Data Structure of Linear Form: An In-Depth Exploration

Software Engineering
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Data Structure of Linear Form: An In-Depth Exploration

Preliminaries

In this article, we will delve into the world of data structures, specifically exploring the linear form, also known as a list. A linear table is a finite sequence of zero or more data elements, characterized by its sequential nature and limited size.

What is a Linear Table?

A linear table is a sequence of elements, where each element has a predecessor and a successor, except for the first and last elements, which only have a predecessor and a successor, respectively. The number of elements in a linear table is limited.

Basic Operations of the Linear List

The Abstract Data Type (ADT) of a linear table includes the following basic operations:

  • InitList(L): Initialize the linear table.
  • IsEmptyList(L): Determine whether the linear table is empty.
  • ClearList(L): Clear the linear table.
  • GetElemList(L, i, *e): Get the i-th position data.
  • SearchList(L, e): Find data elements equal to e.
  • InsertNodeList(L, i, e): Insert elements.
  • DeleteNodeList(L, i, *e): Delete the i-th position data.
  • GetLengthList(L): Get the length of the linear table.

What is a Sequential Storage Structure?

A sequential storage structure of a linear form refers to the data elements being stored in consecutive addresses within a storage unit. This is similar to an array, which is a sequential storage structure.

What is a Chain Storage Structure?

A chain storage structure is a type of storage structure where the memory unit stores a set of arbitrary linear form elements. Unlike a sequential storage structure, the elements in a chain storage structure can be stored in any location in memory.

What is a List?

A list is a linear chain of linked storage tables, where the logical connection between the nodes forms a linked storage structure. The memory cell storage node may be continuous or discontinuous, and the physical storage order does not matter.

Sequence Table (Sequential List)

A sequence table is a linear sequence storage table structure, where the data elements are stored in a contiguous array. The sequence table has the following characteristics:

  • The position of the storage space is an array of data.
  • The maximum capacity of the sequence table is MAXSIZE, which is the array length.
  • The current length of the sequence table is stored in the length variable.

Insertion and Deletion in a Sequence Table

Insertion and deletion in a sequence table involve shifting the elements to accommodate the new or deleted element. The insertion algorithm involves:

  1. Exception handling (insertion position is unreasonable, sequence table is full, etc.).
  2. Traversing the last element forward to the i-th position, moving each element back one place.
  3. Inserting the new element at the i-th position.
  4. Incrementing the table length.

The deletion algorithm involves:

  1. Exception handling (deletion position is unreasonable, sequence table is empty, etc.).
  2. Traversing the last element forward to the i-th position, moving each element forward in turn.
  3. Deleting the i-th position element.
  4. Decrementing the table length.

Code for Sequence Table

// Define the initial size of the storage space
#define MAXSIZE 10

// Define the data type
typedef int DataType;

// Define the structure for the sequence table
typedef struct {
    DataType data[MAXSIZE]; // Array to store the data
    int length; // Actual length
} SqlList;

Conclusion

In this article, we have explored the basics of linear tables, including the definition, basic operations, and storage structures. We have also discussed the sequence table, including its characteristics and insertion and deletion algorithms. In the next article, we will delve into the world of singly linked lists, circular lists, and doubly linked lists.