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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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<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
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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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<span class="md-nav__icon md-icon"></span>
Chapter 6. Hashing
Chapter 6. Hash Table
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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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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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<li>In the coin change problem, for certain coin combinations, greedy algorithms can guarantee finding the optimal solution; for other coin combinations, however, greedy algorithms may find very poor solutions.</li>
<li>Problems suitable for solving with greedy algorithms have two major properties: greedy choice property and optimal substructure. The greedy choice property represents the effectiveness of the greedy strategy.</li>
<li>For some complex problems, proving the greedy choice property is not simple. Relatively speaking, disproving it is easier, such as in the coin change problem.</li>
<li>Solving greedy problems mainly consists of three steps: problem analysis, determining the greedy strategy, and correctness proof. Among these, determining the greedy strategy is the core step, and correctness proof is often the difficult point.</li>
<li>The fractional knapsack problem, based on the 0-1 knapsack problem, allows selecting a portion of items, and therefore can be solved using greedy algorithms. The correctness of the greedy strategy can be proven using proof by contradiction.</li>
<li>The max capacity problem can be solved using exhaustive enumeration with time complexity <span class="arithmatex">\(O(n^2)\)</span>. By designing a greedy strategy to move the short partition inward in each round, the time complexity can be optimized to <span class="arithmatex">\(O(n)\)</span>.</li>
<li>Solving greedy problems mainly consists of three steps: problem analysis, determining the greedy strategy, and correctness proof. Among these, determining the greedy strategy is the core step, and correctness proof is often the main difficulty.</li>
<li>The fractional knapsack problem, based on the 0-1 knapsack problem, allows selecting fractions of items, and therefore can be solved using greedy algorithms. The correctness of the greedy strategy can be proven using proof by contradiction.</li>
<li>The max capacity problem can be solved using exhaustive enumeration with time complexity <span class="arithmatex">\(O(n^2)\)</span>. By designing a greedy strategy to move the shorter side inward in each round, the time complexity can be optimized to <span class="arithmatex">\(O(n)\)</span>.</li>
<li>In the max product cutting problem, we successively derive two greedy strategies: integers <span class="arithmatex">\(\geq 4\)</span> should all continue to be split, and the optimal splitting factor is <span class="arithmatex">\(3\)</span>. The code includes exponentiation operations, and the time complexity depends on the implementation method of exponentiation, typically being <span class="arithmatex">\(O(1)\)</span> or <span class="arithmatex">\(O(\log n)\)</span>.</li>
</ul>