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Diffstat (limited to 'sequences.lisp')
| -rw-r--r-- | sequences.lisp | 555 |
1 files changed, 555 insertions, 0 deletions
diff --git a/sequences.lisp b/sequences.lisp new file mode 100644 index 0000000000..21464f5376 --- /dev/null +++ b/sequences.lisp @@ -0,0 +1,555 @@ +(in-package :alexandria) + +;; Make these inlinable by declaiming them INLINE here and some of them +;; NOTINLINE at the end of the file. Exclude functions that have a compiler +;; macro, because NOTINLINE is required to prevent compiler-macro expansion. +(declaim (inline copy-sequence sequence-of-length-p)) + +(defun sequence-of-length-p (sequence length) + "Return true if SEQUENCE is a sequence of length LENGTH. Signals an error if +SEQUENCE is not a sequence. Returns FALSE for circular lists." + (declare (type array-index length) + #-lispworks (inline length) + (optimize speed)) + (etypecase sequence + (null + (zerop length)) + (cons + (let ((n (1- length))) + (unless (minusp n) + (let ((tail (nthcdr n sequence))) + (and tail + (null (cdr tail))))))) + (vector + (= length (length sequence))) + (sequence + (= length (length sequence))))) + +(defun rotate-tail-to-head (sequence n) + (declare (type (integer 1) n)) + (if (listp sequence) + (let ((m (mod n (proper-list-length sequence)))) + (if (null (cdr sequence)) + sequence + (let* ((tail (last sequence (+ m 1))) + (last (cdr tail))) + (setf (cdr tail) nil) + (nconc last sequence)))) + (let* ((len (length sequence)) + (m (mod n len)) + (tail (subseq sequence (- len m)))) + (replace sequence sequence :start1 m :start2 0) + (replace sequence tail) + sequence))) + +(defun rotate-head-to-tail (sequence n) + (declare (type (integer 1) n)) + (if (listp sequence) + (let ((m (mod (1- n) (proper-list-length sequence)))) + (if (null (cdr sequence)) + sequence + (let* ((headtail (nthcdr m sequence)) + (tail (cdr headtail))) + (setf (cdr headtail) nil) + (nconc tail sequence)))) + (let* ((len (length sequence)) + (m (mod n len)) + (head (subseq sequence 0 m))) + (replace sequence sequence :start1 0 :start2 m) + (replace sequence head :start1 (- len m)) + sequence))) + +(defun rotate (sequence &optional (n 1)) + "Returns a sequence of the same type as SEQUENCE, with the elements of +SEQUENCE rotated by N: N elements are moved from the end of the sequence to +the front if N is positive, and -N elements moved from the front to the end if +N is negative. SEQUENCE must be a proper sequence. N must be an integer, +defaulting to 1. + +If absolute value of N is greater then the length of the sequence, the results +are identical to calling ROTATE with + + (* (signum n) (mod n (length sequence))). + +Note: the original sequence may be destructively altered, and result sequence may +share structure with it." + (if (plusp n) + (rotate-tail-to-head sequence n) + (if (minusp n) + (rotate-head-to-tail sequence (- n)) + sequence))) + +(defun shuffle (sequence &key (start 0) end) + "Returns a random permutation of SEQUENCE bounded by START and END. +Original sequence may be destructively modified, and (if it contains +CONS or lists themselv) share storage with the original one. +Signals an error if SEQUENCE is not a proper sequence." + (declare (type fixnum start) + (type (or fixnum null) end)) + (etypecase sequence + (list + (let* ((end (or end (proper-list-length sequence))) + (n (- end start))) + (do ((tail (nthcdr start sequence) (cdr tail))) + ((zerop n)) + (rotatef (car tail) (car (nthcdr (random n) tail))) + (decf n)))) + (vector + (let ((end (or end (length sequence)))) + (loop for i from start below end + do (rotatef (aref sequence i) + (aref sequence (+ i (random (- end i)))))))) + (sequence + (let ((end (or end (length sequence)))) + (loop for i from (- end 1) downto start + do (rotatef (elt sequence i) + (elt sequence (+ i (random (- end i))))))))) + sequence) + +(defun random-elt (sequence &key (start 0) end) + "Returns a random element from SEQUENCE bounded by START and END. Signals an +error if the SEQUENCE is not a proper non-empty sequence, or if END and START +are not proper bounding index designators for SEQUENCE." + (declare (sequence sequence) (fixnum start) (type (or fixnum null) end)) + (let* ((size (if (listp sequence) + (proper-list-length sequence) + (length sequence))) + (end2 (or end size))) + (cond ((zerop size) + (error 'type-error + :datum sequence + :expected-type `(and sequence (not (satisfies emptyp))))) + ((not (and (<= 0 start) (< start end2) (<= end2 size))) + (error 'simple-type-error + :datum (cons start end) + :expected-type `(cons (integer 0 (,end2)) + (or null (integer (,start) ,size))) + :format-control "~@<~S and ~S are not valid bounding index designators for ~ + a sequence of length ~S.~:@>" + :format-arguments (list start end size))) + (t + (let ((index (+ start (random (- end2 start))))) + (elt sequence index)))))) + +(declaim (inline remove/swapped-arguments)) +(defun remove/swapped-arguments (sequence item &rest keyword-arguments) + (apply #'remove item sequence keyword-arguments)) + +(define-modify-macro removef (item &rest keyword-arguments) + remove/swapped-arguments + "Modify-macro for REMOVE. Sets place designated by the first argument to +the result of calling REMOVE with ITEM, place, and the KEYWORD-ARGUMENTS.") + +(declaim (inline delete/swapped-arguments)) +(defun delete/swapped-arguments (sequence item &rest keyword-arguments) + (apply #'delete item sequence keyword-arguments)) + +(define-modify-macro deletef (item &rest keyword-arguments) + delete/swapped-arguments + "Modify-macro for DELETE. Sets place designated by the first argument to +the result of calling DELETE with ITEM, place, and the KEYWORD-ARGUMENTS.") + +(deftype proper-sequence () + "Type designator for proper sequences, that is proper lists and sequences +that are not lists." + `(or proper-list + (and (not list) sequence))) + +(eval-when (:compile-toplevel :load-toplevel :execute) + (when (and (find-package '#:sequence) + (find-symbol (string '#:emptyp) '#:sequence)) + (pushnew 'sequence-emptyp *features*))) + +#-alexandria::sequence-emptyp +(defun emptyp (sequence) + "Returns true if SEQUENCE is an empty sequence. Signals an error if SEQUENCE +is not a sequence." + (etypecase sequence + (list (null sequence)) + (sequence (zerop (length sequence))))) + +#+alexandria::sequence-emptyp +(declaim (ftype (function (sequence) (values boolean &optional)) emptyp)) +#+alexandria::sequence-emptyp +(setf (symbol-function 'emptyp) (symbol-function 'sequence:emptyp)) +#+alexandria::sequence-emptyp +(define-compiler-macro emptyp (sequence) + `(sequence:emptyp ,sequence)) + +(defun length= (&rest sequences) + "Takes any number of sequences or integers in any order. Returns true iff +the length of all the sequences and the integers are equal. Hint: there's a +compiler macro that expands into more efficient code if the first argument +is a literal integer." + (declare (dynamic-extent sequences) + (inline sequence-of-length-p) + (optimize speed)) + (unless (cdr sequences) + (error "You must call LENGTH= with at least two arguments")) + ;; There's room for optimization here: multiple list arguments could be + ;; traversed in parallel. + (let* ((first (pop sequences)) + (current (if (integerp first) + first + (length first)))) + (declare (type array-index current)) + (dolist (el sequences) + (if (integerp el) + (unless (= el current) + (return-from length= nil)) + (unless (sequence-of-length-p el current) + (return-from length= nil))))) + t) + +(define-compiler-macro length= (&whole form length &rest sequences) + (cond + ((zerop (length sequences)) + form) + (t + (let ((optimizedp (integerp length))) + (with-unique-names (tmp current) + (declare (ignorable current)) + `(locally + (declare (inline sequence-of-length-p)) + (let ((,tmp) + ,@(unless optimizedp + `((,current ,length)))) + ,@(unless optimizedp + `((unless (integerp ,current) + (setf ,current (length ,current))))) + (and + ,@(loop + :for sequence :in sequences + :collect `(progn + (setf ,tmp ,sequence) + (if (integerp ,tmp) + (= ,tmp ,(if optimizedp + length + current)) + (sequence-of-length-p ,tmp ,(if optimizedp + length + current))))))))))))) + +(defun copy-sequence (type sequence) + "Returns a fresh sequence of TYPE, which has the same elements as +SEQUENCE." + (if (typep sequence type) + (copy-seq sequence) + (coerce sequence type))) + +(defun first-elt (sequence) + "Returns the first element of SEQUENCE. Signals a type-error if SEQUENCE is +not a sequence, or is an empty sequence." + ;; Can't just directly use ELT, as it is not guaranteed to signal the + ;; type-error. + (cond ((consp sequence) + (car sequence)) + ((and (typep sequence 'sequence) (not (emptyp sequence))) + (elt sequence 0)) + (t + (error 'type-error + :datum sequence + :expected-type '(and sequence (not (satisfies emptyp))))))) + +(defun (setf first-elt) (object sequence) + "Sets the first element of SEQUENCE. Signals a type-error if SEQUENCE is +not a sequence, is an empty sequence, or if OBJECT cannot be stored in SEQUENCE." + ;; Can't just directly use ELT, as it is not guaranteed to signal the + ;; type-error. + (cond ((consp sequence) + (setf (car sequence) object)) + ((and (typep sequence 'sequence) (not (emptyp sequence))) + (setf (elt sequence 0) object)) + (t + (error 'type-error + :datum sequence + :expected-type '(and sequence (not (satisfies emptyp))))))) + +(defun last-elt (sequence) + "Returns the last element of SEQUENCE. Signals a type-error if SEQUENCE is +not a proper sequence, or is an empty sequence." + ;; Can't just directly use ELT, as it is not guaranteed to signal the + ;; type-error. + (let ((len 0)) + (cond ((consp sequence) + (lastcar sequence)) + ((and (typep sequence '(and sequence (not list))) (plusp (setf len (length sequence)))) + (elt sequence (1- len))) + (t + (error 'type-error + :datum sequence + :expected-type '(and proper-sequence (not (satisfies emptyp)))))))) + +(defun (setf last-elt) (object sequence) + "Sets the last element of SEQUENCE. Signals a type-error if SEQUENCE is not a proper +sequence, is an empty sequence, or if OBJECT cannot be stored in SEQUENCE." + (let ((len 0)) + (cond ((consp sequence) + (setf (lastcar sequence) object)) + ((and (typep sequence '(and sequence (not list))) (plusp (setf len (length sequence)))) + (setf (elt sequence (1- len)) object)) + (t + (error 'type-error + :datum sequence + :expected-type '(and proper-sequence (not (satisfies emptyp)))))))) + +(defun starts-with-subseq (prefix sequence &rest args + &key + (return-suffix nil return-suffix-supplied-p) + &allow-other-keys) + "Test whether the first elements of SEQUENCE are the same (as per TEST) as the elements of PREFIX. + +If RETURN-SUFFIX is T the function returns, as a second value, a +sub-sequence or displaced array pointing to the sequence after PREFIX." + (declare (dynamic-extent args)) + (let ((sequence-length (length sequence)) + (prefix-length (length prefix))) + (when (< sequence-length prefix-length) + (return-from starts-with-subseq (values nil nil))) + (flet ((make-suffix (start) + (when return-suffix + (cond + ((not (arrayp sequence)) + (if start + (subseq sequence start) + (subseq sequence 0 0))) + ((not start) + (make-array 0 + :element-type (array-element-type sequence) + :adjustable nil)) + (t + (make-array (- sequence-length start) + :element-type (array-element-type sequence) + :displaced-to sequence + :displaced-index-offset start + :adjustable nil)))))) + (let ((mismatch (apply #'mismatch prefix sequence + (if return-suffix-supplied-p + (remove-from-plist args :return-suffix) + args)))) + (cond + ((not mismatch) + (values t (make-suffix nil))) + ((= mismatch prefix-length) + (values t (make-suffix mismatch))) + (t + (values nil nil))))))) + +(defun ends-with-subseq (suffix sequence &key (test #'eql)) + "Test whether SEQUENCE ends with SUFFIX. In other words: return true if +the last (length SUFFIX) elements of SEQUENCE are equal to SUFFIX." + (let ((sequence-length (length sequence)) + (suffix-length (length suffix))) + (when (< sequence-length suffix-length) + ;; if SEQUENCE is shorter than SUFFIX, then SEQUENCE can't end with SUFFIX. + (return-from ends-with-subseq nil)) + (loop for sequence-index from (- sequence-length suffix-length) below sequence-length + for suffix-index from 0 below suffix-length + when (not (funcall test (elt sequence sequence-index) (elt suffix suffix-index))) + do (return-from ends-with-subseq nil) + finally (return t)))) + +(defun starts-with (object sequence &key (test #'eql) (key #'identity)) + "Returns true if SEQUENCE is a sequence whose first element is EQL to OBJECT. +Returns NIL if the SEQUENCE is not a sequence or is an empty sequence." + (let ((first-elt (typecase sequence + (cons (car sequence)) + (sequence + (if (emptyp sequence) + (return-from starts-with nil) + (elt sequence 0))) + (t + (return-from starts-with nil))))) + (funcall test (funcall key first-elt) object))) + +(defun ends-with (object sequence &key (test #'eql) (key #'identity)) + "Returns true if SEQUENCE is a sequence whose last element is EQL to OBJECT. +Returns NIL if the SEQUENCE is not a sequence or is an empty sequence. Signals +an error if SEQUENCE is an improper list." + (let ((last-elt (typecase sequence + (cons + (lastcar sequence)) ; signals for improper lists + (sequence + ;; Can't use last-elt, as that signals an error + ;; for empty sequences + (let ((len (length sequence))) + (if (plusp len) + (elt sequence (1- len)) + (return-from ends-with nil)))) + (t + (return-from ends-with nil))))) + (funcall test (funcall key last-elt) object))) + +(defun map-combinations (function sequence &key (start 0) end length (copy t)) + "Calls FUNCTION with each combination of LENGTH constructable from the +elements of the subsequence of SEQUENCE delimited by START and END. START +defaults to 0, END to length of SEQUENCE, and LENGTH to the length of the +delimited subsequence. (So unless LENGTH is specified there is only a single +combination, which has the same elements as the delimited subsequence.) If +COPY is true (the default) each combination is freshly allocated. If COPY is +false all combinations are EQ to each other, in which case consequences are +unspecified if a combination is modified by FUNCTION." + (let* ((end (or end (length sequence))) + (size (- end start)) + (length (or length size)) + (combination (subseq sequence 0 length)) + (function (ensure-function function))) + (if (= length size) + (funcall function combination) + (flet ((call () + (funcall function (if copy + (copy-seq combination) + combination)))) + (etypecase sequence + ;; When dealing with lists we prefer walking back and + ;; forth instead of using indexes. + (list + (labels ((combine-list (c-tail o-tail) + (if (not c-tail) + (call) + (do ((tail o-tail (cdr tail))) + ((not tail)) + (setf (car c-tail) (car tail)) + (combine-list (cdr c-tail) (cdr tail)))))) + (combine-list combination (nthcdr start sequence)))) + (vector + (labels ((combine (count start) + (if (zerop count) + (call) + (loop for i from start below end + do (let ((j (- count 1))) + (setf (aref combination j) (aref sequence i)) + (combine j (+ i 1))))))) + (combine length start))) + (sequence + (labels ((combine (count start) + (if (zerop count) + (call) + (loop for i from start below end + do (let ((j (- count 1))) + (setf (elt combination j) (elt sequence i)) + (combine j (+ i 1))))))) + (combine length start))))))) + sequence) + +(defun map-permutations (function sequence &key (start 0) end length (copy t)) + "Calls function with each permutation of LENGTH constructable +from the subsequence of SEQUENCE delimited by START and END. START +defaults to 0, END to length of the sequence, and LENGTH to the +length of the delimited subsequence." + (let* ((end (or end (length sequence))) + (size (- end start)) + (length (or length size))) + (labels ((permute (seq n) + (let ((n-1 (- n 1))) + (if (zerop n-1) + (funcall function (if copy + (copy-seq seq) + seq)) + (loop for i from 0 upto n-1 + do (permute seq n-1) + (if (evenp n-1) + (rotatef (elt seq 0) (elt seq n-1)) + (rotatef (elt seq i) (elt seq n-1))))))) + (permute-sequence (seq) + (permute seq length))) + (if (= length size) + ;; Things are simple if we need to just permute the + ;; full START-END range. + (permute-sequence (subseq sequence start end)) + ;; Otherwise we need to generate all the combinations + ;; of LENGTH in the START-END range, and then permute + ;; a copy of the result: can't permute the combination + ;; directly, as they share structure with each other. + (let ((permutation (subseq sequence 0 length))) + (flet ((permute-combination (combination) + (permute-sequence (replace permutation combination)))) + (declare (dynamic-extent #'permute-combination)) + (map-combinations #'permute-combination sequence + :start start + :end end + :length length + :copy nil))))))) + +(defun map-derangements (function sequence &key (start 0) end (copy t)) + "Calls FUNCTION with each derangement of the subsequence of SEQUENCE denoted +by the bounding index designators START and END. Derangement is a permutation +of the sequence where no element remains in place. SEQUENCE is not modified, +but individual derangements are EQ to each other. Consequences are unspecified +if calling FUNCTION modifies either the derangement or SEQUENCE." + (let* ((end (or end (length sequence))) + (size (- end start)) + ;; We don't really care about the elements here. + (derangement (subseq sequence 0 size)) + ;; Bitvector that has 1 for elements that have been deranged. + (mask (make-array size :element-type 'bit :initial-element 0))) + (declare (dynamic-extent mask)) + ;; ad hoc algorith + (labels ((derange (place n) + ;; Perform one recursive step in deranging the + ;; sequence: PLACE is index of the original sequence + ;; to derange to another index, and N is the number of + ;; indexes not yet deranged. + (if (zerop n) + (funcall function (if copy + (copy-seq derangement) + derangement)) + ;; Itarate over the indexes I of the subsequence to + ;; derange: if I != PLACE and I has not yet been + ;; deranged by an earlier call put the element from + ;; PLACE to I, mark I as deranged, and recurse, + ;; finally removing the mark. + (loop for i from 0 below size + do + (unless (or (= place (+ i start)) (not (zerop (bit mask i)))) + (setf (elt derangement i) (elt sequence place) + (bit mask i) 1) + (derange (1+ place) (1- n)) + (setf (bit mask i) 0)))))) + (derange start size) + sequence))) + +(declaim (notinline sequence-of-length-p)) + +(defun extremum (sequence predicate &key key (start 0) end) + "Returns the element of SEQUENCE that would appear first if the subsequence +bounded by START and END was sorted using PREDICATE and KEY. + +EXTREMUM determines the relationship between two elements of SEQUENCE by using +the PREDICATE function. PREDICATE should return true if and only if the first +argument is strictly less than the second one (in some appropriate sense). Two +arguments X and Y are considered to be equal if (FUNCALL PREDICATE X Y) +and (FUNCALL PREDICATE Y X) are both false. + +The arguments to the PREDICATE function are computed from elements of SEQUENCE +using the KEY function, if supplied. If KEY is not supplied or is NIL, the +sequence element itself is used. + +If SEQUENCE is empty, NIL is returned." + (let* ((pred-fun (ensure-function predicate)) + (key-fun (unless (or (not key) (eq key 'identity) (eq key #'identity)) + (ensure-function key))) + (real-end (or end (length sequence)))) + (cond ((> real-end start) + (if key-fun + (flet ((reduce-keys (a b) + (if (funcall pred-fun + (funcall key-fun a) + (funcall key-fun b)) + a + b))) + (declare (dynamic-extent #'reduce-keys)) + (reduce #'reduce-keys sequence :start start :end real-end)) + (flet ((reduce-elts (a b) + (if (funcall pred-fun a b) + a + b))) + (declare (dynamic-extent #'reduce-elts)) + (reduce #'reduce-elts sequence :start start :end real-end)))) + ((= real-end start) + nil) + (t + (error "Invalid bounding indexes for sequence of length ~S: ~S ~S, ~S ~S" + (length sequence) + :start start + :end end))))) |