split geo
This commit is contained in:
Benjamin Qi
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---
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id: geo
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title: "Geometry"
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id: geo-pri
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title: "Geometry Primitives"
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author: Benjamin Qi
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description: Geometry primitives and convex hull.
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description: Basic setup for geometry problems and introduction to line sweep.
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---
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## Primitives
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@ -16,7 +16,6 @@ You should know basic operations like cross product and dot product. For platinu
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- convex hulls
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- polygon area
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- point in polygon
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- closest pair of points
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- CPH 29
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- [TopCoder - Basic Geometry Concepts](https://www.topcoder.com/community/competitive-programming/tutorials/geometry-concepts-basic-concepts/)
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- [CF - Point Class](https://codeforces.com/blog/entry/48122)
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@ -53,40 +52,3 @@ You should know basic operations like cross product and dot product. For platinu
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- [Cow Steepchase II (Silver)](http://www.usaco.org/index.php?page=viewproblem2&cpid=943)
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- :|
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- [Kattis Closest Pair](https://open.kattis.com/problems/closestpair2)
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## [Convex Hull](https://en.wikipedia.org/wiki/Convex_hull_algorithms)
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- [Kattis Convex Hull](https://open.kattis.com/problems/convexhull)
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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
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- [USACO Plat Balance](http://www.usaco.org/index.php?page=viewproblem2&cpid=864)
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- [USACO Plat Falling](http://www.usaco.org/index.php?page=viewproblem2&cpid=998)
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- [USACO Old Gold - Fencing](http://www.usaco.org/index.php?page=viewproblem2&cpid=534)
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- [USACO Old Gold - Cow Curling](http://www.usaco.org/index.php?page=viewproblem2&cpid=382)
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- [Kattis Fence Orthogonality](https://open.kattis.com/problems/fenceortho)
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- [AGC 44 Random Pawn](https://atcoder.jp/contests/agc044/tasks/agc044_e)
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- Generalization of "Balance"
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## Half-Plane Intersection / Convex Stuff
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- [Blogewoosh (Half-Plane Intersection w/ Ternary Search)](https://codeforces.com/blog/entry/61710)
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- [retrograd Half-Plane Intersection](https://codeforces.com/blog/entry/61710?#comment-457662)
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- [Petr (Linear Half-Plane Intersection)](https://petr-mitrichev.blogspot.com/2016/07/a-half-plane-week.html)
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- [KACTL LineContainer](https://github.com/kth-competitive-programming/kactl/blob/master/content/data-structures/LineContainer.h)
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- [Lichao Segment Tree](http://codeforces.com/blog/entry/51275?#comment-351510)
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### Problems
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- [Bridges](https://csacademy.com/contest/archive/task/building-bridges/)
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- direct application of LineContainer
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45
content/6_Plat/Hull.md
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45
content/6_Plat/Hull.md
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@ -0,0 +1,45 @@
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---
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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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---
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## [Convex Hull](https://en.wikipedia.org/wiki/Convex_hull_algorithms)
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- [Kattis Convex Hull](https://open.kattis.com/problems/convexhull)
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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
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- [USACO Plat Balance](http://www.usaco.org/index.php?page=viewproblem2&cpid=864)
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- [USACO Plat Falling](http://www.usaco.org/index.php?page=viewproblem2&cpid=998)
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- [USACO Old Gold - Fencing](http://www.usaco.org/index.php?page=viewproblem2&cpid=534)
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- [USACO Old Gold - Cow Curling](http://www.usaco.org/index.php?page=viewproblem2&cpid=382)
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- [Kattis Fence Orthogonality](https://open.kattis.com/problems/fenceortho)
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- [AGC 44 Random Pawn](https://atcoder.jp/contests/agc044/tasks/agc044_e)
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- Generalization of "Balance"
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Minkowski addition?
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## Half-Plane Intersection / Convex Stuff
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- [Blogewoosh (Half-Plane Intersection w/ Ternary Search)](https://codeforces.com/blog/entry/61710)
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- [retrograd Half-Plane Intersection](https://codeforces.com/blog/entry/61710?#comment-457662)
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- [Petr (Linear Half-Plane Intersection)](https://petr-mitrichev.blogspot.com/2016/07/a-half-plane-week.html)
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- [KACTL LineContainer](https://github.com/kth-competitive-programming/kactl/blob/master/content/data-structures/LineContainer.h)
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- [Lichao Segment Tree](http://codeforces.com/blog/entry/51275?#comment-351510)
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### Problems
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- [Bridges](https://csacademy.com/contest/archive/task/building-bridges/)
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- direct application of LineContainer
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@ -4,7 +4,7 @@ title: "Slope Trick"
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author: Benjamin Qi
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prerequisites:
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-
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- some familiarity with at least one of the two tutorials mentioned in this module
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- Platinum - Convex Hull
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description: Ways to manipulate piecewise linear convex functions.
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---
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@ -22,7 +22,7 @@ From the latter link (modified):
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> - It can be divided into multiple sections, where each section is a linear function (usually) with an integer slope.
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> - It is a convex/concave function. In other words, the slope of each section is non-decreasing or non-increasing when scanning the function from left to right.
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It's generally applicable as a DP optimization. Usually you can come up with a slower DP (ex. $O(N^2)$) first and then optimize it to $O(N\log N)$ with slope trick.
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It's generally applicable as a DP optimization. Usually you can come up with a slower DP (ex. $O(N^2)$) first and then optimize it to $O(N\log N)$ with slope trick. The rest of this module assumes that you are somewhat familiar with at least one of the tutorials mentioned above.
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## [Buy Low Sell High](https://codeforces.com/contest/866/problem/D)
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@ -138,7 +138,13 @@ const ModuleOrdering = {
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"string-search",
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]
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},
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"geo",
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{
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name: "Geometry",
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items: [
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"geo-pri",
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"hull",
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]
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},
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"bitsets",
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"fracture",
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]
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