle#The_modern_algorithm
;;
;; -- To shuffle an array a of n elements (indices 0..n-1):
;; for i from n-1 downto 1 do
;;      j <- random integer such that 0 <= j <= i
;;      exchange a[j] and a[i]


; Input is a list
(setf data-list (list 0 1 2 3 4 5 6 7 8 9))


(defun shuffle (data)
"Shuffle a list for a random permutation."
  (let ((n (length data)))
    (do* ((i (1- n) (1- i))
          (j (random (1+ i))(random (1+ i))))
         ((= i 1) data-list)
      (swap (nth i data) (nth j data)))))

(defmacro swap (x y)
  `(let ((temp ,x))
      (setf ,x ,y)
      (setf ,y temp)))

; Test it
(let ((input (format nil "~a" data-list)))  ;keep a copy so we can print it
  (format nil "Input:\t ~a~%Output:\t ~a"
              input
              (shuffle data-list)))


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steve
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