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This recursive property of Merge has been claimed to be a fundamental characteristic that distinguishes language from other cognitive faculties. As Noam Chomsky (1999) puts it, Merge is "an indispensable operation of a recursive system ... which takes two syntactic objects A and B and forms the new object G={A,B}" (p. 2). [1]
A list containing a single element is, by definition, sorted. Repeatedly merge sublists to create a new sorted sublist until the single list contains all elements. The single list is the sorted list. The merge algorithm is used repeatedly in the merge sort algorithm. An example merge sort is given in the illustration.
An example of such is the classic merge that appears frequently in merge sort examples. 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.
Example C-like code using indices for top-down merge sort algorithm that recursively splits the list (called runs in this example) into sublists until sublist size is 1, then merges those sublists to produce a sorted list. The copy back step is avoided with alternating the direction of the merge with each level of recursion (except for an ...
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
"Recursive algorithms are particularly appropriate when the underlying problem or the data to be treated are defined in recursive terms." [27] The examples in this section illustrate what is known as "structural recursion". This term refers to the fact that the recursive procedures are acting on data that is defined recursively.
The user can search for elements in an associative array, and delete elements from the array. The following shows how multi-dimensional associative arrays can be simulated in standard AWK using concatenation and the built-in string-separator variable SUBSEP:
The most important basic example of a datatype that can be defined by mutual recursion is a tree, which can be defined mutually recursively in terms of a forest (a list of trees). Symbolically: f: [t[1], ..., t[k]] t: v f A forest f consists of a list of trees, while a tree t consists of a pair of a value v and a forest f (its children). This ...