Timsort implementation using Python

Timsort

#!/usr/lib/python
# -*- coding: utf-8 -*-
#
#       This is a re-implementation of Python's timsort in Python
#       itself. This is purely for learning purposes. :)
#       References: [
#           https://en.wikipedia.org/wiki/Timsort,
#           http://wiki.c2.com/?TimSort
#       ]
#
# Copyright 2017 Nandaja Varma <nandajavarma@gmail.com>
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
# 02110-1301,
# USA.


def binary_search(the_array, item, start, end):
    if start == end:
        if the_array[start] > item:
            return start
        else:
            return start + 1
    if start > end:
        return start

    mid = (start + end)/ 2
    if the_array[mid] < item:
        return binary_search(the_array, item, mid + 1, end)
    elif the_array[mid] > item:
        return binary_search(the_array, item, start, mid - 1)
    else:
        return mid


"""
Insertion sort that the heap sort uses if the array size is small or if
the size of the "run" is small
"""
def insertion_sort(the_array):
    l = len(the_array)
    for index in range(1, l):
        value = the_array[index]
        pos = binary_search(the_array, value, 0, index - 1)
        the_array = the_array[:pos] + [value] + the_array[pos:index] + the_array[index+1:]
    return the_array

def merge(left, right):
    """Takes two sorted lists and returns a single sorted list by comparing the
    elements one at a time.

    [1, 2, 3, 4, 5, 6]
    """
    if not left:
        return right
    if not right:
        return left
    if left[0] < right[0]:
        return [left[0]] + merge(left[1:], right)
    return [right[0]] + merge(left, right[1:])


def timsort(the_array):
    runs, sorted_runs = [], []
    l = len(the_array)
    new_run = [the_array[0]]
    for i in range(1, l):
        if i == l-1:
            new_run.append(the_array[i])
            runs.append(new_run)
            break
        if the_array[i] < the_array[i-1]:
            if not new_run:
                runs.append([the_array[i-1]])
                new_run.append(the_array[i])
            else:
                runs.append(new_run)
                new_run = []
        else:
            new_run.append(the_array[i])
    for each in runs:
        sorted_runs.append(insertion_sort(each))
    sorted_array = []
    for run in sorted_runs:
        sorted_array = merge(sorted_array, run)
    print sorted_array

Using your algorithm I found a few flaws. First off, when identifying which is the mid value in binary_search, a round function should be used as mid can be a float otherwise and lists don't use floats for indexes. Second which is little confusing, it removed on average about 20% of the values from the list when sorting it. I found the problem to be in the section placing items into arrays. The solution I found was to remove this line:
runs.append([the_array[i-1]])
because it added duplicate items to the runs array, and add this line:
runs.append([the_array[i]])
to add an item to the runs array if new_run isnt empty

I wrote up this Gist, which is the code as OP posted with PenguinLiam's suggestions

https://gist.github.com/bee-san/f6ccc000ab6527769999fd0a9ebf59de

@PenguinLiam Actually to make the code work on both python2 and python3, don't use round method, using // instead:

mid = (start + end) // 2

This is not Timsort! Timsort uses a stack with specific constraints on the top entries to decide which runs to merge and when.

@bee-san your example is unavailable now.
@ctlaux, what about this code, then?

@6r1d: I haven't worked through that code entirely, but it does not find existing runs or reverse them before performing insertion sort. I believe this is required for Timsort.

@bee-san your example is unavailable now.
@ctlaux, what about this code, then?

Updated, I changed my username :)

I think that line 90 should be new_run = [the_array[i]], this will not remove any values when divide the array into runs I guess.

This code work on both python2 and python3. Please use mid = int((start + end)/ 2) or mid = (start + end) // 2 instead of mid = (start + end)/ 2