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+(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)))))