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The sequential merge sort procedure can be described in two phases, the divide phase and the merge phase. The first consists of many recursive calls that repeatedly perform the same division process until the subsequences are trivially sorted (containing one or no element). An intuitive approach is the parallelization of those recursive calls. [19]
The sort-merge join (also known as merge join) is a join algorithm and is used in the implementation of a relational database management system. The basic problem of a join algorithm is to find, for each distinct value of the join attribute, the set of tuples in each relation which display that value. The key idea of the sort-merge algorithm is ...
In the merge sort algorithm, this subroutine is typically used to merge two sub-arrays A[lo..mid], A[mid+1..hi] of a single array A. This can be done by copying the sub-arrays into a temporary array, then applying the merge algorithm above. [1] The allocation of a temporary array can be avoided, but at the expense of speed and programming ease.
Suppose that such an algorithm existed, then we could construct a comparison-based sorting algorithm with running time O(n f(n)) as follows: Chop the input array into n arrays of size 1. Merge these n arrays with the k-way merge algorithm. The resulting array is sorted and the algorithm has a running time in O(n f(n)).
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Pandas is built around data structures called Series and DataFrames. Data for these collections can be imported from various file formats such as comma-separated values, JSON, Parquet, SQL database tables or queries, and Microsoft Excel. [8] A Series is a 1-dimensional data structure built on top of NumPy's array.
Apple stock received a rare downgrade to "sell" from an analyst on Tuesday. The downgrade highlights premium-valuation concerns and some negative headlines in recent months.
President-elect Donald Trump speaks to members of the media following a meeting at the US Capitol on Jan. 8, 2025 in Washington, DC. Credit - Valerie Plesch—Bloomberg via Getty Images