Data structures and algorithms-Learning Note 3

Linear table (list)

Definition: A finite sequence consisting of 0 or more data elements.

Keywords

① sequence: It is a sequence, and the elements are sequentially

② If there are multiple elements: the first element has no precursor , the latter element has no successor, and the other element has only one precursor and subsequent

③ Limited.

The mathematical language is defined as follows

If the linear memento is (A1,...,ai-1,ai,ai+1,...,an), the table Ai-1 lead Ai,ai ahead of Ai+1, said Ai-1 is the direct precursor of AI, ai+1 is the direct successor of the AI elements

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The number of linear variable elements n (n>=0) is defined as the length of the linear table, when N=0 is, called the empty table .

Abstract data types

Definition of a data type: Refers to a set of properties of the same nature, and defines the general name of some operations on this set (such as Integer, float, etc.)

Data types in C can be divided into two categories

Atomic type: A basic type that can no longer be decomposed, such as Integer, float, character, and so on.

struct type: A combination of several types that can be decomposed, such as an integer array

abstract : Refers to extracting the nature of the universality of a transaction. It requires extracting the characteristics of the problem and ignoring the non-essential details, which is a generalization of things. Abstraction is a way of thinking, and it hides the intricacies of detail.

We abstract the existing data types, and we have abstract data types.

Abstract data type (ADT) refers to a mathematical model and defines a set of operations on the model

Meaning: Mathematical abstraction of data types

Standard format for abstract data types (pseudo-code):

ADT Abstract Data type

Data

Definition of logical relationship between data elements

Operation

Operation

Endadt

Abstract data type definitions for linear tables:

ADT Linear table (list)

Data:

The set of data objects for a linear table is {A1,A2,..., an}, and each element is of type datatype. wherein, in addition to the first A1, each of the meta-and only a direct precursor element, in addition to the last element an, each meta-and only a successor element, the data element is a one-to-ones relationship

Operation: Some of the following actions

initlist (*l): initialize operation, establish an empty linear table L

Listempty (L): Determine if the linear table is a null table, if the linear table is empty, return true, otherwise false

clearlist (*l): Empty the linear table

Getelem (l,i,*e): returns the first position element value in the linear table L to E

Locateelem (l,e): finds an element in the linear table L that is equal to the given value E, if the lookup succeeds, the return element in the table indicates success; otherwise, 0 indicates failure.

Listinsert (*l,i,e): inserts a new element in the linear table L in the first position E

Listdelete (*l,i,e): removes the i-position element in the linear table L and returns its value with E

listlength (L): Returns the number of elements of the linear table L

Endadt

Example: Implementing A=A∪B

The basic combination of operations we need to use

Listlength (L)--Returns the number of elements

Getelem (l,i,*e)--Returns the value of the I position element in the linear table L to E

Locataelem (L,e)--Finds an element in the linear table L that is equal to the given value E, if the lookup succeeds, the return element in the table indicates success; otherwise, a return of 0 indicates a failure.

Listinsert (*l,i,e)--Inserting a new element in the linear table L at the first position E

Instance code:

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Two types of storage structures for linear tables

Sequential storage: A data element (such as an array) that stores linear tables sequentially in sequential storage units

Sequential storage Structure Code:

#define MAXSIZE 20

typedef int ELEMTYPE;

typedef struct

{

Elemtype Data[maxsize];

int length;

}sqlist;

The structure package requires three properties:

The starting position of the storage space, array data, where it is stored is the storage location of the linear table storage space

Maximum storage capacity for linear tables: array length maxsize

Current length of linear table: length

Address calculation method:

Assuming that Elemtype occupies a C storage unit, the relationship between the i+1 data element and the first data element in your linear table is

LOC (ai+1) =loc (AI) +c

Code snippet:

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Chain-Store:

Data structures and algorithms-Learning Note 3