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Conceptually, the merge sort algorithm consists of two steps: Recursively divide the list into sublists of (roughly) equal length, until each sublist contains only one element, or in the case of iterative (bottom up) merge sort, consider a list of n elements as n sub-lists of size 1. A list containing a single element is, by definition, sorted.
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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.
<lists_t> is a sequence of tables to be combined]] local function list_combine (lists_t) local out_t = {}; for _, list_t in ipairs (lists_t) do-- for each list in <lists_t> for k, v in pairs (list_t) do-- extract each k/v pair out_t [k] = v;-- add to <out_t> end end return out_t;-- and done end--[[-----< T E M P L A T E _ L I S T _ G E T ...
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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]