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The first phase of patience sort, the card game simulation, can be implemented to take O(n log n) comparisons in the worst case for an n-element input array: there will be at most n piles, and by construction, the top cards of the piles form an increasing sequence from left to right, so the desired pile can be found by binary search. [1]
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.
Because log(x) is the sum of the terms of the form log(1 + 2 −k) corresponding to those k for which the factor 1 + 2 −k was included in the product P, log(x) may be computed by simple addition, using a table of log(1 + 2 −k) for all k. Any base may be used for the logarithm table. [53]
The main disadvantage of merge sort is that it is an out-of-place algorithm, so when operating on arrays, efficient implementations require O(n) auxiliary space (vs. O(log n) for quicksort with in-place partitioning and tail recursion, or O(1) for heapsort).
In computer science, merge sort (also commonly spelled as mergesort and as merge-sort[2]) is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the relative order of equal elements is the same in the input and output.
The red boxes combine to form blue and green boxes. Every such box has the same structure: a red box is applied to the entire input sequence, then to each half of the result, then to each half of each of those results, and so on. All arrows point down (blue) or all point up (green). This structure is known as a butterfly network. If the input ...
Merge sort. In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending.
Partial sorting. In computer science, partial sorting is a relaxed variant of the sorting problem. Total sorting is the problem of returning a list of items such that its elements all appear in order, while partial sorting is returning a list of the k smallest (or k largest) elements in order. The other elements (above the k smallest ones) may ...