Convert List of Numbers to String Ranges

Question

I'd like to know if there is a simple (or already created) way of doing the opposite of this: Generate List of Numbers from Hyphenated.... This link could be used to do:

>> list(hyphen_range('1-9,12,15-20,23'))
[1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 16, 17, 18, 19, 20, 23]:

I'm looking to do the opposite (note that 10 and 21 are included so it would be compatible with the range function, where range(1,10)=[1,2,3,4,5,6,7,8,9]):

>> list_to_ranges([1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 16, 17, 18, 19, 20, 23])
'1-10,12,15-21,23'

Eventually, I would like to have the output also incorporate a step where the last number of the output indicates the step:

>> list_to_ranges([1, 3, 5, 7, 8, 9, 10, 11])
'1-13:2,8,10'

Essentially, this would end up being kind of like an "inverse" range function

>> tmp = list_to_ranges([1, 3, 5])
>> print tmp
'1-7:2'
>> range(1, 7, 2)
[1, 3, 5]

My guess is that there is no really easy/simple way to do this, but I thought I would ask on here before I go make some brute force, long method.

EDIT

Using the code from an answer to this post as an example, I came up with a simple way to do the first part. But I think that identifying the patterns to do steps would be a bit harder.

from itertools import groupby
from operator import itemgetter

data = [ 1,  4,5,6, 10, 15,16,17,18, 22, 25,26,27,28]
print data, '\n'

str_list = []
for k, g in groupby(enumerate(data), lambda (i,x):i-x):
   ilist = map(itemgetter(1), g)
   print ilist
   if len(ilist) > 1:
      str_list.append('%d-%d' % (ilist[0], ilist[-1]+1))
   else:
      str_list.append('%d' % ilist[0])
print '\n', ','.join(str_list)

EDIT 2

Here is my attempt at including the step size...it is pretty close, but the first numbers get repeated. I think that with a little bit of tweaking of this, it will be close to what I want - or at least good enough.

import numpy as np
from itertools import groupby

def list_to_ranges(data):
   data = sorted(data)
   diff_data = np.diff(data).tolist()
   ranges = []
   i = 0
   for k, iterable in groupby(diff_data, None):
      rng = list(iterable)
      step = rng[0]
      if len(rng) == 1:
         ranges.append('%d' % data[i])
      elif step == 1:
         ranges.append('%d-%d' % (data[i], data[i+len(rng)]+step))
      else:
         ranges.append('%d-%d:%d' % (data[i], data[i+len(rng)]+step, step))
      i += len(rng)
   return ','.join(ranges)

data = [1, 3, 5, 6, 7, 11, 13, 15, 16, 17, 18, 19, 22, 25, 28]
print data
data_str = list_to_ranges(data)
print data_str

_list = []
for r in data_str.replace('-',':').split(','):
   r = [int(a) for a in r.split(':')]
   if len(r) == 1:
      _list.extend(r)
   elif len(r) == 2:
      _list.extend(range(r[0], r[1]))
   else:
      _list.extend(range(r[0], r[1], r[2]))
print _list
print list(set(_list))

Answer 1

One approach could be "eating" piece by piece the input sequence and store the partial range results untill you've got them all:

def formatter(start, end, step):
    return '{}-{}:{}'.format(start, end, step)
    # return '{}-{}:{}'.format(start, end + step, step)

def helper(lst):
    if len(lst) == 1:
        return str(lst[0]), []
    if len(lst) == 2:
        return ','.join(map(str,lst)), []

    step = lst[1] - lst[0]
    for i,x,y in zip(itertools.count(1), lst[1:], lst[2:]):
        if y-x != step:
            if i > 1:
                return formatter(lst[0], lst[i], step), lst[i+1:]
            else:
                return str(lst[0]), lst[1:]
    return formatter(lst[0], lst[-1], step), []

def re_range(lst):
    result = []
    while lst:
        partial,lst = helper(lst)
        result.append(partial)
    return ','.join(result)

I test it with a bunch of unit tests and it passed them all, it can handle negative numbers too, but they'll look kind of ugly (it's really anybody's fault).

Example:

>>> re_range([1,  4,5,6, 10, 15,16,17,18, 22, 25,26,27,28])
'1,4-6:1,10,15-18:1,22,25-28:1'
>>> re_range([1, 3, 5, 7, 8, 9, 10, 11, 13, 15, 17])
'1-7:2,8-11:1,13-17:2'

Note: I wrote the code for Python 3.

---

Performance

I didn't put any performance effort in the solution above. In particular, every time a list get re-builded with slicing, it might take some time if the input list has a particular shape. So, the first simple improvement would be using itertools.islice() where possible.

Anyway here's another implementation of the same algorithm, that scan through the input list with a scan index instead of slicing:

def re_range(lst):
    n = len(lst)
    result = []
    scan = 0
    while n - scan > 2:
        step = lst[scan + 1] - lst[scan]
        if lst[scan + 2] - lst[scan + 1] != step:
            result.append(str(lst[scan]))
            scan += 1
            continue

        for j in range(scan+2, n-1):
            if lst[j+1] - lst[j] != step:
                result.append(formatter(lst[scan], lst[j], step))
                scan = j+1
                break
        else:
            result.append(formatter(lst[scan], lst[-1], step))
            return ','.join(result)

    if n - scan == 1:
        result.append(str(lst[scan]))
    elif n - scan == 2:
        result.append(','.join(map(str, lst[scan:])))

    return ','.join(result)

I stopped working on it once it got ~65% faster than the previous top solution, it seemed enough :)

Anyway I'd say that there might still be room for improvement (expecially in the middle for-loop).

Answer 2

This is a comparison of the 3 methods. Change the amount of data and the density via the values below...no matter what values I use, the first solution seems to be the quickest for me. For very large sets of data, the third solution becomes very slow.

EDITED

Edited to include comments below and add in a new solution. The last solution seems to be the quickest now.

import numpy as np
import itertools
import random
import timeit

# --- My Solution --------------------------------------------------------------
def list_to_ranges1(data):
   data = sorted(data)
   diff_data = np.diff(data)
   ranges = []
   i = 0
   skip_next = False
   for k, iterable in itertools.groupby(diff_data, None):
      rng = list(iterable)
      step = rng[0]
      if skip_next:
         skip_next = False
         rng.pop()

      if len(rng) == 0:
         continue
      elif len(rng) == 1:
         ranges.append('%d' % data[i])
      elif step == 1:
         ranges.append('%d-%d' % (data[i], data[i+len(rng)]+step))
         i += 1
         skip_next = True
      else:
         ranges.append('%d-%d:%d' % (data[i], data[i+len(rng)]+step, step))
         i += 1
         skip_next = True
      i += len(rng)

   if len(rng) == 0 or len(rng) == 1:
      ranges.append('%d' % data[i])
   return ','.join(ranges)

# --- Kaidence Solution --------------------------------------------------------
# With a minor edit for use in range function
def list_to_ranges2(data):
   onediff = np.diff(data)
   twodiff = np.diff(onediff)
   increments, breakingindices = [], []
   for i in range(len(twodiff)):
       if twodiff[i] != 0:
           breakingindices.append(i+2)  # Correct index because of the two diffs
           increments.append(onediff[i]) # Record the increment for this section

  # Increments and breakingindices should be the same size
   str_list = []
   start = data[0]
   for i in range(len(breakingindices)):
       str_list.append("%d-%d:%d" % (start,
                                     data[breakingindices[i]-1] + increments[i],
                                     increments[i]))
       start = data[breakingindices[i]]
   str_list.append("%d-%d:%d" % (start,
                                 data[len(data)-1] + onediff[len(onediff)-1],
                                 onediff[len(onediff)-1]))
   return ','.join(str_list)

# --- Rik Poggi Solution -------------------------------------------------------
# With a minor edit for use in range function
def helper(lst):
    if len(lst) == 1:
        return str(lst[0]), []
    if len(lst) == 2:
        return ','.join(map(str,lst)), []

    step = lst[1] - lst[0]
    #for i,x,y in itertools.izip(itertools.count(1), lst[1:], lst[2:]):
    for i,x,y in itertools.izip(itertools.count(1),
                                itertools.islice(lst, 1, None, 1),
                                itertools.islice(lst, 2, None, 1)):
        if y-x != step:
            if i > 1:
                return '{}-{}:{}'.format(lst[0], lst[i]+step, step), lst[i+1:]
            else:
                return str(lst[0]), lst[1:]
    return '{}-{}:{}'.format(lst[0], lst[-1]+step, step), []

def list_to_ranges3(lst):
    result = []
    while lst:
        partial,lst = helper(lst)
        result.append(partial)
    return ','.join(result)

# --- Rik Poggi Solution 2 -----------------------------------------------------
def formatter(start, end, step):
    #return '{}-{}:{}'.format(start, end, step)
    return '{}-{}:{}'.format(start, end + step, step)

def list_to_ranges4(lst):
    n = len(lst)
    result = []
    scan = 0
    while n - scan > 2:
        step = lst[scan + 1] - lst[scan]
        if lst[scan + 2] - lst[scan + 1] != step:
            result.append(str(lst[scan]))
            scan += 1
            continue

        for j in xrange(scan+2, n-1):
            if lst[j+1] - lst[j] != step:
                result.append(formatter(lst[scan], lst[j], step))
                scan = j+1
                break
        else:
            result.append(formatter(lst[scan], lst[-1], step))
            return ','.join(result)

    if n - scan == 1:
        result.append(str(lst[scan]))
    elif n - scan == 2:
        result.append(','.join(itertools.imap(str, lst[scan:])))

    return ','.join(result)

# --- Test Function ------------------------------------------------------------
def test_data(data, f_to_test):
   data_str = f_to_test(data)
   _list = []
   for r in data_str.replace('-',':').split(','):
      r = [int(a) for a in r.split(':')]
      if len(r) == 1:
         _list.extend(r)
      elif len(r) == 2:
         _list.extend(range(r[0], r[1]))
      else:
         _list.extend(range(r[0], r[1], r[2]))
   return _list

# --- Timing Tests -------------------------------------------------------------
# Generate some sample data...
data_list = []
for i in range(5):
   # Note: using the "4000" and "5000" values below, the relative density of
   # the data can be changed.  This has a huge effect on the results
   # (particularly on the results for list_to_ranges3 which uses recursion).
   data_list.append(sorted(list(set([random.randint(1,4000) for a in \
                                      range(random.randint(5,5000))]))))

testfuncs = list_to_ranges1, list_to_ranges2, list_to_ranges3, list_to_ranges4
for f in testfuncs:
   print '\n', f.__name__
   for i, data in enumerate(data_list):
      t = timeit.Timer('f(data)', 'from __main__ import data, f')
      #print f(data)
      print i, data==test_data(data, f), round(t.timeit(200), 3)

Answer 3

This is most likely what you are looking for.

Edit: I see you already found the post. My apologies.

To help with the second part, I've tinkered a bit myself. This is what I came up with:

from numpy import diff

data = [ 1, 3, 5, 7, 8, 9, 10, 11, 13, 15, 17 ]
onediff, twodiff = diff(data), diff(diff(data))
increments, breakingindices = [], []
for i in range(len(twodiff)):
    if twodiff[i] != 0:
        breakingindices.append(i+2) # Correct index because of the two diffs
        increments.append(onediff[i]) # Record the increment for this section

# Increments and breakingindices should be the same size
str_list = []
start = data[0]
for i in range(len(breakingindices)):
    str_list.append("%d-%d:%d" % (start, data[breakingindices[i]-1], increments[i]))
    start = data[breakingindices[i]]
str_list.append("%d-%d:%d" % (start, data[len(data)-1], onediff[len(onediff)-1]))
print str_list

For the given input list, this gives: ['1-7:2', '8-11:1', '13-17:2']. The code could do with a bit of cleanup, but this sorts with your problem assuming the grouping can be done sequentially.

{caution: for [1,2,3,5,6,7] this gives ['1-3:1', '5-5:2', '6-7:1'] instead of ['1-3:1', '5-7:1']}