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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.
For example, the Lisp expression (cons 1 2) constructs a cell holding 1 in its left half (the so-called car field) and 2 in its right half (the cdr field). In Lisp notation, the value (cons 1 2) looks like: (1 . 2) Note the dot between 1 and 2; this indicates that the S-expression is a "dotted pair" (a so-called "cons pair"), rather than a "list."
Lists of pairs and functional maps both provide a purely functional interface. By contrast, hash tables provide an imperative interface. For many operations, hash tables are significantly faster than lists of pairs and functional maps.
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.
For example, one can add N numbers either by a simple loop that adds each datum to a single variable, or by a D&C algorithm called pairwise summation that breaks the data set into two halves, recursively computes the sum of each half, and then adds the two sums. While the second method performs the same number of additions as the first and pays ...
add a new (,) pair to the collection, mapping the key to its new value. Any existing mapping is overwritten. The arguments to this operation are the key and the value. Remove or delete remove a (,) pair from the collection, unmapping a given key from its value. The argument to this operation is the key.
The following is a list of well-known algorithms along with one-line descriptions for ... score between two pairs of text strings ... Used in Python 2.3 and up, and ...
Additionally, unless the list is regularly pruned to remove elements with duplicate keys, multiple values associated with the same key will increase the size of the list, and thus the time to search, without providing any compensatory advantage. One advantage of association lists is that a new element can be added in constant time.