notes we must find some way of representing the adts in terms of the data types and operators supported by the programming language itself to represent the mathematical model underlying an adtwe use data structureswhich are collection of variablespossibly of several data typesconnected in various ways the cell is the basic building block of data structures we can picture cell as box that is capable of holding value drawn from some basic or composite data type data structures are created by giving names to aggregates of cells and (optionallyinterpreting the values of some cells as representing relationships or connections ( pointersamong cells task value definition is one part of adt the second one is definition of data structure data structure is set of data values along with the relationship between the data values sincethe operations that can be performed on the data values depend on what kind of relationships exists among themwe can specify the relationship amongst the data values by specifying the operations permitted on the data values thereforewe can say that data structure is set of values along with the set of operations permitted on them it is also required to specify the semantics of the operations permitted on the data valuesand this is done by using set of axiomswhich describes how these operations workand therefore data structure is made of set of data values set of functions specifying the operations permitted on the data values set of axioms describing how these operations work hencewe conclude that data structure is triple ( , , )where is set of data values is set of functions is set of axioms triple (dfais referred to as an abstract data structure because it does not tell anything about its actual implementation it does not tell anything about how these values will be physically represented in the computer memory and these functions will be actually implemented therefore every abstract data structure is required to be implementedand the implementation of an abstract data structure requires mapping of the abstract data structure to be implemented into the data structure supported by the computer for exampleif the abstract data structure to be implemented is integerthen it can be implemented by mapping into bits which is data structure supported by hardware this requires that every integer data value is to be represented using suitable bit patterns and expressing the operations on integer data values in terms of operations for manipulating bits data structure mainly two types linear type data structure non-linear type data structure linear data structurea linear data structure traverses the data elements sequentiallyin which only one data element can directly be reached exarrayslinked lists lovely professional university