tsequences.lisp - clic - Clic is an command line interactive client for gopher written in Common LISP
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tsequences.lisp (24604B)
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1 (in-package :alexandria)
2
3 ;; Make these inlinable by declaiming them INLINE here and some of them
4 ;; NOTINLINE at the end of the file. Exclude functions that have a compiler
5 ;; macro, because NOTINLINE is required to prevent compiler-macro expansion.
6 (declaim (inline copy-sequence sequence-of-length-p))
7
8 (defun sequence-of-length-p (sequence length)
9 "Return true if SEQUENCE is a sequence of length LENGTH. Signals an error if
10 SEQUENCE is not a sequence. Returns FALSE for circular lists."
11 (declare (type array-index length)
12 #-lispworks (inline length)
13 (optimize speed))
14 (etypecase sequence
15 (null
16 (zerop length))
17 (cons
18 (let ((n (1- length)))
19 (unless (minusp n)
20 (let ((tail (nthcdr n sequence)))
21 (and tail
22 (null (cdr tail)))))))
23 (vector
24 (= length (length sequence)))
25 (sequence
26 (= length (length sequence)))))
27
28 (defun rotate-tail-to-head (sequence n)
29 (declare (type (integer 1) n))
30 (if (listp sequence)
31 (let ((m (mod n (proper-list-length sequence))))
32 (if (null (cdr sequence))
33 sequence
34 (let* ((tail (last sequence (+ m 1)))
35 (last (cdr tail)))
36 (setf (cdr tail) nil)
37 (nconc last sequence))))
38 (let* ((len (length sequence))
39 (m (mod n len))
40 (tail (subseq sequence (- len m))))
41 (replace sequence sequence :start1 m :start2 0)
42 (replace sequence tail)
43 sequence)))
44
45 (defun rotate-head-to-tail (sequence n)
46 (declare (type (integer 1) n))
47 (if (listp sequence)
48 (let ((m (mod (1- n) (proper-list-length sequence))))
49 (if (null (cdr sequence))
50 sequence
51 (let* ((headtail (nthcdr m sequence))
52 (tail (cdr headtail)))
53 (setf (cdr headtail) nil)
54 (nconc tail sequence))))
55 (let* ((len (length sequence))
56 (m (mod n len))
57 (head (subseq sequence 0 m)))
58 (replace sequence sequence :start1 0 :start2 m)
59 (replace sequence head :start1 (- len m))
60 sequence)))
61
62 (defun rotate (sequence &optional (n 1))
63 "Returns a sequence of the same type as SEQUENCE, with the elements of
64 SEQUENCE rotated by N: N elements are moved from the end of the sequence to
65 the front if N is positive, and -N elements moved from the front to the end if
66 N is negative. SEQUENCE must be a proper sequence. N must be an integer,
67 defaulting to 1.
68
69 If absolute value of N is greater then the length of the sequence, the results
70 are identical to calling ROTATE with
71
72 (* (signum n) (mod n (length sequence))).
73
74 Note: the original sequence may be destructively altered, and result sequence may
75 share structure with it."
76 (if (plusp n)
77 (rotate-tail-to-head sequence n)
78 (if (minusp n)
79 (rotate-head-to-tail sequence (- n))
80 sequence)))
81
82 (defun shuffle (sequence &key (start 0) end)
83 "Returns a random permutation of SEQUENCE bounded by START and END.
84 Original sequence may be destructively modified, and (if it contains
85 CONS or lists themselv) share storage with the original one.
86 Signals an error if SEQUENCE is not a proper sequence."
87 (declare (type fixnum start)
88 (type (or fixnum null) end))
89 (etypecase sequence
90 (list
91 (let* ((end (or end (proper-list-length sequence)))
92 (n (- end start)))
93 (do ((tail (nthcdr start sequence) (cdr tail)))
94 ((zerop n))
95 (rotatef (car tail) (car (nthcdr (random n) tail)))
96 (decf n))))
97 (vector
98 (let ((end (or end (length sequence))))
99 (loop for i from start below end
100 do (rotatef (aref sequence i)
101 (aref sequence (+ i (random (- end i))))))))
102 (sequence
103 (let ((end (or end (length sequence))))
104 (loop for i from (- end 1) downto start
105 do (rotatef (elt sequence i)
106 (elt sequence (+ i (random (- end i)))))))))
107 sequence)
108
109 (defun random-elt (sequence &key (start 0) end)
110 "Returns a random element from SEQUENCE bounded by START and END. Signals an
111 error if the SEQUENCE is not a proper non-empty sequence, or if END and START
112 are not proper bounding index designators for SEQUENCE."
113 (declare (sequence sequence) (fixnum start) (type (or fixnum null) end))
114 (let* ((size (if (listp sequence)
115 (proper-list-length sequence)
116 (length sequence)))
117 (end2 (or end size)))
118 (cond ((zerop size)
119 (error 'type-error
120 :datum sequence
121 :expected-type `(and sequence (not (satisfies emptyp)))))
122 ((not (and (<= 0 start) (< start end2) (<= end2 size)))
123 (error 'simple-type-error
124 :datum (cons start end)
125 :expected-type `(cons (integer 0 (,end2))
126 (or null (integer (,start) ,size)))
127 :format-control "~@<~S and ~S are not valid bounding index designators for ~
128 a sequence of length ~S.~:@>"
129 :format-arguments (list start end size)))
130 (t
131 (let ((index (+ start (random (- end2 start)))))
132 (elt sequence index))))))
133
134 (declaim (inline remove/swapped-arguments))
135 (defun remove/swapped-arguments (sequence item &rest keyword-arguments)
136 (apply #'remove item sequence keyword-arguments))
137
138 (define-modify-macro removef (item &rest keyword-arguments)
139 remove/swapped-arguments
140 "Modify-macro for REMOVE. Sets place designated by the first argument to
141 the result of calling REMOVE with ITEM, place, and the KEYWORD-ARGUMENTS.")
142
143 (declaim (inline delete/swapped-arguments))
144 (defun delete/swapped-arguments (sequence item &rest keyword-arguments)
145 (apply #'delete item sequence keyword-arguments))
146
147 (define-modify-macro deletef (item &rest keyword-arguments)
148 delete/swapped-arguments
149 "Modify-macro for DELETE. Sets place designated by the first argument to
150 the result of calling DELETE with ITEM, place, and the KEYWORD-ARGUMENTS.")
151
152 (deftype proper-sequence ()
153 "Type designator for proper sequences, that is proper lists and sequences
154 that are not lists."
155 `(or proper-list
156 (and (not list) sequence)))
157
158 (eval-when (:compile-toplevel :load-toplevel :execute)
159 (when (and (find-package '#:sequence)
160 (find-symbol (string '#:emptyp) '#:sequence))
161 (pushnew 'sequence-emptyp *features*)))
162
163 #-alexandria::sequence-emptyp
164 (defun emptyp (sequence)
165 "Returns true if SEQUENCE is an empty sequence. Signals an error if SEQUENCE
166 is not a sequence."
167 (etypecase sequence
168 (list (null sequence))
169 (sequence (zerop (length sequence)))))
170
171 #+alexandria::sequence-emptyp
172 (declaim (ftype (function (sequence) (values boolean &optional)) emptyp))
173 #+alexandria::sequence-emptyp
174 (setf (symbol-function 'emptyp) (symbol-function 'sequence:emptyp))
175 #+alexandria::sequence-emptyp
176 (define-compiler-macro emptyp (sequence)
177 `(sequence:emptyp ,sequence))
178
179 (defun length= (&rest sequences)
180 "Takes any number of sequences or integers in any order. Returns true iff
181 the length of all the sequences and the integers are equal. Hint: there's a
182 compiler macro that expands into more efficient code if the first argument
183 is a literal integer."
184 (declare (dynamic-extent sequences)
185 (inline sequence-of-length-p)
186 (optimize speed))
187 (unless (cdr sequences)
188 (error "You must call LENGTH= with at least two arguments"))
189 ;; There's room for optimization here: multiple list arguments could be
190 ;; traversed in parallel.
191 (let* ((first (pop sequences))
192 (current (if (integerp first)
193 first
194 (length first))))
195 (declare (type array-index current))
196 (dolist (el sequences)
197 (if (integerp el)
198 (unless (= el current)
199 (return-from length= nil))
200 (unless (sequence-of-length-p el current)
201 (return-from length= nil)))))
202 t)
203
204 (define-compiler-macro length= (&whole form length &rest sequences)
205 (cond
206 ((zerop (length sequences))
207 form)
208 (t
209 (let ((optimizedp (integerp length)))
210 (with-unique-names (tmp current)
211 (declare (ignorable current))
212 `(locally
213 (declare (inline sequence-of-length-p))
214 (let ((,tmp)
215 ,@(unless optimizedp
216 `((,current ,length))))
217 ,@(unless optimizedp
218 `((unless (integerp ,current)
219 (setf ,current (length ,current)))))
220 (and
221 ,@(loop
222 :for sequence :in sequences
223 :collect `(progn
224 (setf ,tmp ,sequence)
225 (if (integerp ,tmp)
226 (= ,tmp ,(if optimizedp
227 length
228 current))
229 (sequence-of-length-p ,tmp ,(if optimizedp
230 length
231 current)))))))))))))
232
233 (defun copy-sequence (type sequence)
234 "Returns a fresh sequence of TYPE, which has the same elements as
235 SEQUENCE."
236 (if (typep sequence type)
237 (copy-seq sequence)
238 (coerce sequence type)))
239
240 (defun first-elt (sequence)
241 "Returns the first element of SEQUENCE. Signals a type-error if SEQUENCE is
242 not a sequence, or is an empty sequence."
243 ;; Can't just directly use ELT, as it is not guaranteed to signal the
244 ;; type-error.
245 (cond ((consp sequence)
246 (car sequence))
247 ((and (typep sequence 'sequence) (not (emptyp sequence)))
248 (elt sequence 0))
249 (t
250 (error 'type-error
251 :datum sequence
252 :expected-type '(and sequence (not (satisfies emptyp)))))))
253
254 (defun (setf first-elt) (object sequence)
255 "Sets the first element of SEQUENCE. Signals a type-error if SEQUENCE is
256 not a sequence, is an empty sequence, or if OBJECT cannot be stored in SEQUENCE."
257 ;; Can't just directly use ELT, as it is not guaranteed to signal the
258 ;; type-error.
259 (cond ((consp sequence)
260 (setf (car sequence) object))
261 ((and (typep sequence 'sequence) (not (emptyp sequence)))
262 (setf (elt sequence 0) object))
263 (t
264 (error 'type-error
265 :datum sequence
266 :expected-type '(and sequence (not (satisfies emptyp)))))))
267
268 (defun last-elt (sequence)
269 "Returns the last element of SEQUENCE. Signals a type-error if SEQUENCE is
270 not a proper sequence, or is an empty sequence."
271 ;; Can't just directly use ELT, as it is not guaranteed to signal the
272 ;; type-error.
273 (let ((len 0))
274 (cond ((consp sequence)
275 (lastcar sequence))
276 ((and (typep sequence '(and sequence (not list))) (plusp (setf len (length sequence))))
277 (elt sequence (1- len)))
278 (t
279 (error 'type-error
280 :datum sequence
281 :expected-type '(and proper-sequence (not (satisfies emptyp))))))))
282
283 (defun (setf last-elt) (object sequence)
284 "Sets the last element of SEQUENCE. Signals a type-error if SEQUENCE is not a proper
285 sequence, is an empty sequence, or if OBJECT cannot be stored in SEQUENCE."
286 (let ((len 0))
287 (cond ((consp sequence)
288 (setf (lastcar sequence) object))
289 ((and (typep sequence '(and sequence (not list))) (plusp (setf len (length sequence))))
290 (setf (elt sequence (1- len)) object))
291 (t
292 (error 'type-error
293 :datum sequence
294 :expected-type '(and proper-sequence (not (satisfies emptyp))))))))
295
296 (defun starts-with-subseq (prefix sequence &rest args
297 &key
298 (return-suffix nil return-suffix-supplied-p)
299 &allow-other-keys)
300 "Test whether the first elements of SEQUENCE are the same (as per TEST) as the elements of PREFIX.
301
302 If RETURN-SUFFIX is T the function returns, as a second value, a
303 sub-sequence or displaced array pointing to the sequence after PREFIX."
304 (declare (dynamic-extent args))
305 (let ((sequence-length (length sequence))
306 (prefix-length (length prefix)))
307 (when (< sequence-length prefix-length)
308 (return-from starts-with-subseq (values nil nil)))
309 (flet ((make-suffix (start)
310 (when return-suffix
311 (cond
312 ((not (arrayp sequence))
313 (if start
314 (subseq sequence start)
315 (subseq sequence 0 0)))
316 ((not start)
317 (make-array 0
318 :element-type (array-element-type sequence)
319 :adjustable nil))
320 (t
321 (make-array (- sequence-length start)
322 :element-type (array-element-type sequence)
323 :displaced-to sequence
324 :displaced-index-offset start
325 :adjustable nil))))))
326 (let ((mismatch (apply #'mismatch prefix sequence
327 (if return-suffix-supplied-p
328 (remove-from-plist args :return-suffix)
329 args))))
330 (cond
331 ((not mismatch)
332 (values t (make-suffix nil)))
333 ((= mismatch prefix-length)
334 (values t (make-suffix mismatch)))
335 (t
336 (values nil nil)))))))
337
338 (defun ends-with-subseq (suffix sequence &key (test #'eql))
339 "Test whether SEQUENCE ends with SUFFIX. In other words: return true if
340 the last (length SUFFIX) elements of SEQUENCE are equal to SUFFIX."
341 (let ((sequence-length (length sequence))
342 (suffix-length (length suffix)))
343 (when (< sequence-length suffix-length)
344 ;; if SEQUENCE is shorter than SUFFIX, then SEQUENCE can't end with SUFFIX.
345 (return-from ends-with-subseq nil))
346 (loop for sequence-index from (- sequence-length suffix-length) below sequence-length
347 for suffix-index from 0 below suffix-length
348 when (not (funcall test (elt sequence sequence-index) (elt suffix suffix-index)))
349 do (return-from ends-with-subseq nil)
350 finally (return t))))
351
352 (defun starts-with (object sequence &key (test #'eql) (key #'identity))
353 "Returns true if SEQUENCE is a sequence whose first element is EQL to OBJECT.
354 Returns NIL if the SEQUENCE is not a sequence or is an empty sequence."
355 (let ((first-elt (typecase sequence
356 (cons (car sequence))
357 (sequence
358 (if (emptyp sequence)
359 (return-from starts-with nil)
360 (elt sequence 0)))
361 (t
362 (return-from starts-with nil)))))
363 (funcall test (funcall key first-elt) object)))
364
365 (defun ends-with (object sequence &key (test #'eql) (key #'identity))
366 "Returns true if SEQUENCE is a sequence whose last element is EQL to OBJECT.
367 Returns NIL if the SEQUENCE is not a sequence or is an empty sequence. Signals
368 an error if SEQUENCE is an improper list."
369 (let ((last-elt (typecase sequence
370 (cons
371 (lastcar sequence)) ; signals for improper lists
372 (sequence
373 ;; Can't use last-elt, as that signals an error
374 ;; for empty sequences
375 (let ((len (length sequence)))
376 (if (plusp len)
377 (elt sequence (1- len))
378 (return-from ends-with nil))))
379 (t
380 (return-from ends-with nil)))))
381 (funcall test (funcall key last-elt) object)))
382
383 (defun map-combinations (function sequence &key (start 0) end length (copy t))
384 "Calls FUNCTION with each combination of LENGTH constructable from the
385 elements of the subsequence of SEQUENCE delimited by START and END. START
386 defaults to 0, END to length of SEQUENCE, and LENGTH to the length of the
387 delimited subsequence. (So unless LENGTH is specified there is only a single
388 combination, which has the same elements as the delimited subsequence.) If
389 COPY is true (the default) each combination is freshly allocated. If COPY is
390 false all combinations are EQ to each other, in which case consequences are
391 unspecified if a combination is modified by FUNCTION."
392 (let* ((end (or end (length sequence)))
393 (size (- end start))
394 (length (or length size))
395 (combination (subseq sequence 0 length))
396 (function (ensure-function function)))
397 (if (= length size)
398 (funcall function combination)
399 (flet ((call ()
400 (funcall function (if copy
401 (copy-seq combination)
402 combination))))
403 (etypecase sequence
404 ;; When dealing with lists we prefer walking back and
405 ;; forth instead of using indexes.
406 (list
407 (labels ((combine-list (c-tail o-tail)
408 (if (not c-tail)
409 (call)
410 (do ((tail o-tail (cdr tail)))
411 ((not tail))
412 (setf (car c-tail) (car tail))
413 (combine-list (cdr c-tail) (cdr tail))))))
414 (combine-list combination (nthcdr start sequence))))
415 (vector
416 (labels ((combine (count start)
417 (if (zerop count)
418 (call)
419 (loop for i from start below end
420 do (let ((j (- count 1)))
421 (setf (aref combination j) (aref sequence i))
422 (combine j (+ i 1)))))))
423 (combine length start)))
424 (sequence
425 (labels ((combine (count start)
426 (if (zerop count)
427 (call)
428 (loop for i from start below end
429 do (let ((j (- count 1)))
430 (setf (elt combination j) (elt sequence i))
431 (combine j (+ i 1)))))))
432 (combine length start)))))))
433 sequence)
434
435 (defun map-permutations (function sequence &key (start 0) end length (copy t))
436 "Calls function with each permutation of LENGTH constructable
437 from the subsequence of SEQUENCE delimited by START and END. START
438 defaults to 0, END to length of the sequence, and LENGTH to the
439 length of the delimited subsequence."
440 (let* ((end (or end (length sequence)))
441 (size (- end start))
442 (length (or length size)))
443 (labels ((permute (seq n)
444 (let ((n-1 (- n 1)))
445 (if (zerop n-1)
446 (funcall function (if copy
447 (copy-seq seq)
448 seq))
449 (loop for i from 0 upto n-1
450 do (permute seq n-1)
451 (if (evenp n-1)
452 (rotatef (elt seq 0) (elt seq n-1))
453 (rotatef (elt seq i) (elt seq n-1)))))))
454 (permute-sequence (seq)
455 (permute seq length)))
456 (if (= length size)
457 ;; Things are simple if we need to just permute the
458 ;; full START-END range.
459 (permute-sequence (subseq sequence start end))
460 ;; Otherwise we need to generate all the combinations
461 ;; of LENGTH in the START-END range, and then permute
462 ;; a copy of the result: can't permute the combination
463 ;; directly, as they share structure with each other.
464 (let ((permutation (subseq sequence 0 length)))
465 (flet ((permute-combination (combination)
466 (permute-sequence (replace permutation combination))))
467 (declare (dynamic-extent #'permute-combination))
468 (map-combinations #'permute-combination sequence
469 :start start
470 :end end
471 :length length
472 :copy nil)))))))
473
474 (defun map-derangements (function sequence &key (start 0) end (copy t))
475 "Calls FUNCTION with each derangement of the subsequence of SEQUENCE denoted
476 by the bounding index designators START and END. Derangement is a permutation
477 of the sequence where no element remains in place. SEQUENCE is not modified,
478 but individual derangements are EQ to each other. Consequences are unspecified
479 if calling FUNCTION modifies either the derangement or SEQUENCE."
480 (let* ((end (or end (length sequence)))
481 (size (- end start))
482 ;; We don't really care about the elements here.
483 (derangement (subseq sequence 0 size))
484 ;; Bitvector that has 1 for elements that have been deranged.
485 (mask (make-array size :element-type 'bit :initial-element 0)))
486 (declare (dynamic-extent mask))
487 ;; ad hoc algorith
488 (labels ((derange (place n)
489 ;; Perform one recursive step in deranging the
490 ;; sequence: PLACE is index of the original sequence
491 ;; to derange to another index, and N is the number of
492 ;; indexes not yet deranged.
493 (if (zerop n)
494 (funcall function (if copy
495 (copy-seq derangement)
496 derangement))
497 ;; Itarate over the indexes I of the subsequence to
498 ;; derange: if I != PLACE and I has not yet been
499 ;; deranged by an earlier call put the element from
500 ;; PLACE to I, mark I as deranged, and recurse,
501 ;; finally removing the mark.
502 (loop for i from 0 below size
503 do
504 (unless (or (= place (+ i start)) (not (zerop (bit mask i))))
505 (setf (elt derangement i) (elt sequence place)
506 (bit mask i) 1)
507 (derange (1+ place) (1- n))
508 (setf (bit mask i) 0))))))
509 (derange start size)
510 sequence)))
511
512 (declaim (notinline sequence-of-length-p))
513
514 (defun extremum (sequence predicate &key key (start 0) end)
515 "Returns the element of SEQUENCE that would appear first if the subsequence
516 bounded by START and END was sorted using PREDICATE and KEY.
517
518 EXTREMUM determines the relationship between two elements of SEQUENCE by using
519 the PREDICATE function. PREDICATE should return true if and only if the first
520 argument is strictly less than the second one (in some appropriate sense). Two
521 arguments X and Y are considered to be equal if (FUNCALL PREDICATE X Y)
522 and (FUNCALL PREDICATE Y X) are both false.
523
524 The arguments to the PREDICATE function are computed from elements of SEQUENCE
525 using the KEY function, if supplied. If KEY is not supplied or is NIL, the
526 sequence element itself is used.
527
528 If SEQUENCE is empty, NIL is returned."
529 (let* ((pred-fun (ensure-function predicate))
530 (key-fun (unless (or (not key) (eq key 'identity) (eq key #'identity))
531 (ensure-function key)))
532 (real-end (or end (length sequence))))
533 (cond ((> real-end start)
534 (if key-fun
535 (flet ((reduce-keys (a b)
536 (if (funcall pred-fun
537 (funcall key-fun a)
538 (funcall key-fun b))
539 a
540 b)))
541 (declare (dynamic-extent #'reduce-keys))
542 (reduce #'reduce-keys sequence :start start :end real-end))
543 (flet ((reduce-elts (a b)
544 (if (funcall pred-fun a b)
545 a
546 b)))
547 (declare (dynamic-extent #'reduce-elts))
548 (reduce #'reduce-elts sequence :start start :end real-end))))
549 ((= real-end start)
550 nil)
551 (t
552 (error "Invalid bounding indexes for sequence of length ~S: ~S ~S, ~S ~S"
553 (length sequence)
554 :start start
555 :end end)))))