14-06-2012, 04:25 PM
MULTIDIMENSIONAL LINKED LIST ON RECURSIVE ALGORITHM
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Abstract:
Multi-dimension linked lists is a new data structure, which has powerful function and well visiting performance. It can be applied in scientific computing analysis, image Processing, database index and so on. With the development of computer science, multi-dimension linked lists may be applied in other rectangular coordinate system’s spatial expression and multi-dimension linked lists recursive algorithm will give us very large significance. By the research of multi-dimension linked lists in this paper, it would be given out of the mathematical model and recursive algorithm of multi-dimension linked lists.
Data Structures
A data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently. Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example B-trees. Data structure is not a programming but this is a design concept of organizing data. Language it is a concise specification of a method for solving a problem. A data structure can be viewed as consisting of a set of Algorithms for performing operations on the data it stores. In conclusion, Data Structure + Algorithm = Programs
Self-Referential Structures:
-A self-referential structure is structure with a special member that points to the another structure variable of the same type, located anywhere on the heap area. In other words, each variable maintains a link to another variable of the same type, thus forming a non-contiguous, loosely linked data structure. This self-referential data structure is also called a linked list.
Functional recursion:-
A function may be partly defined in terms of itself. A familiar example is the Fibonacci number sequence: F (n) = F (n − 1) + F (n − 2). For such a definition to be useful, it must lead to values which are non-recursively defined, in this case F (0) = 0 and F (1) = 1. A famous recursive function is the Ackermann function which, unlike the Fibonacci sequence, cannot be expressed without recursion.
Recursion in computer science:-
A common method of simplification is to divide a problem into sub problems of the same type. As a computer programming technique, this is called divide and conquer and is key to the design of many important algorithms. Divide and conquer serves as a top-down approach to problem solving, where problems are solved by solving smaller and smaller instances. A contrary approach is dynamic programming. This approach serves as a bottom-up approach, where problems are solved by solving larger and larger instances, until the desired size is reached. A classic example of recursion is the definition of the factorial function, given here in C code:
Recursive Algorithms :
Recursion is a form of definition and of algorithms that is very important in computer science theory as well as in practice. Recursive algorithms can be inefficient or efficient. A recursive definition or a recursive algorithm is characterized by self-reference. Typically with recursion, a function is defined in terms of an earlier version of itself. Since this self-reference can't go on forever, there must be a termination condition. The termination condition is checked first and if it does not apply then the algorithm goes through with the self-reference.