71 lines
2.7 KiB
Text
71 lines
2.7 KiB
Text
---
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id: hull
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title: "Convex Hull"
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author: Benjamin Qi
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description: Smallest convex polygon containing a set of points on a grid.
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prerequisites:
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- Platinum - Geometry Primitives
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frequency: 2
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---
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import { Problem } from "../models";
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export const metadata = {
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problems: {
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sample: [
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new Problem("Kattis", "Convex Hull", "convexhull", "Intro", false, ["convex"], ""),
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],
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sample2: [
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new Problem("Kattis","Robert Hood", "roberthood", "Intro", false, ["convex"], "doesn't require convex hull since coordinates are small"),
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],
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general: [
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new Problem("Plat", "Balance Beam", "864", "Easy", false, ["convex"], ""),
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new Problem("CF", "Water Balance", "problemset/problem/1299/C", "Easy", false, ["convex"], ""),
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new Problem("CF", "Geometers Anonymous", "problemset/problem/1195/F", "Normal", false, ["convex", "PURS"], ""),
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new Problem("Old Gold", "Cow Curling", "382", "Normal", false, ["convex"], "testing whether points are inside hull"),
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new Problem("AC", "AGC E - Random Pawn", "https://atcoder.jp/contests/agc044/tasks/agc044_e", "Very Hard", false, ["convex"], ""),
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],
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rotating: [
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new Problem("Kattis", "Fence Orthogonality", "fenceortho", "Normal", false, ["convex"], "enclosing rectangle"),
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],
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cht: [
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new Problem("Plat", "Circular Barn", "626", "Normal", false, ["DP", "convex"], ""),
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new Problem("Plat", "Falling Portals", "998", "Hard", false, ["convex"], ""),
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],
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}
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};
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## [Convex Hull](https://en.wikipedia.org/wiki/Convex_hull_algorithms)
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<problems-list problems={metadata.problems.sample} />
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### Tutorial
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- Graham Scan
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- [cp-algo](https://cp-algorithms.com/geometry/grahams-scan-convex-hull.html)
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- [My Implementation](https://github.com/bqi343/USACO/blob/master/Implementations/content/geometry%20(13)/Polygons/ConvexHull2.h)
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- Monotone Chain
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- CPH 30.3 (brief)
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- [Wikipedia](https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain)
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- [My Implementation](https://github.com/bqi343/USACO/blob/master/Implementations/content/geometry%20(13)/Polygons/ConvexHull%20(13.2).h)
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<problems-list problems={metadata.problems.general} />
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## Rotating Caliphers
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<problems-list problems={metadata.problems.sample2} />
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<resources>
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<resource source="CF" title="Rotating calipers technique and applications" url="blog/entry/46162"> </resource>
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</resources>
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<problems-list problems={metadata.problems.rotating} />
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## Convex Hull Trick
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<resources>
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<resource source="cp-algo" title="Convex Hull Trick" url="geometry/convex_hull_trick.html" starred> </resource>
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<resource source="CF" title="Convex Hull Trick - Geo Being Useful" url="blog/entry/63823" starred> </resource>
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</resources>
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<problems-list problems={metadata.problems.cht} />
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