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en/chapter_stack_and_queue/deque/index.html
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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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<span class="md-ellipsis">
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
</label>
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<span class="md-ellipsis">
4.4 Memory and Cache *
4.4 Random-Access Memory and Cache *
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<span class="md-ellipsis">
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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<span class="md-ellipsis">
5.3 Double-Ended Queue
5.3 Deque
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<span class="md-ellipsis">
5.3 Double-Ended Queue
5.3 Deque
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<span class="md-ellipsis">
Chapter 6. Hashing
Chapter 6. Hash Table
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<span class="md-nav__icon md-icon"></span>
Chapter 6. Hashing
Chapter 6. Hash Table
</label>
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<span class="md-ellipsis">
7.3 Array Representation of Tree
7.3 Array Representation of Binary Trees
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<span class="md-ellipsis">
8.2 Building a Heap
8.2 Heap Construction Operation
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<span class="md-ellipsis">
8.3 Top-K Problem
8.3 Top-k Problem
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<span class="md-ellipsis">
10.2 Binary Search Insertion
10.2 Binary Search Insertion Point
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<span class="md-ellipsis">
10.3 Binary Search Edge Cases
10.3 Binary Search Boundaries
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<span class="md-ellipsis">
10.5 Search Algorithms Revisited
10.5 Searching Algorithms Revisited
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<span class="md-ellipsis">
11.1 Sorting Algorithms
11.1 Sorting Algorithm
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<span class="md-ellipsis">
12.4 Hanoi Tower Problem
12.4 Hanota Problem
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16.3 Terminology Table
16.3 Glossary
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<!-- Page content -->
<h1 id="53-deque">5.3 &nbsp; Deque<a class="headerlink" href="#53-deque" title="Permanent link">&para;</a></h1>
<p>In a queue, we can only remove elements from the front or add elements at the rear. As shown in Figure 5-7, a <u>double-ended queue (deque)</u> provides greater flexibility, allowing the addition or removal of elements at both the front and rear.</p>
<p>In a queue, we can only remove elements from the front or add elements at the rear. As shown in Figure 5-7, a <u>double-ended queue (deque)</u> provides greater flexibility, allowing elements to be added or removed at both the front and the rear.</p>
<p><img alt="Operations of deque" class="animation-figure" src="../deque.assets/deque_operations.png" /></p>
<p align="center"> Figure 5-7 &nbsp; Operations of deque </p>
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</tbody>
</table>
</div>
<p>Similarly, we can directly use the deque classes already implemented in programming languages:</p>
<p>Similarly, we can directly use the deque classes provided by the programming language:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
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en/chapter_stack_and_queue/index.html
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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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<title>Chapter 5. Stack and Queue - Hello Algo</title>
<title>Chapter 5. Stacks and Queues - Hello Algo</title>
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Chapter 5. &nbsp; Stack and Queue
Chapter 5. &nbsp; Stacks and Queues
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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
</label>
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<span class="md-ellipsis">
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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<span class="md-ellipsis">
4.4 Memory and Cache *
4.4 Random-Access Memory and Cache *
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<span class="md-ellipsis">
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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<span class="md-ellipsis">
5.3 Double-Ended Queue
5.3 Deque
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<span class="md-ellipsis">
Chapter 6. Hashing
Chapter 6. Hash Table
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Chapter 6. Hashing
Chapter 6. Hash Table
</label>
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<span class="md-ellipsis">
7.3 Array Representation of Tree
7.3 Array Representation of Binary Trees
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<span class="md-ellipsis">
8.2 Building a Heap
8.2 Heap Construction Operation
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<span class="md-ellipsis">
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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<span class="md-ellipsis">
11.1 Sorting Algorithms
11.1 Sorting Algorithm
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<span class="md-ellipsis">
12.4 Hanoi Tower Problem
12.4 Hanota Problem
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<span class="md-ellipsis">
16.3 Terminology Table
16.3 Glossary
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<!-- Page content -->
<h1 id="chapter-5-stack-and-queue">Chapter 5. &nbsp; Stack and Queue<a class="headerlink" href="#chapter-5-stack-and-queue" title="Permanent link">&para;</a></h1>
<p><img alt="Stack and Queue" class="cover-image" src="../assets/covers/chapter_stack_and_queue.jpg" /></p>
<h1 id="chapter-5-stacks-and-queues">Chapter 5. &nbsp; Stacks and Queues<a class="headerlink" href="#chapter-5-stacks-and-queues" title="Permanent link">&para;</a></h1>
<p><img alt="Stacks and Queues" class="cover-image" src="../assets/covers/chapter_stack_and_queue.jpg" /></p>
<div class="admonition abstract">
<p class="admonition-title">Abstract</p>
<p>Stacks are like stacking cats, while queues are like cats lining up.</p>
<p>They represent LIFO (Last In First Out) and FIFO (First In First Out) logic, respectively.</p>
<p>A stack is like cats piled on top of one another, while a queue is like cats lining up.</p>
<p>They represent the logical relationships of LIFO (Last In, First Out) and FIFO (First In, First Out), respectively.</p>
</div>
<h2 id="chapter-contents">Chapter contents<a class="headerlink" href="#chapter-contents" title="Permanent link">&para;</a></h2>
<ul>
<li><a href="stack/">5.1 &nbsp; Stack</a></li>
<li><a href="queue/">5.2 &nbsp; Queue</a></li>
<li><a href="deque/">5.3 &nbsp; Double-Ended Queue</a></li>
<li><a href="deque/">5.3 &nbsp; Deque</a></li>
<li><a href="summary/">5.4 &nbsp; Summary</a></li>
</ul>
en/chapter_stack_and_queue/queue/index.html
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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">
@@ -576,7 +576,7 @@
<span class="md-ellipsis">
Chapter 1. Encounter With Algorithms
Chapter 1. Encounter with Algorithms
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<span class="md-nav__icon md-icon"></span>
Chapter 1. Encounter With Algorithms
Chapter 1. Encounter with Algorithms
</label>
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<span class="md-ellipsis">
Chapter 4. Array and Linked List
Chapter 4. Arrays and Linked Lists
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<span class="md-nav__icon md-icon"></span>
Chapter 4. Array and Linked List
Chapter 4. Arrays and Linked Lists
</label>
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<span class="md-ellipsis">
4.4 Memory and Cache *
4.4 Random-Access Memory and Cache *
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<span class="md-ellipsis">
Chapter 5. Stack and Queue
Chapter 5. Stacks and Queues
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<span class="md-nav__icon md-icon"></span>
Chapter 5. Stack and Queue
Chapter 5. Stacks and Queues
</label>
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<span class="md-ellipsis">
5.3 Double-Ended Queue
5.3 Deque
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<span class="md-ellipsis">
Chapter 6. Hashing
Chapter 6. Hash Table
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<span class="md-nav__icon md-icon"></span>
Chapter 6. Hashing
Chapter 6. Hash Table
</label>
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<span class="md-ellipsis">
7.3 Array Representation of Tree
7.3 Array Representation of Binary Trees
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<span class="md-ellipsis">
8.2 Building a Heap
8.2 Heap Construction Operation
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<span class="md-ellipsis">
8.3 Top-K Problem
8.3 Top-k Problem
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<span class="md-ellipsis">
10.2 Binary Search Insertion
10.2 Binary Search Insertion Point
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<span class="md-ellipsis">
10.3 Binary Search Edge Cases
10.3 Binary Search Boundaries
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<span class="md-ellipsis">
10.5 Search Algorithms Revisited
10.5 Searching Algorithms Revisited
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<span class="md-ellipsis">
11.1 Sorting Algorithms
11.1 Sorting Algorithm
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<span class="md-ellipsis">
12.4 Hanoi Tower Problem
12.4 Hanota Problem
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<span class="md-ellipsis">
16.3 Terminology Table
16.3 Glossary
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<!-- Page content -->
<h1 id="52-queue">5.2 &nbsp; Queue<a class="headerlink" href="#52-queue" title="Permanent link">&para;</a></h1>
<p>A <u>queue</u> is a linear data structure that follows the First In First Out (FIFO) rule. As the name suggests, a queue simulates the phenomenon of lining up, where newcomers continuously join the end of the queue, while people at the front of the queue leave one by one.</p>
<p>A <u>queue</u> is a linear data structure that follows the First In, First Out (FIFO) rule. As the name suggests, it models people lining up: newcomers continuously join the rear of the queue, while the people at the front leave one by one.</p>
<p>As shown in Figure 5-4, we call the front of the queue the "front" and the end the "rear." The operation of adding an element to the rear is called "enqueue," and the operation of removing the front element is called "dequeue."</p>
<p><img alt="FIFO rule of queue" class="animation-figure" src="../queue.assets/queue_operations.png" /></p>
<p align="center"> Figure 5-4 &nbsp; FIFO rule of queue </p>
<h2 id="521-common-queue-operations">5.2.1 &nbsp; Common Queue Operations<a class="headerlink" href="#521-common-queue-operations" title="Permanent link">&para;</a></h2>
<p>The common operations on a queue are shown in Table 5-2. Note that method names may vary across different programming languages. We adopt the same naming convention as for stacks here.</p>
<p>The common operations on a queue are shown in Table 5-2. Note that method names may vary across programming languages. Here, we use the same naming convention as for stacks.</p>
<p align="center"> Table 5-2 &nbsp; Efficiency of Queue Operations </p>
<div class="center-table">
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</tbody>
</table>
</div>
<p>We can directly use the ready-made queue classes in programming languages:</p>
<p>We can directly use the queue classes provided by the programming language:</p>
<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
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<a
href="../deque/"
class="md-footer__link md-footer__link--next"
aria-label="Next: 5.3 Double-Ended Queue"
aria-label="Next: 5.3 Deque"
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>
<div class="md-footer__title">
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Next
</span>
<div class="md-ellipsis">
5.3 Double-Ended Queue
5.3 Deque
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<div class="md-footer__button md-icon">
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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">
@@ -576,7 +576,7 @@
<span class="md-ellipsis">
Chapter 1. Encounter With Algorithms
Chapter 1. Encounter with Algorithms
@@ -598,7 +598,7 @@
<span class="md-nav__icon md-icon"></span>
Chapter 1. Encounter With Algorithms
Chapter 1. Encounter with Algorithms
</label>
@@ -1183,7 +1183,7 @@
<span class="md-ellipsis">
Chapter 4. Array and Linked List
Chapter 4. Arrays and Linked Lists
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<span class="md-nav__icon md-icon"></span>
Chapter 4. Array and Linked List
Chapter 4. Arrays and Linked Lists
</label>
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<span class="md-ellipsis">
4.4 Memory and Cache *
4.4 Random-Access Memory and Cache *
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<span class="md-ellipsis">
Chapter 5. Stack and Queue
Chapter 5. Stacks and Queues
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<span class="md-nav__icon md-icon"></span>
Chapter 5. Stack and Queue
Chapter 5. Stacks and Queues
</label>
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<span class="md-ellipsis">
5.3 Double-Ended Queue
5.3 Deque
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<span class="md-ellipsis">
Chapter 6. Hashing
Chapter 6. Hash Table
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<span class="md-nav__icon md-icon"></span>
Chapter 6. Hashing
Chapter 6. Hash Table
</label>
@@ -2010,7 +2010,7 @@
<span class="md-ellipsis">
7.3 Array Representation of Tree
7.3 Array Representation of Binary Trees
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<span class="md-ellipsis">
8.2 Building a Heap
8.2 Heap Construction Operation
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<span class="md-ellipsis">
8.3 Top-K Problem
8.3 Top-k Problem
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<span class="md-ellipsis">
10.2 Binary Search Insertion
10.2 Binary Search Insertion Point
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<span class="md-ellipsis">
10.3 Binary Search Edge Cases
10.3 Binary Search Boundaries
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<span class="md-ellipsis">
10.5 Search Algorithms Revisited
10.5 Searching Algorithms Revisited
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<span class="md-ellipsis">
11.1 Sorting Algorithms
11.1 Sorting Algorithm
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<span class="md-ellipsis">
12.4 Hanoi Tower Problem
12.4 Hanota Problem
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<span class="md-ellipsis">
16.3 Terminology Table
16.3 Glossary
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<!-- Page content -->
<h1 id="51-stack">5.1 &nbsp; Stack<a class="headerlink" href="#51-stack" title="Permanent link">&para;</a></h1>
<p>A <u>stack</u> is a linear data structure that follows the Last In First Out (LIFO) logic.</p>
<p>A <u>stack</u> is a linear data structure that follows the Last In, First Out (LIFO) principle.</p>
<p>We can compare a stack to a pile of plates on a table. If we specify that only one plate can be moved at a time, then to get the bottom plate, we must first remove the plates above it one by one. If we replace the plates with various types of elements (such as integers, characters, objects, etc.), we get the stack data structure.</p>
<p>As shown in Figure 5-1, we call the top of the stacked elements the "top" and the bottom the "base." The operation of adding an element to the top is called "push," and the operation of removing the top element is called "pop."</p>
<p>As shown in Figure 5-1, we call the top of the stacked elements the "top" and the bottom the "bottom." The operation of adding an element to the top is called "push," and the operation of removing the top element is called "pop."</p>
<p><img alt="LIFO rule of stack" class="animation-figure" src="../stack.assets/stack_operations.png" /></p>
<p align="center"> Figure 5-1 &nbsp; LIFO rule of stack </p>
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</tbody>
</table>
</div>
<p>Typically, we can directly use the built-in stack class provided by the programming language. However, some languages may not provide a dedicated stack class. In these cases, we can use the language's "array" or "linked list" as a stack and ignore operations unrelated to the stack in the program logic.</p>
<p>Typically, we can directly use the built-in stack class provided by the programming language. However, some languages may not provide a dedicated stack class. In such cases, we can use the language's "array" or "linked list" as a stack and simply avoid using operations unrelated to stack behavior.</p>
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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
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7.3 Array Representation of Tree
7.3 Array Representation of Binary Trees
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11.1 Sorting Algorithms
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16.3 Glossary
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<h3 id="1-key-review">1. &nbsp; Key Review<a class="headerlink" href="#1-key-review" title="Permanent link">&para;</a></h3>
<ul>
<li>A stack is a data structure that follows the LIFO principle and can be implemented using arrays or linked lists.</li>
<li>In terms of time efficiency, the array implementation of a stack has higher average efficiency, but during expansion, the time complexity of a single push operation degrades to <span class="arithmatex">\(O(n)\)</span>. In contrast, the linked list implementation of a stack provides more stable efficiency performance.</li>
<li>In terms of time efficiency, the array implementation of a stack has higher average efficiency, but during expansion, the time complexity of a single push operation degrades to <span class="arithmatex">\(O(n)\)</span>. In contrast, the linked-list implementation of a stack offers more stable performance.</li>
<li>In terms of space efficiency, the array implementation of a stack may lead to some degree of space wastage. However, it should be noted that the memory space occupied by linked list nodes is larger than that of array elements.</li>
<li>A queue is a data structure that follows the FIFO principle and can also be implemented using arrays or linked lists. The conclusions regarding time efficiency and space efficiency comparisons for queues are similar to those for stacks mentioned above.</li>
<li>A deque is a queue with greater flexibility that allows adding and removing elements at both ends.</li>
</ul>
<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
<p><strong>Q</strong>: Is the browser's forward and backward functionality implemented with a doubly linked list?</p>
<p>The forward and backward functionality of a browser is essentially a manifestation of a "stack." When a user visits a new page, that page is added to the top of the stack; when the user clicks the back button, that page is popped from the top of the stack. Using a deque can conveniently implement some additional operations, as mentioned in the "Deque" section.</p>
<p>The browser's forward and backward behavior is essentially an application of a "stack." When a user visits a new page, that page is added to the top of the stack; when the user clicks the back button, that page is popped from the top of the stack. A deque can conveniently support some additional operations, as mentioned in the "Deque" section.</p>
<p><strong>Q</strong>: After popping from the stack, do we need to free the memory of the popped node?</p>
<p>If the popped node will still be needed later, then memory does not need to be freed. If it won't be used afterward, languages like Java and Python have automatic garbage collection, so manual memory deallocation is not required; in C and C++, manual memory deallocation is necessary.</p>
<p><strong>Q</strong>: A deque seems like two stacks joined together. What is its purpose?</p>
<p>A deque is like a combination of a stack and a queue, or two stacks joined together. It exhibits the logic of both stack and queue, so it can implement all applications of stacks and queues, and is more flexible.</p>
<p>A deque is like a combination of a stack and a queue, or two stacks joined together. It combines the logic of both, so it can support all applications of stacks and queues while offering greater flexibility.</p>
<p><strong>Q</strong>: How are undo and redo specifically implemented?</p>
<p>Use two stacks: stack <code>A</code> for undo and stack <code>B</code> for redo.</p>
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