+ Plat
This commit is contained in:
Benjamin Qi
parent
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7 changed files with 189 additions and 35 deletions
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@ -83,8 +83,11 @@ Note that if it were not the case that all elements of the input array were dist
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* as far as I know, all gold problems have had only one possible output ...
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* [Out of Sorts (harder?)](http://www.usaco.org/index.php?page=viewproblem2&cpid=837)
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* Other Problems:
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* [USACO Plat Mincross](http://www.usaco.org/index.php?page=viewproblem2&cpid=720)
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* [Mega Inversions](https://open.kattis.com/problems/megainversions)
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* also just inversion counting
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* [Out of Sorts (USACO Silver)](http://usaco.org/index.php?page=viewproblem2&cpid=834)
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* aka [Sorting Steps](https://csacademy.com/contest/round-42/task/sorting-steps/) [](42)
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* Of course, this doesn't require anything other than sorting but fast range sum queries may make this easier.
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* Of course, this doesn't require anything other than sorting but fast range sum queries may make this easier.
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* [Twin Permutations](https://www.hackerearth.com/practice/data-structures/advanced-data-structures/fenwick-binary-indexed-trees/practice-problems/algorithm/mancunian-and-twin-permutations-d988930c/description/)
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* Offline 2D -> 1D
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@ -1,7 +1,7 @@
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---
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slug: /gold/topological-sort
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title: "Gold - Topological Sort"
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author: Unknown
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author: Benjamin Qi
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---
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## Gold - Topological Sort
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@ -18,4 +18,4 @@ author: Unknown
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### USACO Gold Problems
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- [Timeline](http://www.usaco.org/index.php?page=viewproblem2&cpid=1017)
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- [Milking Order](http://www.usaco.org/index.php?page=viewproblem2&cpid=838)
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- [Milking Order](http://www.usaco.org/index.php?page=viewproblem2&cpid=838)
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@ -12,32 +12,61 @@ Author: Benjamin Qi
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### Range Minimum Query
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* Tutorial
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* [Wikipedia](https://en.wikipedia.org/wiki/Range_minimum_query)
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* (add)
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- Tutorial
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- [Wikipedia](https://en.wikipedia.org/wiki/Range_minimum_query)
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- (add)
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### General Static Range Queries
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### General Static Range Queries (Online)
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* Static range queries in $O(1)$ time and $O(N\log N)$ preprocessing for any associative operation?
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* (add)
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- Static range queries in $O(1)$ time and $O(N\log N)$ preprocessing for any associative operation
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- (add)
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### Divide & Conquer
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- [DMOJ Continued Fractions](https://dmoj.ca/problem/dmopc19c7p4)
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- [USACO Plat NonDec](http://www.usaco.org/index.php?page=viewproblem2&cpid=997)
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## Segment Tree
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Author: Benjamin Qi
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This data structure allows you to do point update and range query in $O(\log N)$ time each for any associative operation.
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This data structure allows you to do point update and range query in $O(\log N)$ time each for any associative operation. In particular, note that **lazy** updates allow you to range updates as well.
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* Tutorial
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* CPH 9.3
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* [CSAcademy Tutorial](https://csacademy.com/lesson/segment_trees/)
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* [cp-algorithms](https://cp-algorithms.com/data_structures/segment_tree.html)
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* [Codeforces Tutorial](http://codeforces.com/blog/entry/18051)
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* [Slides from CPC.3](https://github.com/SuprDewd/T-414-AFLV/tree/master/03_data_structures)
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- Tutorial
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- CPH 9.3
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- [Codeforces Tutorial](http://codeforces.com/blog/entry/18051)
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- [CSAcademy Tutorial](https://csacademy.com/lesson/segment_trees/)
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- [cp-algorithms](https://cp-algorithms.com/data_structures/segment_tree.html)
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- [Slides from CPC.3](https://github.com/SuprDewd/T-414-AFLV/tree/master/03_data_structures)
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### Practice Problems
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* [USACO Springboards](http://www.usaco.org/index.php?page=viewproblem2&cpid=995)
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* can use segment tree with min query in place of the map mentioned in analysis
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* [POI Cards](https://szkopul.edu.pl/problemset/problem/qpsk3ygf8MU7D_1Es0oc_xd8/site/?key=statement) [](81)
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* [Counting Haybales (USACO Plat)](http://www.usaco.org/index.php?page=viewproblem2&cpid=578)
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* Lazy Updates
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### Problems
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- Normal SegTree
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- [USACO Old Gold Seating](http://www.usaco.org/index.php?page=viewproblem2&cpid=231) (check ...)
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- [USACO Old Gold Optimal Milking](http://www.usaco.org/index.php?page=viewproblem2&cpid=365) (check ...)
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- [USACO Old Gold Marathon](http://www.usaco.org/index.php?page=viewproblem2&cpid=495) (check ...)
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- [USACO Plat Balancing](http://www.usaco.org/index.php?page=viewproblem2&cpid=624) (check ...)
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- [USACO Plat Nocross](http://www.usaco.org/index.php?page=viewproblem2&cpid=721)
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- [USACO Gold Springboards](http://www.usaco.org/index.php?page=viewproblem2&cpid=995)
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- can use segment tree with min query in place of the map mentioned in analysis
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- [POI Cards](https://szkopul.edu.pl/problemset/problem/qpsk3ygf8MU7D_1Es0oc_xd8/site/?key=statement) [](81)
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- Lazy Updates
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- [USACO Old Gold The Lazy Cow](http://www.usaco.org/index.php?page=viewproblem2&cpid=418) (check ...)
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- [USACO Plat Counting Haybales](http://www.usaco.org/index.php?page=viewproblem2&cpid=578)
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## BIT Revisited
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Binary Indexed Trees can support range increments in addition to range sum queries.
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- [GFG Range Update Point Query](https://www.geeksforgeeks.org/binary-indexed-tree-range-updates-point-queries/)
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- [GFG Range Update Range Query](https://www.geeksforgeeks.org/binary-indexed-tree-range-update-range-queries/)
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- [My Implementation](https://github.com/bqi343/USACO/blob/master/Implementations/content/data-structures/1D%20Range%20Queries%20(9.2)/BITrange.h)
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Example problem:
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- [DMOJ Range Update Range Query](https://dmoj.ca/problem/acc3p4)
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You can extend this to higher dimensions as well (USACO Camp - "Cows Play Global Thermonuclear War").
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- [Paper](https://arxiv.org/pdf/1311.6093.pdf)
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@ -1,7 +1,40 @@
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---
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slug: /plat/2DRQ
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title: "Platinum - 2D Range Queries"
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author: ?
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author: Benjamin Qi
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---
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# Platinum - 2D Range Queries
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# Platinum - 2D Range Queries
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See [my implementations](https://github.com/bqi343/USACO/tree/master/Implementations/content/data-structures/2D%20Range%20Queries%20(15.2)).
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## Static Array Queries
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- [Multi-Dimensional RMQ (retrograd)](https://codeforces.com/blog/entry/53810)
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- GP of Serbia 2020 B
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## 2D BIT
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### Tutorials
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- [GFG 2D BIT](https://www.geeksforgeeks.org/two-dimensional-binary-indexed-tree-or-fenwick-tree/)
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- [TopCoder BIT](https://www.topcoder.com/community/competitive-programming/tutorials/binary-indexed-trees/)
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### Problems
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- [CSES Forest Queries II](https://cses.fi/problemset/task/1739)
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- [DMOJ Soriya's Programming Project](https://dmoj.ca/problem/dmopc19c7p5)
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- compressed 2D BIT
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- or do divide & conquer with a 1D BIT
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- [IOI 2007 Pairs](https://wcipeg.com/problem/ioi0722)
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- [DMOJ Crowded Cities](https://dmoj.ca/problem/bfs17p6)
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## 2D Segment Tree
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- Short Description
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- CSES 28.2, 28.4
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- Problems
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- [USACO Plat Friendcross](http://www.usaco.org/index.php?page=viewproblem2&cpid=722)
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- [USACO Plat Mowing](http://www.usaco.org/index.php?page=viewproblem2&cpid=601)
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- [POI Tetris 3D](https://szkopul.edu.pl/problemset/problem/OQjANSOOD_-c38gh8p6g3Gxp/site/?key=statement)
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- [IOI 2013 Game](http://wcipeg.com/problem/ioi1323)
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@ -1,10 +1,50 @@
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---
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slug: /plat/geo
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title: "Platinum - Geometry"
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author: ?
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author: Benjamin Qi
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---
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- Cross product, dot product, geometry primitives (shoelace, etc.)
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- Sweepline
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- CPH 29, 30.1?
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- Convex Hull
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# Platinum - Geometry
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## Primitives
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You should know basic operations like cross product and dot product. For platinum specifically, you should be fine as long as you know how to code convex hull.
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### Tutorial
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- CPH 29, 30.1
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- [TopCoder](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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- [C++ - std::complex](https://codeforces.com/blog/entry/22175)
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- [cp-algo - "Elementary Operations"](https://cp-algorithms.com/)
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- [vlecomte - geo book](https://codeforces.com/blog/entry/59129)
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- [My Templates](https://github.com/bqi343/USACO/tree/master/Implementations/content/geometry%20(13)/Primitives)
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## Sweep Line
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- [TopCoder Line Sweep](https://www.topcoder.com/community/competitive-programming/tutorials/line-sweep-algorithms/)
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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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## Convex Hull
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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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- [AGC 44 Random Pawn](https://atcoder.jp/contests/agc044/tasks/agc044_e)
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- Generalization of "Balance"
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13
content/4_Plat/Plat_Graphs.md
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13
content/4_Plat/Plat_Graphs.md
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@ -0,0 +1,13 @@
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---
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slug: /plat/trees
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title: "Platinum - Graphs"
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author: ?
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---
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SCC
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[USACO Old Gold Grass](http://www.usaco.org/index.php?page=viewproblem2&cpid=516)
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BCC
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[USACO Plat Push a Box](http://www.usaco.org/index.php?page=viewproblem2&cpid=769)
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---
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slug: /plat/trees
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title: "Platinum - Trees"
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author: ?
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author: Benjamin Qi
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---
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# Platinum - Trees
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- CPH 14, 18?
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- hasn’t been *required* aside from
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- *probably* won't see a repeat of this
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- [Milk Visits](http://www.usaco.org/index.php?page=viewproblem2&cpid=970) also mentions it
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- but no binary jumping required ...
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## Tree Diameter
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### Tutorial
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- CPH 14.2
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### Problems
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- [USACO Plat Newbarns](http://www.usaco.org/index.php?page=viewproblem2&cpid=817)
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- Copy of [Brain Network "Hard"](https://codeforces.com/contest/690/problem/C3)
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## Lowest Common Ancestor
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### Tutorial
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- CPH 18
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- [cp-algorithms: Lowest Common Ancestor](https://cp-algorithms.com/)
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### Problems
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- [USACO Plat Max Flow](http://www.usaco.org/index.php?page=viewproblem2&cpid=576)
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- [USACO Gold Milk Visits](http://www.usaco.org/index.php?page=viewproblem2&cpid=970)
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- [USACO Gold Cow Land](http://www.usaco.org/index.php?page=viewproblem2&cpid=921)
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- LCA + BIT
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- [USACO Plat Promote](http://www.usaco.org/index.php?page=viewproblem2&cpid=696)
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- Subtree + BIT
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- [USACO Plat Disrupt](http://www.usaco.org/index.php?page=viewproblem2&cpid=842)
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- HLD is possible, but just do binary jumps
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- [USACO Plat Tree Boxes](http://www.usaco.org/index.php?page=viewproblem2&cpid=948)
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- interactive!!
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- [USACO Plat Gathering](http://www.usaco.org/index.php?page=viewproblem2&cpid=866)
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- [USACO Plat Exercise](http://www.usaco.org/index.php?page=viewproblem2&cpid=901)
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- tricky
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## Centroid Decomposition
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- [USACO Plat - At Large](http://www.usaco.org/index.php?page=viewproblem2&cpid=793)
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- very tricky
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- [DMOJ Bob Equilibrium](https://dmoj.ca/problem/dmopc19c7p6)
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## Heavy-Light Decomposition
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