Space complexity is defined as how much additional space the algorithm needs in terms of the N elements. And even though according to the docs, the sort method sorts a list in place, it does use some additional space, as stated in the description of the implementation:
timsort can require a temp array containing as many as N//2 pointers, which means as many as 2*N extra bytes on 32-bit boxes. It can be expected to require a temp array this large when sorting random data; on data with significant structure, it may get away without using any extra heap memory.
Therefore the worst case space complexity is O(N) and best case O(1)
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Space complexity is defined as how much additional space the algorithm needs in terms of the N elements. And even though according to the docs, the sort method sorts a list in place, it does use some additional space, as stated in the description of the implementation:
timsort can require a temp array containing as many as N//2 pointers, which means as many as 2*N extra bytes on 32-bit boxes. It can be expected to require a temp array this large when sorting random data; on data with significant structure, it may get away without using any extra heap memory.
Therefore the worst case space complexity is O(N) and best case O(1)
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Python's built in sort method is a spin off of merge sort called Timsort, more information here - https://en.wikipedia.org/wiki/Timsort.
It's essentially no better or worse than merge sort, which means that its run time on average is O(n log n) and its space complexity is Ω(n)
Reddit
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r/algorithms on Reddit: Question about sorting space complexity
July 22, 2022 -
It seems that Python uses Timsort to sort lists which in the worse case requires O(n) extra space, but there seem to exist in place sorts like heap sort which are O(n log n) but only require O(1) extra memory. Why does Python use Timsort which in the worse case requires O(n) extra space and not an algorithm like heap sort which only requires O(1) extra space?
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Using O(N) extra space is typically not a big deal. It's more important to be stable, and fast, which means having an adaptive sort that is also cache-friendly. Timsort is stable, adaptive, and cache-friendly, while heapsort is not.
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Timsort is faster in the average case and is stable here is an unnecessarily long article about Timsort implementation. It seems Python developers prioritized speed and stability over memory use
Why is the importance of time complexity in sorting algorithms?
Time complexity is crucial because it helps predict the performance of an algorithm. Efficient algorithms with lower time complexity (like O(n log n)) are preferable for large datasets, while less efficient ones (like O(n²)) may be too slow.
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Time and Space Complexity of All Sorting Algorithms
Which sorting algorithm has the best average-case time complexity?
Merge Sort, Quick Sort, and Heap Sort all have an average-case time complexity of O(n log n), making them efficient for general use.
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Time and Space Complexity of All Sorting Algorithms
What is the best sorting algorithm for random data?
Quick Sort is generally the best sorting algorithm for random data due to its average-case time complexity of O(n log n) and practical efficiency.
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Time and Space Complexity of All Sorting Algorithms
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Time and space complexity of sorting algorithms
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Python sorting algorithms and complexity analysis with GPT-3 - YouTube
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Sorting Algorithms Time and Space Complexity | Sorting Algorithms ...
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Time & Space Complexity Cheatsheet for Sorting Algorithms - YouTube
Analytics Vidhya
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Complete Guide on Sorting Techniques in Python [2025 Edition] - Analytics Vidhya
November 28, 2024 - The time complexity of sorting ... O(nk) for Radix Sort. Space complexity measures the amount of memory used by an algorithm to solve a problem as a function of the input size....
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Time and Space Complexities of Sorting Algorithms Explained
December 22, 2024 - Since we are not using any extra data structure apart from the input array, the space complexity is O(1). Like selection sort, the insertion sort algorithm also divides the array into two parts: a subarray of already sorted elements and a subarray ...
Built In
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Sorting Algorithms: Slowest to Fastest | Built In
There will be at most n calls in the stack, and hence, the space complexity will be O(n). More on Software Engineering: How to Use Pass, Continue and Break in Python · Since we sort the elements after comparing them with each other, each of the above algorithms are all comparison-based.
CodeRivers
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Python Sort Time and Space Complexity: A Comprehensive Guide - CodeRivers
April 6, 2025 - Similar to time complexity, it is expressed in Big O notation. For example: - O(1) (Constant Space): The algorithm uses a fixed amount of extra memory, regardless of the input size. - O(n) (Linear Space): The amount of extra memory used is proportional to the size of the input. sorted(): This ...
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Time and Space Complexity of All Sorting Algorithms
November 26, 2025 - Learn the time and space complexity of all sorting algorithms, including quicksort, mergesort, heapsort, and more, in this step-by-step tutorial.
Wikipedia
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Sorting algorithm - Wikipedia
1 week ago - When sorting arrays, it has additional O(n) space complexity, and involves a large number of copies in simple implementations; however, linked lists can be merge sorted with constant extra space, as such it is the algorithm of choice for sorting linked lists. Merge sort has seen a relatively recent surge in popularity for practical implementations, due to its use in the sophisticated algorithm Timsort, which is used for the standard sort routine in the programming languages Python ...
Programiz
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Sorting Algorithm
Become a certified Python programmer. Try Programiz PRO! ... A sorting algorithm is used to arrange elements of an array/list in a specific order. For example, ... Here, we are sorting the array in ascending order. There are various sorting algorithms that can be used to complete this operation. And, we can use any algorithm based on the requirement. ... The efficiency of any sorting algorithm is determined by the time complexity and space complexity of the algorithm.
GeeksforGeeks
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Space Complexity of List Operations in Python - GeeksforGeeks
July 23, 2025 - If a new list is created for sorting (e.g., with sorted()), the space complexity would be O(n), since a new sorted list is returned. reverse() method is used to reverse the elements of a list in place.
GeeksforGeeks
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Time Complexities of all Sorting Algorithms - GeeksforGeeks
September 23, 2016 - Both are calculated as the function of input size(n). One important thing here is that despite these parameters, the efficiency of an algorithm also depends upon the nature and size of the input. Time Complexity is defined as order of growth of time taken in terms of input size rather than the total time taken. It is because the total time taken also depends on some external factors like the compiler used, the processor's speed, etc. Auxiliary Space is extra space (apart from input and output) required for an algorithm.
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Time and Space Complexity of Sorting Algorithms
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StudyRaid
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Understanding Sorting Algorithm Complexity - Python Data Structures and Algorithms | StudyRaid
O(n): Linear time sorting is possible ... of input and aren't general-purpose. Space complexity measures the amount of memory an algorithm needs in addition to the input data....
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Provided itemgetter(0) is O(1) when used with data, the sort is O(n log n) both on average and in the worst case.
For more information on the sorting method used in Python, see Wikipedia.
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sorted is like sort except that the first builds a new sorted list from an iterable while sort do sort in place. The main difference will be space complexity.
Readthedocs
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Sorting, searching and algorithm analysis — Object-Oriented Programming in Python 1 documentation
Here are the space complexities of the algorithms above (for the worst case, and excluding the space required to store the input): None of these algorithms require a significant amount of storage space in addition to that used by the input list, except for the merge sort – which, as we saw in a previous section, requires temporary storage which is the same size as the input (and thus scales linearly with the input size). ... The Python ...
Programiz PRO
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Exploring Time and Space Complexities of Counting Sort
December 20, 2024 - So, regardless of the distribution of values, the total time complexity is O(n + k). Comparing the Number of Operations Required for Different Input Sizes · Counting sort requires two main arrays: the count array and the output array. In this algorithm: The size of the count array is determined ...
Medium
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A journey to master Sorting Algorithms | by Sylvain Tiset | Medium
October 31, 2024 - For the space complexity, it requires additional space for merging the sorted blocks so O(n) in the worst case. ... Tim Sort is used in Python’s sorted() function. Tree sort algorithm is based on Binary Search Tree (BST) data structure.
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Space Complexity in Python | PrepInsta
August 1, 2025 - On average, Quick Sort has a time complexity of O(n log n), making it significantly faster than Bubble Sort for larger datasets. In the worst case scenario, however, Quick Sort can degrade to O(n^2), particularly when the pivot selection leads ...
Built In
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Bubble Sort Time Complexity and Algorithm Explained | Built In
This means the space complexity is constant, or O(1). This makes it an in-place algorithm that works by modifying the input directly. This section implements the bubble sort algorithm using Python.
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Python, Sorting Algorithms, and Time and Space Complexities: Accessible Overview: 9798878566704: Computer Science Books @ Amazon.com
Python, Sorting Algorithms, and Time and Space Complexities: Accessible Overview: 9798878566704: Computer Science Books @ Amazon.com
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