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slow.html
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Document</title>
<style>
body {
background-color: #131236;
color: #fff;
font-family: Arial, sans-serif;
padding: 20px;
margin: 0;
}
.container {
max-width: 800px;
margin: 0 auto;
}
.section {
margin-bottom: 20px;
}
.section h2 {
font-size: 1.5rem;
margin-top: 0;
}
.section p {
line-height: 1.6;
}
</style>
</head>
<body>
<div class="container">
<div class="section">
<h2>Slow Convex Hull Algorithm</h2>
<p>
A slower approach to computing the convex hull involves a straightforward examination of all possible combinations of points to determine which ones form the boundary of the convex hull. This approach is less efficient compared to more optimized algorithms but is conceptually simple and easy to understand.
</p>
</div>
<div class="section">
<h2>Basic Outline of the Approach</h2>
<p><strong>Generate Combinations:</strong> Start by generating all possible combinations of points from the input set. Since the convex hull is formed by a subset of the input points, each combination represents a potential candidate for the convex hull.</p>
<p><strong>Check Convexity:</strong> For each combination of points, check if they form a convex shape. This can be done by examining the angles between consecutive points in the combination. If the angles are all less than 180 degrees, the points form a convex shape.</p>
<p><strong>Check Inclusion:</strong> Once a candidate convex shape is identified, check if all other points in the input set lie within or on the boundary of this shape. If a point lies outside the shape, discard the combination as it does not represent the convex hull.</p>
<p><strong>Repeat:</strong> Repeat steps 2 and 3 for all combinations of points.</p>
<p><strong>Identify Convex Hull:</strong> After examining all combinations, the convex hull is formed by the points that are part of the valid combinations. These points constitute the vertices of the convex hull.</p>
<p><strong>Output:</strong> Return the vertices of the convex hull as the final result.</p>
</div>
<div class="section">
<h2>Efficiency and Limitations</h2>
<p>This approach is straightforward but has a time complexity that grows exponentially with the number of input points, making it impractical for large datasets. However, it can be useful for educational purposes or for small input sizes where computational efficiency is not a concern.</p>
</div>
</div>
</body>
</html>