Analysis
Merge algorithms generally run in time proportional to the sum of the lengths of the lists; merge algorithms that operate on large numbers of lists at once will multiply the sum of the lengths of the lists by the time to figure out which of the pointers points to the lowest item, which can be accomplished with a heap-based priority queue in O(log n) time, for O(m log n) time, where n is the number of lists being merged and m is the sum of the lengths of the lists. When merging two lists of length m, there is a lower bound of 2m − 1 comparisons required in the worst case.
The classic merge (the one used in merge sort) 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.
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