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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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<h2 id="411-common-array-operations">4.1.1 &nbsp; Common Array Operations<a class="headerlink" href="#411-common-array-operations" title="Permanent link">&para;</a></h2>
<h3 id="1-initializing-arrays">1. &nbsp; Initializing Arrays<a class="headerlink" href="#1-initializing-arrays" title="Permanent link">&para;</a></h3>
<p>We can choose between two array initialization methods based on our needs: without initial values or with given initial values. When no initial values are specified, most programming languages will initialize array elements to <span class="arithmatex">\(0\)</span>:</p>
<p>We can choose between two array initialization methods based on our needs: with or without initial values. When no initial values are specified, most programming languages initialize array elements to <span class="arithmatex">\(0\)</span>:</p>
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<h3 id="3-inserting-elements">3. &nbsp; Inserting Elements<a class="headerlink" href="#3-inserting-elements" title="Permanent link">&para;</a></h3>
<p>Array elements are stored "tightly adjacent" in memory, with no space between them to store any additional data. As shown in Figure 4-3, if we want to insert an element in the middle of an array, we need to shift all elements after that position backward by one position, and then assign the value to that index.</p>
<p>Array elements are packed tightly together in memory, with no extra space between them for additional data. As shown in Figure 4-3, if we want to insert an element in the middle of an array, we need to shift all subsequent elements one position to the right and then assign the value at that index.</p>
<p><img alt="Example of inserting an element into an array" class="animation-figure" src="../array.assets/array_insert_element.png" /></p>
<p align="center"> Figure 4-3 &nbsp; Example of inserting an element into an array </p>
<p>It is worth noting that since the length of an array is fixed, inserting an element will inevitably cause the element at the end of the array to be "lost". We will leave the solution to this problem for discussion in the "List" chapter.</p>
<p>It is worth noting that since the length of an array is fixed, inserting an element will inevitably push the last element out of the array. We will leave the solution to this problem for discussion in the "List" chapter.</p>
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<p><img alt="Example of removing an element from an array" class="animation-figure" src="../array.assets/array_remove_element.png" /></p>
<p align="center"> Figure 4-4 &nbsp; Example of removing an element from an array </p>
<p>Note that after the deletion is complete, the original last element becomes "meaningless", so we do not need to specifically modify it.</p>
<p>Note that after the deletion is complete, the original last element is no longer meaningful, so we do not need to modify it explicitly.</p>
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<ul>
<li><strong>High time complexity</strong>: The average time complexity for both insertion and deletion in arrays is <span class="arithmatex">\(O(n)\)</span>, where <span class="arithmatex">\(n\)</span> is the length of the array.</li>
<li><strong>Loss of elements</strong>: Since the length of an array is immutable, after inserting an element, elements that exceed the array's length will be lost.</li>
<li><strong>Memory waste</strong>: We can initialize a relatively long array and only use the front portion, so that when inserting data, the lost elements at the end are "meaningless", but this causes some memory space to be wasted.</li>
<li><strong>Memory waste</strong>: We can initialize a relatively long array and use only the front portion, so that any overwritten tail elements are merely unused placeholders, but this wastes some memory space.</li>
</ul>
<h3 id="5-traversing-arrays">5. &nbsp; Traversing Arrays<a class="headerlink" href="#5-traversing-arrays" title="Permanent link">&para;</a></h3>
<p>In most programming languages, we can traverse an array either by index or by directly iterating through each element in the array:</p>
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Chapter 4. &nbsp; Array and Linked List
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