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<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1">
<meta name="description" content="Data Structures and Algorithms Crash Course with Animated Illustrations and Off-the-Shelf Code">
<meta name="description" content="Data structures and algorithms tutorial with animated illustrations and ready-to-run code">
<meta name="author" content="krahets">
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<span class="md-ellipsis">
Chapter 1. Encounter With Algorithms
Chapter 1. Encounter with Algorithms
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Chapter 1. Encounter With Algorithms
Chapter 1. Encounter with Algorithms
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Chapter 4. Array and Linked List
Chapter 4. Arrays and Linked Lists
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Chapter 4. Array and Linked List
Chapter 4. Arrays and Linked Lists
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4.4 Memory and Cache *
4.4 Random-Access Memory and Cache *
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Chapter 5. Stack and Queue
Chapter 5. Stacks and Queues
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Chapter 5. Stack and Queue
Chapter 5. Stacks and Queues
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5.3 Double-Ended Queue
5.3 Deque
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Chapter 6. Hashing
Chapter 6. Hash Table
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Chapter 6. Hashing
Chapter 6. Hash Table
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7.3 Array Representation of Tree
7.3 Array Representation of Binary Trees
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8.2 Building a Heap
8.2 Heap Construction Operation
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8.3 Top-K Problem
8.3 Top-k Problem
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10.2 Binary Search Insertion
10.2 Binary Search Insertion Point
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10.3 Binary Search Edge Cases
10.3 Binary Search Boundaries
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10.5 Search Algorithms Revisited
10.5 Searching Algorithms Revisited
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11.1 Sorting Algorithms
11.1 Sorting Algorithm
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12.4 Hanoi Tower Problem
12.4 Hanota Problem
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16.3 Terminology Table
16.3 Glossary
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<h1 id="31-classification-of-data-structures">3.1 &nbsp; Classification of Data Structures<a class="headerlink" href="#31-classification-of-data-structures" title="Permanent link">&para;</a></h1>
<p>Common data structures include arrays, linked lists, stacks, queues, hash tables, trees, heaps, and graphs. They can be classified from two dimensions: "logical structure" and "physical structure".</p>
<h2 id="311-logical-structure-linear-and-non-linear">3.1.1 &nbsp; Logical Structure: Linear and Non-Linear<a class="headerlink" href="#311-logical-structure-linear-and-non-linear" title="Permanent link">&para;</a></h2>
<p><strong>Logical structure reveals the logical relationships between data elements</strong>. In arrays and linked lists, data is arranged in a certain order, embodying the linear relationship between data; while in trees, data is arranged hierarchically from top to bottom, showing the derived relationship between "ancestors" and "descendants"; graphs are composed of nodes and edges, reflecting complex network relationships.</p>
<p><strong>Logical structure reveals the logical relationships between data elements</strong>. In arrays and linked lists, data is arranged in a certain order, embodying linear relationships between elements; while in trees, data is arranged hierarchically from top to bottom, showing parent-descendant relationships; graphs are composed of nodes and edges, reflecting complex network relationships.</p>
<p>As shown in Figure 3-1, logical structures can be divided into two major categories: "linear" and "non-linear". Linear structures are more intuitive, indicating that data is linearly arranged in logical relationships; non-linear structures are the opposite, arranged non-linearly.</p>
<ul>
<li><strong>Linear data structures</strong>: Arrays, linked lists, stacks, queues, hash tables, where elements have a one-to-one sequential relationship.</li>
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<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>It is worth noting that comparing memory to an Excel spreadsheet is a simplified analogy. The actual working mechanism of memory is quite complex, involving concepts such as address space, memory management, cache mechanisms, virtual memory, and physical memory.</p>
<p>It should be noted that comparing memory to an Excel spreadsheet is only a simplified analogy. The actual workings of memory are much more complex, involving concepts such as address space, memory management, cache mechanisms, virtual memory, and physical memory.</p>
</div>
<p>Memory is a shared resource for all programs. When a block of memory is occupied by a program, it usually cannot be used by other programs at the same time. <strong>Therefore, in the design of data structures and algorithms, memory resources are an important consideration</strong>. For example, the peak memory occupied by an algorithm should not exceed the remaining free memory of the system; if there is a lack of contiguous large memory blocks, then the data structure chosen must be able to be stored in dispersed memory spaces.</p>
<p>As shown in Figure 3-3, <strong>physical structure reflects the way data is stored in computer memory</strong>, and can be divided into contiguous space storage (arrays) and dispersed space storage (linked lists). The two physical structures exhibit complementary characteristics in terms of time efficiency and space efficiency.</p>
<p>As shown in Figure 3-3, <strong>physical structure reflects the way data is stored in computer memory</strong>. It can be divided into contiguous-space storage (arrays) and dispersed-space storage (linked lists). At a low level, physical structure determines how data is accessed, updated, inserted, and deleted. These two physical structures exhibit complementary characteristics in terms of time efficiency and space efficiency.</p>
<p><img alt="Contiguous space storage and dispersed space storage" class="animation-figure" src="../classification_of_data_structure.assets/classification_phisical_structure.png" /></p>
<p align="center"> Figure 3-3 &nbsp; Contiguous space storage and dispersed space storage </p>
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<li><strong>Can be implemented based on arrays</strong>: Stacks, queues, hash tables, trees, heaps, graphs, matrices, tensors (arrays with dimensions <span class="arithmatex">\(\geq 3\)</span>), etc.</li>
<li><strong>Can be implemented based on linked lists</strong>: Stacks, queues, hash tables, trees, heaps, graphs, etc.</li>
</ul>
<p>After initialization, linked lists can still adjust their length during program execution, so they are also called "dynamic data structures". After initialization, the length of arrays cannot be changed, so they are also called "static data structures". It is worth noting that arrays can achieve length changes by reallocating memory, thus possessing a certain degree of "dynamism".</p>
<p>After initialization, linked lists can still adjust their length during program execution, so they are also called "dynamic data structures". After initialization, the length of arrays cannot be changed, so they are also called "static data structures". It is worth noting that arrays can change length by reallocating memory, thus retaining a limited degree of flexibility.</p>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>If you find it difficult to understand physical structure, it is recommended to read the next chapter first, and then review this section.</p>