Detailed explanation of data structure: from array to tree, and then to hash table

This article discusses several common data structures in depth, including arrays, linked lists, binary search trees (BSTs) and hash tables, and explains their organization in memory and their advantages and disadvantages.

Information structure and abstract data structure

Information structure refers to the way information is organized in memory, while abstract data structures are our conceptual understanding of these structures. Understanding abstract data structures helps us better implement various data structures in practice.

Stack and Queue

Queues are an abstract data structure that follows the FIFO (first in, first out) principle, similar to waiting in line. Its main operations include enqueuing (adding elements to the tail of the queue) and dequeuing (removing the head elements of the queue).

The stack follows the LIFO (Last In First Out) principle, just like stacking a plate. Its operations include pushing (adding elements to the top of the stack) and popping (removing top elements of the stack).

Array

An array is a structure that continuously stores data in memory. As shown in the figure below, arrays occupy continuous storage space in memory.

Other programs, functions, and variables may exist in memory, as well as redundant data that has been used before. If you need to add new elements to the array, you need to reallocate memory and copy the entire array, which can be inefficient.

Although pre-allocating too much memory can reduce copy operations, it will waste system resources. Therefore, it is crucial to allocate memory according to actual needs.

Link List

Linked lists are powerful data structures that allow concatenation of values ??located in different memory regions into a list and support dynamic expansion or reduction.

Each CS- Week 5 contains two values: the data value and a pointer to the next CS- Week 5. The pointer value of the last CS- Week 5 is NULL, indicating the end of the linked list.

In C language, CS- Week 5s can be defined as follows:

 <code class="c">typedef struct CS- Week 5 { int number; struct CS- Week 5 *next; } CS- Week 5;</code>

The following example shows the process of creating a linked list:

Disadvantages of linked lists include the need for additional memory storage pointers and the inability to directly access elements through indexes.

Binary Search Tree (BST)

A binary search tree is a tree structure that efficiently stores, searches and retrieves data.

The advantages of BST are dynamic and search efficiency (O(log n)), and the disadvantage is that the search efficiency drops to O(n) when the tree is unbalanced and requires additional memory storage pointers.

Hash table

A hash table is similar to a dictionary and contains key-value pairs. It uses a hash function to map keys to array indexes, thus achieving the average lookup time of O(1).

Hash conflicts (multiple keys mapped to the same index) can be resolved by linked lists or other methods. The design of hash functions is crucial to the performance of hash tables. An example of a simple hash function is as follows:

 <code class="c">#include <ctype.h> unsigned int hash(const char *word) { return toupper(word[0]) - 'A'; }</ctype.h></code>

This article is compiled based on cs50x 2024 source code.

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