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| <h1 class="text-3xl font-extrabold text-white sm:text-4xl"> | |
| Sorting Algorithms Visualization | |
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| <p class="mt-3 max-w-2xl mx-auto text-xl text-gray-300"> | |
| Understand how different sorting algorithms work through interactive visualizations | |
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| <h2 class="text-xl font-bold text-white mb-4">Sorting Algorithms</h2> | |
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| <h3 class="font-medium text-white">Bubble Sort</h3> | |
| <p class="text-sm text-gray-300 mt-1">Simple comparison-based algorithm</p> | |
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| <h3 class="font-medium text-white">Merge Sort</h3> | |
| <p class="text-sm text-gray-300 mt-1">Divide and conquer approach</p> | |
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| <h3 class="font-medium text-white">Quick Sort</h3> | |
| <p class="text-sm text-gray-300 mt-1">Efficient partitioning algorithm</p> | |
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| <h3 class="font-medium text-white">Heap Sort</h3> | |
| <p class="text-sm text-gray-300 mt-1">Uses binary heap data structure</p> | |
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| <h3 class="font-medium text-white">Insertion Sort</h3> | |
| <p class="text-sm text-gray-300 mt-1">Builds final sorted array one item at a time</p> | |
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| <h3 class="font-medium text-white mb-3">Array Size</h3> | |
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| <h2 class="text-2xl font-bold text-white">Bubble Sort Visualization</h2> | |
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| Time: O(n²) | |
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| Space: O(1) | |
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| <div class="array-bar w-8 h-40 comparing"></div> | |
| <div class="array-bar w-8 h-28 swapping"></div> | |
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| <div class="array-bar w-8 h-44"></div> | |
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| <h3 class="font-bold text-white mb-2">Current Step</h3> | |
| <p class="text-gray-300">Comparing elements at positions 2 and 3. Since 40 > 28, we swap them.</p> | |
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| <!-- Pseudocode --> | |
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| <h3 class="font-bold text-white mb-2">Pseudocode</h3> | |
| <pre class="text-green-400 text-sm"> | |
| for i = 0 to n-1: | |
| for j = 0 to n-i-2: | |
| if array[j] > array[j+1]: | |
| swap(array[j], array[j+1])</pre> | |
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| <h3 class="font-bold text-white mb-3">Mathematical Analysis</h3> | |
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| \( \text{Worst Case: } O(n^2) \) | |
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| <p class="text-gray-300 mt-3"> | |
| In the worst case (reverse sorted array), bubble sort requires \( n-1 \) passes, | |
| with the \( i^{th} \) pass making \( n-i \) comparisons. The total number of | |
| comparisons is: | |
| </p> | |
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| \( \sum_{i=1}^{n-1}(n-i) = \frac{n(n-1)}{2} = O(n^2) \) | |
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