Python sort elements in array

How to Sort Array in Python

Python arrays can be sorted using different sorting algorithms, varying in their runtime and efficiency based on the algorithm chosen. We investigate some of these approaches towards sorting array elements.

Using sorted() on Python iterable objects

Python uses some extremely efficient algorithms for performing sorting. The sorted() method, for example, uses an algorithm called Timsort (which is a combination of Insertion Sort and Merge Sort) for performing highly optimized sorting.

Any Python iterable object such as a list or an array can be sorted using this method.

import array # Declare a list type object list_object = [3, 4, 1, 5, 2] # Declare an integer array object array_object = array.array('i', [3, 4, 1, 5, 2]) print('Sorted list ->', sorted(list_object)) print('Sorted array ->', sorted(array_object))

Sorted list -> [1, 2, 3, 4, 5] Sorted array -> [1, 2, 3, 4, 5]

Implementing MergeSort and QuickSort

Here, we investigate two other commonly used Sorting techniques used in actual practice, namely the MergeSort and the QuickSort algorithms.

1. MergeSort Algorithm

The algorithm uses a bottom-up Divide and Conquer approach, first dividing the original array into subarrays and then merging the individually sorted subarrays to yield the final sorted array.

In the below code snippet, the mergesort_helper() method does the actual splitting into subarrays and the perform_merge() method merges two previously sorted arrays into a new sorted array.

import array def mergesort(a, arr_type): def perform_merge(a, arr_type, start, mid, end): # Merges two previously sorted arrays # a[start:mid] and a[mid:end] tmp = array.array(arr_type, [i for i in a]) def compare(tmp, i, j): if tmp[i] mid and j > end: break curr += 1 def mergesort_helper(a, arr_type, start, end): # Divides the array into two parts # recursively and merges the subarrays # in a bottom up fashion, sorting them # via Divide and Conquer if start < end: mergesort_helper(a, arr_type, start, (end + start)//2) mergesort_helper(a, arr_type, (end + start)//2 + 1, end) perform_merge(a, arr_type, start, (start + end)//2, end) # Sorts the array using mergesort_helper mergesort_helper(a, arr_type, 0, len(a)-1)

a = array.array('i', [3, 1, 2, 4, 5, 1, 3, 12, 7, 6]) print('Before MergeSort ->', a) mergesort(a, 'i') print('After MergeSort ->', a)

Before MergeSort -> array('i', [3, 1, 2, 4, 5, 1, 3, 12, 7, 6]) After MergeSort -> array('i', [1, 1, 2, 3, 3, 4, 5, 6, 7, 12])

2. QuickSort Algorithm

This algorithm also uses a Divide and Conquer strategy, but uses a top-down approach instead, first partitioning the array around a pivot element (here, we always choose the last element of the array to be the pivot).

Thus ensuring that after every step, the pivot is at its designated position in the final sorted array.

After ensuring that the array is partitioned around the pivot (Elements lesser than the pivot are to the left, and the elements which are greater than the pivot are to the right), we continue applying the partition function to the rest of the array, until all the elements are at their respective position, which is when the array is completely sorted.

Note: There are other approaches to this algorithm for choosing the pivot element. Some variants choose the median element as the pivot, while others make use of a random selection strategy for the pivot.

def quicksort(a, arr_type): def do_partition(a, arr_type, start, end): # Performs the partitioning of the subarray a[start:end] # We choose the last element as the pivot pivot_idx = end pivot = a[pivot_idx] # Keep an index for the first partition # subarray (elements lesser than the pivot element) idx = start - 1 def increment_and_swap(j): nonlocal idx idx += 1 a[idx], a[j] = a[j], a[idx] [increment_and_swap(j) for j in range(start, end) if a[j] < pivot] # Finally, we need to swap the pivot (a[end] with a[idx+1]) # since we have reached the position of the pivot in the actual # sorted array a[idx+1], a[end] = a[end], a[idx+1] # Return the final updated position of the pivot # after partitioning return idx+1 def quicksort_helper(a, arr_type, start, end): if start < end: # Do the partitioning first and then go via # a top down divide and conquer, as opposed # to the bottom up mergesort pivot_idx = do_partition(a, arr_type, start, end) quicksort_helper(a, arr_type, start, pivot_idx-1) quicksort_helper(a, arr_type, pivot_idx+1, end) quicksort_helper(a, arr_type, 0, len(a)-1)

Here, the quicksort_helper method does the step of the Divide and Conquer approach, while the do_partition method partitions the array around the pivot and returns the position of the pivot, around which we continue to recursively partition the subarray before and after the pivot until the entire array is sorted.

b = array.array('i', [3, 1, 2, 4, 5, 1, 3, 12, 7, 6]) print('Before QuickSort ->', b) quicksort(b, 'i') print('After QuickSort ->', b)

Before QuickSort -> array('i', [3, 1, 2, 4, 5, 1, 3, 12, 7, 6]) After QuickSort -> array('i', [1, 1, 2, 3, 3, 4, 5, 6, 7, 12])

Conclusion

In this article, we went through the MergeSort and QuickSort algorithms for performing sorting on Python arrays, gaining an understanding of how we can use Divide and Conquer in a top-down as well as in a bottom-up fashion. We also briefly looked at the native sorted() method that the language provides to sort iterables.

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Sorting HOW TO¶

Python lists have a built-in list.sort() method that modifies the list in-place. There is also a sorted() built-in function that builds a new sorted list from an iterable.

In this document, we explore the various techniques for sorting data using Python.

Sorting Basics¶

A simple ascending sort is very easy: just call the sorted() function. It returns a new sorted list:

>>> sorted([5, 2, 3, 1, 4]) [1, 2, 3, 4, 5] 

You can also use the list.sort() method. It modifies the list in-place (and returns None to avoid confusion). Usually it’s less convenient than sorted() - but if you don’t need the original list, it’s slightly more efficient.

>>> a = [5, 2, 3, 1, 4] >>> a.sort() >>> a [1, 2, 3, 4, 5] 

Another difference is that the list.sort() method is only defined for lists. In contrast, the sorted() function accepts any iterable.

>>> sorted(1: 'D', 2: 'B', 3: 'B', 4: 'E', 5: 'A'>) [1, 2, 3, 4, 5] 

Key Functions¶

Both list.sort() and sorted() have a key parameter to specify a function (or other callable) to be called on each list element prior to making comparisons.

For example, here’s a case-insensitive string comparison:

>>> sorted("This is a test string from Andrew".split(), key=str.lower) ['a', 'Andrew', 'from', 'is', 'string', 'test', 'This'] 

The value of the key parameter should be a function (or other callable) that takes a single argument and returns a key to use for sorting purposes. This technique is fast because the key function is called exactly once for each input record.

A common pattern is to sort complex objects using some of the object’s indices as keys. For example:

>>> student_tuples = [ . ('john', 'A', 15), . ('jane', 'B', 12), . ('dave', 'B', 10), . ] >>> sorted(student_tuples, key=lambda student: student[2]) # sort by age [('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)] 

The same technique works for objects with named attributes. For example:

>>> class Student: . def __init__(self, name, grade, age): . self.name = name . self.grade = grade . self.age = age . def __repr__(self): . return repr((self.name, self.grade, self.age)) >>> student_objects = [ . Student('john', 'A', 15), . Student('jane', 'B', 12), . Student('dave', 'B', 10), . ] >>> sorted(student_objects, key=lambda student: student.age) # sort by age [('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)] 

Operator Module Functions¶

The key-function patterns shown above are very common, so Python provides convenience functions to make accessor functions easier and faster. The operator module has itemgetter() , attrgetter() , and a methodcaller() function.

Using those functions, the above examples become simpler and faster:

>>> from operator import itemgetter, attrgetter >>> sorted(student_tuples, key=itemgetter(2)) [('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)] >>> sorted(student_objects, key=attrgetter('age')) [('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)] 

The operator module functions allow multiple levels of sorting. For example, to sort by grade then by age:

>>> sorted(student_tuples, key=itemgetter(1,2)) [('john', 'A', 15), ('dave', 'B', 10), ('jane', 'B', 12)] >>> sorted(student_objects, key=attrgetter('grade', 'age')) [('john', 'A', 15), ('dave', 'B', 10), ('jane', 'B', 12)] 

Ascending and Descending¶

Both list.sort() and sorted() accept a reverse parameter with a boolean value. This is used to flag descending sorts. For example, to get the student data in reverse age order:

>>> sorted(student_tuples, key=itemgetter(2), reverse=True) [('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)] >>> sorted(student_objects, key=attrgetter('age'), reverse=True) [('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)] 

Sort Stability and Complex Sorts¶

Sorts are guaranteed to be stable. That means that when multiple records have the same key, their original order is preserved.

>>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)] >>> sorted(data, key=itemgetter(0)) [('blue', 1), ('blue', 2), ('red', 1), ('red', 2)] 

Notice how the two records for blue retain their original order so that ('blue', 1) is guaranteed to precede ('blue', 2) .

This wonderful property lets you build complex sorts in a series of sorting steps. For example, to sort the student data by descending grade and then ascending age, do the age sort first and then sort again using grade:

>>> s = sorted(student_objects, key=attrgetter('age')) # sort on secondary key >>> sorted(s, key=attrgetter('grade'), reverse=True) # now sort on primary key, descending [('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)] 

This can be abstracted out into a wrapper function that can take a list and tuples of field and order to sort them on multiple passes.

>>> def multisort(xs, specs): . for key, reverse in reversed(specs): . xs.sort(key=attrgetter(key), reverse=reverse) . return xs >>> multisort(list(student_objects), (('grade', True), ('age', False))) [('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)] 

The Timsort algorithm used in Python does multiple sorts efficiently because it can take advantage of any ordering already present in a dataset.

Decorate-Sort-Undecorate¶

This idiom is called Decorate-Sort-Undecorate after its three steps:

• First, the initial list is decorated with new values that control the sort order.
• Second, the decorated list is sorted.
• Finally, the decorations are removed, creating a list that contains only the initial values in the new order.

For example, to sort the student data by grade using the DSU approach:

>>> decorated = [(student.grade, i, student) for i, student in enumerate(student_objects)] >>> decorated.sort() >>> [student for grade, i, student in decorated] # undecorate [('john', 'A', 15), ('jane', 'B', 12), ('dave', 'B', 10)] 

This idiom works because tuples are compared lexicographically; the first items are compared; if they are the same then the second items are compared, and so on.

It is not strictly necessary in all cases to include the index i in the decorated list, but including it gives two benefits:

• The sort is stable – if two items have the same key, their order will be preserved in the sorted list.
• The original items do not have to be comparable because the ordering of the decorated tuples will be determined by at most the first two items. So for example the original list could contain complex numbers which cannot be sorted directly.

Another name for this idiom is Schwartzian transform, after Randal L. Schwartz, who popularized it among Perl programmers.

Now that Python sorting provides key-functions, this technique is not often needed.

Comparison Functions¶

Unlike key functions that return an absolute value for sorting, a comparison function computes the relative ordering for two inputs.

For example, a balance scale compares two samples giving a relative ordering: lighter, equal, or heavier. Likewise, a comparison function such as cmp(a, b) will return a negative value for less-than, zero if the inputs are equal, or a positive value for greater-than.

It is common to encounter comparison functions when translating algorithms from other languages. Also, some libraries provide comparison functions as part of their API. For example, locale.strcoll() is a comparison function.

To accommodate those situations, Python provides functools.cmp_to_key to wrap the comparison function to make it usable as a key function:

sorted(words, key=cmp_to_key(strcoll)) # locale-aware sort order 

Odds and Ends¶

• For locale aware sorting, use locale.strxfrm() for a key function or locale.strcoll() for a comparison function. This is necessary because “alphabetical” sort orderings can vary across cultures even if the underlying alphabet is the same.
• The reverse parameter still maintains sort stability (so that records with equal keys retain the original order). Interestingly, that effect can be simulated without the parameter by using the builtin reversed() function twice:

>>> data = [('red', 1), ('blue', 1), ('red', 2), ('blue', 2)] >>> standard_way = sorted(data, key=itemgetter(0), reverse=True) >>> double_reversed = list(reversed(sorted(reversed(data), key=itemgetter(0)))) >>> assert standard_way == double_reversed >>> standard_way [('red', 1), ('red', 2), ('blue', 1), ('blue', 2)] 

>>> Student.__lt__ = lambda self, other: self.age  other.age >>> sorted(student_objects) [('dave', 'B', 10), ('jane', 'B', 12), ('john', 'A', 15)] 

>>> students = ['dave', 'john', 'jane'] >>> newgrades = 'john': 'F', 'jane':'A', 'dave': 'C'> >>> sorted(students, key=newgrades.__getitem__) ['jane', 'dave', 'john'] 

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