How would you display an array of integers as a set of ranges? (algorithm)

Question

Given an array of integers, what is the simplest way to iterate over it and figure out all the ranges it covers? for example, for an array such as:

$numbers = ar         


        

Answer 1

If the array is sorted, as in your example, I would define buckets containing a min and a max.

Initialize: Create a bucket with a min and a max equal to the first value.

Loop: Compare each value with the max of the current bucket. If it is equal to or 1 more than the current max, update the max. If it is more than 1 greater than the max, save the bucket to a list of buckets and start a new bucket.

At the end you will have a set of buckets with a min and a max in each. If the min is the same as the max, print a single number (ie: in your example, the first bucket would have a min and a max of 1). If they are different, print as a range.

Example implementation in lisp:

CL-USER> (defun print-ranges (integer-list)
           (let ((sorted-list (sort integer-list #'<)))
             (loop with buckets = ()
                   with current-bucket
                   for int in sorted-list
                     initially (setf current-bucket (cons (first sorted-list) (first sorted-list)))
                   do (cond ((= int (cdr current-bucket))) ; do nothing, this number is already in range
                            ((= (1- int) (cdr current-bucket)) ; number is 1 higher--update bucket's max
                             (setf (cdr current-bucket) int))
                            (t
                             (push current-bucket buckets)
                             (setf current-bucket (cons int int)))) ; set up a new bucket
                   finally (push current-bucket buckets)
                           (loop for firstp = t then nil
                                 for bucket in (nreverse buckets) do
                                   (cond ((= (car bucket) (cdr bucket))
                                          (format t "~:[,~;~]~D" firstp (car bucket)))
                                         (t
                                          (format t "~:[,~;~]~D-~D" firstp (car bucket) (cdr bucket))))))))
PRINT-RANGES
CL-USER> (print-ranges (list 1 3 4 5 6 8 11 12 14 15 16))
1,3-6,8,11-12,14-16
NIL
CL-USER> 

Basically you end up with a list of things, where each thing has (lowest-in-bucket, highest-in-bucket). Those are your ranges.

If the list is not already sorted, sort it first.