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When the inputs are linked lists, this algorithm can be implemented to use only a constant amount of working space; the pointers in the lists' nodes can be reused for bookkeeping and for constructing the final merged list. 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 ...
If the running time (number of comparisons) of merge sort for a list of length n is T(n), then the recurrence relation T(n) = 2T(n/2) + n follows from the definition of the algorithm (apply the algorithm to two lists of half the size of the original list, and add the n steps taken to merge the resulting two lists). [5]
Another example is the merging two sorted lists: if their sentinels have data fields set to +∞, the choice of the next output node does not need special handling for empty lists. However, sentinel nodes use up extra space (especially in applications that use many short lists), and they may complicate other operations (such as the creation of ...
Merge sort takes advantage of the ease of merging already sorted lists into a new sorted list. It starts by comparing every two elements (i.e., 1 with 2, then 3 with 4...) and swapping them if the first should come after the second. It then merges each of the resulting lists of two into lists of four, then merges those lists of four, and so on ...
The classic merge outputs the data item with the lowest key at each step; given some sorted lists, it produces a sorted list containing all the elements in any of the input lists, and it does so in time proportional to the sum of the lengths of the input lists. Denote by A[1..p] and B[1..q] two arrays sorted in increasing order.
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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.
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