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Concept
Timsort
Summary
Timsort is a hybrid, sorting algorithm, derived from merge sort and insertion sort, designed to perform well on many kinds of real-world data. It was implemented by Tim Peters in 2002 for use in the Python programming language. The algorithm finds subsequences of the data that are already ordered (runs) and uses them to sort the remainder more efficiently. This is done by merging runs until certain criteria are fulfilled. Timsort has been Python's standard sorting algorithm since version 2.3. It is also used to sort arrays of non-primitive type in Java SE 7, on the Android platform, in GNU Octave, on V8, Swift, and Rust.
It uses techniques from Peter McIlroy's 1993 paper "Optimistic Sorting and Information Theoretic Complexity".
Timsort was designed to take advantage of runs of consecutive ordered elements that already exist in most real-world data, natural runs. It iterates over the data collecting elements into runs and simultaneously putting those runs in a stack. Whenever the runs on the top of the stack match a merge criterion, they are merged. This goes on until all data is traversed; then, all runs are merged two at a time and only one sorted run remains. The advantage of merging ordered runs instead of merging fixed size sub-lists (as done by traditional mergesort) is that it decreases the total number of comparisons needed to sort the entire list.
Each run has a minimum size, which is based on the size of the input and is defined at the start of the algorithm. If a run is smaller than this minimum run size, insertion sort is used to add more elements to the run until the minimum run size is reached.
Timsort is a stable sorting algorithm (order of elements with same key is kept) and strives to perform balanced merges (a merge thus merges runs of similar sizes).
In order to achieve sorting stability, only consecutive runs are merged. Between two non-consecutive runs, there can be an element with the same key inside the runs. Merging those two runs would change the order of equal keys.
Official source
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