freqs
This commit is contained in:
Benjamin Qi
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@ -29,14 +29,14 @@ For those of you with experience in software development, note that competitive
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The [USA Computing Olympiad](http://www.usaco.org/index.php?page=contests) is a national programming competition that occurs four times a year, with December, January, February, and US Open (March) contests. The regular contests are four hours long, and the US Open is five hours long. Each contest contains three problems. Solutions are evaluated and scored against a set of predetermined test cases that are not visible to the student. Scoring is out of 1000 points, with each problem being weighted equally (\~333 points). There are four divisions of contests: Bronze, Silver, Gold, and Platinum. After each contest, students who meet the contest-dependent cutoff for promotion will compete in the next division for future contests.
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## Guide Languages
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## About This Guide
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### Languages
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- For Bronze and Silver, we will provide code snippets in C++, Java, and Python.
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- For Gold, we will provide code snippets in C++ and Java and (sometimes) Python.
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- For Platinum, code snippets may only be provided in one language (typically either C++ or Java).
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All material in this guide will be grouped into **modules** such as the one you're reading right now.
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### Guidelines
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- For Bronze, Silver, and Gold contestants, we aim to be a "**one stop shop**," meaning that this is the only site you have to use to be exposed to most (if not all) of the topics required for Bronze - Gold.
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@ -46,21 +46,37 @@ All material in this guide will be grouped into **modules** such as the one you'
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- There are plenty of resources out there, but we do not expect you to click through all of them to find the information you want.
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- This means in addition to the link itself, we will try our best to provide information about what the link is about as well as the quality of the link.
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- We won't write something like "learn DP, here are 50 links that can teach you that." Instead, we will write "learn DP by first reading this one article, then reading this other article. For reference, here are some other links you can explore as you wish."
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- For Platinum contestants, there are too many topics for us to effectively cover all of them. We'll try our best to cover the main topics, but if you want to do well in Platinum, you will have to find additional resources on your own in addition to this site.
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- For Platinum contestants, there are too many topics for us to effectively cover all of them.
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- We'll try our best to cover the main topics, but if you want to do well in Platinum, you will have to find additional resources on your own in addition to this site.
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- Platinum modules may have more vague explanations compared to earlier divisions. If you're confused, you'll have to research the topic more on your own.
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### Lesson
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### Modules
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The first part of a module is the lesson.
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All material in this guide will be grouped into **modules** such as the one you're reading right now.
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<info-block title="Pro Tip">
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Hopefully these are helpful.
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</info-block>
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#### Lesson
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- Consists of text, videos, and simple problems.
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- Goal is to introduce you to the concept.
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- Everything should be completed in order.
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- Any problems here will generally be pure implementation.
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### Practice
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<optional-content title="Optional Content">
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It's okay to skip over these. Some material might not be useful for competitive programming.
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</optional-content>
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#### Practice
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- Link the relevant past USACO problems (and other recommended problems).
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- Problems should be sorted in order of how they are recommended be completed.
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- Add comments regarding difficulty and / or solution sketches.
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- Possibly include additional problems.
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- Add comments regarding solution sketches.
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- Possibly include additional problems.
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- Difficulty is relative to division. (?)
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@ -3,6 +3,7 @@ id: complete-search
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title: "Complete Search"
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author: Darren Yao
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description: In many problems (especially in Bronze) it suffices to check all possible cases in the solution space.
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frequency: 4
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---
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import { Problem } from "../models";
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@ -2,7 +2,8 @@
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id: intro-graphs
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title: Introduction to Graphs
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author: Darren Yao, Benjamin Qi
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description: "Graph theory is one of the most important topics at the Silver level and above, although some basic problems occasionally appear in Bronze."
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description: "?"
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frequency: 2
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---
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import { Problem } from "../models";
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@ -19,6 +20,12 @@ export const metadata = {
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}
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};
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<info-block title="Pro Tip">
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Very important at the Silver level and above, not very frequent in bronze.
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</info-block>
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Graphs can be used to represent many things, from images to wireless signals, but one of the simplest analogies is to a map. Consider a map with several cities and highways connecting the cities. Some problems relating to graphsare:
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- If we have a map with some cities and roads, what's the shortest distance I have to travel to get from point A to point B?
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@ -3,7 +3,7 @@ id: rect-geo
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title: "Rectangle Geometry"
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author: Darren Yao, Michael Cao, Benjamin Qi
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description: "Geometry problems on USACO Bronze are usually quite simple and limited to intersections and unions of squares or rectangles."
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frequency: 2
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---
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import { Problem } from "../models";
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@ -3,6 +3,7 @@ id: simulation
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title: "Simulation"
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author: Darren Yao
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description: "In many problems, we can just simulate what we're told to do by the problem statement."
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frequency: 4
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---
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import { Problem } from "../models"
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@ -6,6 +6,7 @@ prerequisites:
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- Silver - Introduction to Sorting
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- Silver - Stacks & Queues
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description: "?"
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frequency: 2
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---
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import { Problem } from "../models";
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@ -4,7 +4,8 @@ title: "Breadth First Search"
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author: Benjamin Qi
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prerequisites:
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- Silver - Depth First Search
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description: Traversing a graph in a way such that vertices closer to the starting vertex are processed first.
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description: "Traversing a graph in a way such that vertices closer to the starting vertex are processed first."
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frequency: 2
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---
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import { Problem } from "../models";
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@ -5,6 +5,7 @@ author: Darren Yao
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prerequisites:
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- Silver - Introduction to Sorting
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description: You should already be familiar with the concept of binary searching for a number in a sorted array. However, binary search can be extended to binary searching on the answer itself.
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frequency: 3
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---
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import { Problem } from "../models";
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@ -28,6 +29,12 @@ export const metadata = {
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}
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};
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<info-block title="Pro Tip">
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Quite frequent at the Silver level.
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</info-block>
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When we binary search on the answer, we start with a search space of size $N$ which we know the answer lies in. Then, each iteration of the binary search cuts the search space in half, so the algorithm tests $O(\log N)$ values. This is efficient and much better than testing each possible value in the search space.
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Let's say we have a function `check(x)` that returns true if the answer of $x$ is possible, and false otherwise. Usually, in such problems, we'll want to find the maximum or minimum value of $x$ such that `check(x)` is true. Similarly to how binary search on an array only works on a sorted array, binary search on the answer only works if the answer function is [monotonic](https://en.wikipedia.org/wiki/Monotonic_function), meaning that it is always non-decreasing or always non-increasing.
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@ -5,6 +5,7 @@ author: Siyong Huang
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prerequisites:
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- Bronze - Introduction to Graphs
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description: A way to traverse a graph using recursion.
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frequency: 4
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---
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import { Problem } from "../models";
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@ -50,6 +51,12 @@ export const metadata = {
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<problems-list problems={metadata.problems.sample} />
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<info-block title="Pro Tip">
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Quite frequent at the Silver level.
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</info-block>
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## Tutorial
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- Recommended:
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@ -5,6 +5,7 @@ author: Siyong Huang
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prerequisites:
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- Silver - Depth First Search
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description: Finding connected components in a graph that is respresented by a grid.
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frequency: 3
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---
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import { Problem } from "../models";
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}
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};
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<info-block title="Pro Tip">
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Quite frequent at the Silver level.
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</info-block>
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<problems-list problems={metadata.problems.sample} />
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## [Flood Fill](https://en.wikipedia.org/wiki/Flood_fill)
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prerequisites:
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- Silver - Depth First Search
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description: A functional graph is a digraph in which every vertex has exactly one outgoing edge.
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frequency: 1
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---
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@ -5,6 +5,7 @@ author: Darren Yao
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prerequisites:
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- Silver - Sorting with Custom Comparators
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description: Greedy algorithms select the optimal choice at each step instead of looking at the solution space as a whole. This reduces the problem to a smaller problem at each step.
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frequency: 3
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---
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import {Problem} from "../models"
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@ -5,6 +5,7 @@ author: Benjamin Qi
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prerequisites:
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- Bronze - Data Structures
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description: "More with iterators?"
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frequency: 2
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---
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(set iterators?)
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title: "Prefix Sums"
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author: Darren Yao, Eric Wei
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description: Computing range sum queries in constant time over a fixed array.
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frequency: 3
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---
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import { Problem } from "../models";
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}
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};
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<info-block title="Pro Tip">
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Quite frequent at the Silver level.
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</info-block>
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<problems-list problems={metadata.problems.sample} />
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## Additional Resources
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}
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};
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<info-block title="Pro Tip">
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Especially important for competitors using Java.
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</info-block>
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## Comparators
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Normally, sorting functions rely on moving objects with a lower value in front of objects with a higher value if sorting in ascending order, and vice versa if in descending order. This is done through comparing two objects at a time.
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## Additional Reading
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- CPH 4.5
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- [PAPS 3.2 3.3, 3.4, 6.2, 6.3, 6.5](https://www.csc.kth.se/~jsannemo/slask/main.pdf)
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- [PAPS 3.2, 3.3, 3.4, 6.2, 6.3, 6.5](https://www.csc.kth.se/~jsannemo/slask/main.pdf)
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## [Stacks](http://www.cplusplus.com/reference/stack/stack/)
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title: "Binary Jumping"
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author: Benjamin Qi
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description: Introduces the problems of finding level ancestors in a tree and computing the lowest common ancestors.
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frequency: 3
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---
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import { Problem } from "../models";
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- Silver - Functional Graphs
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- Gold - Breadth First Search
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description: A simple cycle is a non-empty path of distinct edges that start and end at the same vertex such that no vertex appears more than once. Describes how to detect cycles in both directed and undirected graphs.
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frequency: 0
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---
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import { Problem } from "../models";
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- Recursion
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- Silver - Prefix Sums
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description: Speeding up naive solutions with memoization.
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frequency: 4
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---
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import { Problem } from "../models";
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- Silver - Depth First Search
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- Gold - Introduction to Dynamic Programming
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description: What it sounds like.
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frequency: 1
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---
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@ -5,6 +5,7 @@ author: Benjamin Qi, Michael Cao
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prerequisites:
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- Silver - Depth First Search
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description: The Disjoint Set Union (DSU) data structure allows you to add edges to an initially empty graph and test whether two vertices of the graph are connected.
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frequency: 3
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---
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import { Problem } from "../models";
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title: "Hashing"
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author: Benjamin Qi
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description: Quickly test equality of substrings with a small probability of failure.
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frequency: 1
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---
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## Tutorial
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prerequisites:
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- Gold - Introduction to Dynamic Programming
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description: Divisibility and Modular Arithmetic
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frequency: 1
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---
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import { Problem } from "../models";
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- Gold - Shortest Paths
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- Gold - Disjoint Set Union
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description: A subset of the edges of a connected, undirected, edge-weighted graph that connects all the vertices to each other of minimum total weight, where no cycles are allowed.
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frequency: 2
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---
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import { Problem } from "../models";
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prerequisites:
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- Silver - Depth First Search
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description: "?"
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frequency: 1
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---
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import { Problem } from "../models";
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- Gold - Static Range Queries
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- Gold - Max Suffix Query with Insertions Only
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description: Range queries for any associative operation over an array with updates, using segment tree.
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frequency: 3
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---
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import { Problem } from "../models";
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prerequisites:
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- Silver - Prefix Sums
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description: Introducing Binary Indexed Trees & Indexed Sets (C++ only).
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frequency: 3
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---
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import { Problem } from "../models";
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prerequisites:
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- Gold - Breadth First Search
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description: Introduces Dijkstra's Algorithm for a single source as well as Floyd-Warshall for All-Pairs Shortest Path.
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frequency: 3
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---
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import { Problem } from "../models";
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Use *Dijkstra's Algorithm*.
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### Standard
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### Tutorial
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- CSES 13.2
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- Usually, it's this one that's applicable.
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- [CPC.8](https://github.com/SuprDewd/T-414-AFLV/tree/master/08_graphs_2)
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### $O(M\log N)$ implementation
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The USACO training pages present a $O(N^2)$ version, although this is rarely used nowadays.
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<optional-content title="Faster Dijkstra">
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Can be done in $O(M+N\log N)$ with Fibonacci heap.
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(link?)
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</optional-content>
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### Problems
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<problems-list problems={metadata.problems.dijk} />
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@ -3,6 +3,7 @@ id: SRQ
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title: "Static Range Queries"
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author: Benjamin Qi
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description: Range queries for any associative operation over a static array.
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frequency: 1
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---
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import { Problem } from "../models";
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## Problems
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<problems-list problems={metadata.problems.general} />
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- Silver - More with Maps & Sets
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- Silver - Amortized Analysis
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description: "Solving USACO Gold - Springboards."
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frequency: 1
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---
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import { Problem } from "../models";
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- Gold - Breadth First Search
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- Gold - Introduction to Dynamic Programming
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description: "?"
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frequency: 1
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---
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import { Problem } from "../models";
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new Problem("CSES", "Game Routes", "1681", "Easy", false, [], "counting paths on DAG"),
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new Problem("Kattis", "Quantum", "https://open.kattis.com/contests/acpc17open/problems/quantumsuperposition", "Easy", false, [], "enumerating paths on DAG"),
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new Problem("Gold", "Timeline", "1017", "Easy", false, [], "not explicitly given, but graph is a DAG"),
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new Problem("Gold", "Milking Order", "838", "Easy", false, ["TopoSort", "Binary Search"]),
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new Problem("Gold", "Milking Order", "838", "Normal", false, ["TopoSort", "Binary Search"]),
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new Problem("CSES", "Course Schedule II", "1681", "Hard", false, [], "equivalent to [Minimal Labels](https://codeforces.com/contest/825/problem/E)"),
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],
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}
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@ -41,10 +42,8 @@ A [topological sort](https://en.wikipedia.org/wiki/Topological_sorting) of a dir
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- DFS
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- [CSAcademy](https://csacademy.com/lesson/topological_sorting)
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- both BFS, DFS
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Consider [Khan's Algorithm](https://en.wikipedia.org/wiki/Topological_sorting#Kahn's_algorithm) for topological sorting.
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(note: lex min toposort?)
|
||||
The BFS version, known as [Kahn's Algorithm](https://en.wikipedia.org/wiki/Topological_sorting#Kahn's_algorithm), makes it obvious how to extract the lexicographically minimum topological sort.
|
||||
|
||||
## Dynamic Programming
|
||||
|
||||
|
|
@ -55,12 +54,20 @@ One useful property of directed acyclic graphs is, as the name suggests, that th
|
|||
Let's consider the classical problem [CSES Longest Flight Route](https://cses.fi/problemset/task/1680), where we must find the longest path in a DAG.
|
||||
|
||||
<spoiler title="Solution">
|
||||
Let `dp[curr] = longest path ending at the node curr`. Then, if we process states in topological order, the transition is relatively straightforward: `dp[curr] = max of all dp[prev] where prev represents a node with an edge going into the current node` (word better?). To reiterate, since the states a processed in topological order, we can guarantee that all possible `dp[prev]` are computed before we compute `dp[curr]`.
|
||||
|
||||
Let $dp[v]$ denote the length of the longest path ending at the node $v$. Clearly
|
||||
|
||||
$$
|
||||
dp[v]=\max_{\text{edge } u\to v \text{ exists}}dp[u]+1,
|
||||
$$
|
||||
|
||||
or zero if $v$ has in-degree $0$. If we process the states in topological order, it is guarangeed that $dp[u]$ will already have been computed before computing $dp[v]$.
|
||||
|
||||
</spoiler>
|
||||
|
||||
However, not all problems clearly give you directed acyclic graphs (ex. [Plat - Cave Paintings](http://usaco.org/index.php?page=viewproblem2&cpid=996)). An important step in many problems is to reduce the statement into a directed acyclic graph. See the editorial of the linked problem for more information.
|
||||
<!-- However, not all problems clearly give you directed acyclic graphs (ex. [Plat - Cave Paintings](http://usaco.org/index.php?page=viewproblem2&cpid=996)). An important step in many problems is to reduce the statement into a directed acyclic graph. See the editorial of the linked problem for more information.
|
||||
|
||||
(Ben - this last paragraph doesn't seem very helpful.)
|
||||
(Ben - this last paragraph doesn't seem very helpful.) -->
|
||||
|
||||
## Problems
|
||||
|
||||
|
|
|
|||
|
|
@ -7,7 +7,7 @@ prerequisites:
|
|||
- Gold - Static Range Queries
|
||||
- Gold - Point Update Range Sum
|
||||
description: Subtree updates and queries and another way to compute lowest common ancestors.
|
||||
frequency: 3
|
||||
frequency: 2
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
prerequisites:
|
||||
- Platinum - Range Update Range Query
|
||||
description: "Extending Range Queries to 2D (and beyond)."
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
See [my implementations](https://github.com/bqi343/USACO/tree/master/Implementations/content/data-structures/2D%20Range%20Queries%20(15.2)).
|
||||
|
|
|
|||
|
|
@ -182,6 +182,8 @@ int main() {
|
|||
|
||||
</spoiler>
|
||||
|
||||
Apparently no test case contains more than $25000$ distinct colors, so we don't actually need to split the calculation into two halves.
|
||||
|
||||
## Lots of Triangles
|
||||
|
||||
<problems-list problems={metadata.problems.lots} />
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
prerequisites:
|
||||
- Silver - Depth First Search
|
||||
description: "?"
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
|
|||
|
|
@ -6,6 +6,7 @@ prerequisites:
|
|||
- Bit Operations
|
||||
- Gold - Introduction to Dynamic Programming
|
||||
description: DP problems that require iterating over subsets.
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
@ -15,6 +16,7 @@ export const metadata = {
|
|||
general: [
|
||||
new Problem("CSES", "Hamiltonian Flights", "1690", "Easy", false, ["Bitmasks"], ""),
|
||||
new Problem("CSES", "Elevator Rides", "1653", "Normal", false, ["Bitmasks"], ""),
|
||||
new Problem("ojuz", "IZhO Bank", "IZhO14_bank", "Normal", false, ["Bitmasks"], ""),
|
||||
new Problem("YS", "Max Indep Set", "maximum_independent_set", "Hard", false, ["Bitmasks", "Meet in Middle"], ""),
|
||||
],
|
||||
}
|
||||
|
|
@ -33,7 +35,7 @@ Has not been the solution to any platinum problem, but appeared in old gold and
|
|||
|
||||
<problems-list problems={metadata.problems.general} />
|
||||
|
||||
- [Old Gold - Moovie Moving](http://www.usaco.org/index.php?page=viewproblem2&cpid=515)
|
||||
- [Old Gold - Moovie Mooving](http://www.usaco.org/index.php?page=viewproblem2&cpid=515)
|
||||
- [AC Matching](https://atcoder.jp/contests/dp/tasks/dp_o)
|
||||
- [CF Square Subsets](https://codeforces.com/contest/895/problem/C)
|
||||
- [CF Guards in the Storehouse](https://codeforces.com/problemset/problem/845/F)
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Michael Cao
|
|||
prerequisites:
|
||||
- Gold - Introduction to Dynamic Programming
|
||||
description: Solving the problem on every contiguous subarray of the original array.
|
||||
frequency: 2
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
prerequisites:
|
||||
- Silver - Depth First Search
|
||||
description: Visiting all edges of a graph exactly once.
|
||||
frequency: 0
|
||||
---
|
||||
|
||||
Has not appeared on a recent USACO contest.
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
description: "?"
|
||||
prerequisites:
|
||||
- "?"
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
prerequisites:
|
||||
- Gold - Breadth First Search
|
||||
description: Introduces maximum flow as well as flow with lower bounds.
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
Has not been the solution to any platinum problem, but appeared in old gold.
|
||||
|
|
|
|||
|
|
@ -6,8 +6,25 @@ prerequisites:
|
|||
- Gold - Minimum Spanning Tree
|
||||
- some familiarity with "Robotic Cow Herd" solution
|
||||
description: A simple solution to "Robotic Cow Herd" that generalizes.
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
||||
export const metadata = {
|
||||
problems: {
|
||||
sample: [
|
||||
new Problem("Plat", "Robotic Cow Herd", "674", "Normal", false, [], ""),
|
||||
],
|
||||
general: [
|
||||
new Problem("CSES", "Baltic OI - Olympiads", "https://cses.fi/248/list/", "Hard", false, [], "Each state has $\le K$ children."),
|
||||
new Problem("DMOJ", "CCO - Shopping Plans", "cco20p6", "Very Hard", false, [], "Generalization of RoboHerd."),
|
||||
new Problem("YS", "K-th Shortest Walk", "k_shortest_walk", "Very Hard", false, [], "(english description?), [Relevant Paper](https://www.ics.uci.edu/~eppstein/pubs/Epp-SJC-98.pdf), Can use to solve RoboHerd!"),
|
||||
],
|
||||
}
|
||||
};
|
||||
|
||||
|
||||
## General Outline
|
||||
|
||||
### Problem
|
||||
|
|
@ -22,7 +39,11 @@ Suppose that you have a rooted tree where each vertex $i$ has a value $v_i$. Als
|
|||
|
||||
We'll focus on the first approach.
|
||||
|
||||
*Note:* There are ways to do this in $O(K)$ time for a binary tree if you don't need to return the values in sorted order (see [here](https://www.sciencedirect.com/science/article/pii/S0890540183710308)), but we won't consider this.
|
||||
<optional-content title="A Faster Solution">
|
||||
|
||||
There are ways to do this in $O(K)$ time for a binary tree if you don't need to return the values in sorted order (see [here](https://www.sciencedirect.com/science/article/pii/S0890540183710308)).
|
||||
|
||||
</optional-content>
|
||||
|
||||
### Generalizing
|
||||
|
||||
|
|
@ -35,13 +56,13 @@ Suppose that you want to find the $K$ objects with the smallest values in some (
|
|||
|
||||
Essentially, we start with the entire search space and then we *fracture* it into *subspaces* based on the children of the root. Then we can finish with either of the two approaches.
|
||||
|
||||
## Finding K-th Smallest Spanning Tree (USACO Camp 2018)
|
||||
## $K$-th Smallest Spanning Tree (USACO Camp 2018)
|
||||
|
||||
Let's look at an example.
|
||||
|
||||
### Problem
|
||||
|
||||
Given a graph with $N\le 50$ vertices and at most $\binom{N}{2}$ edges, find the $K$-th ($K\le 10^4$) smallest spanning tree.
|
||||
> Given a graph with $N\le 50$ vertices and at most $\binom{N}{2}$ edges, find the $K$-th ($K\le 10^4$) smallest spanning tree.
|
||||
|
||||
(Note: not solved in contest.)
|
||||
|
||||
|
|
@ -124,7 +145,9 @@ int main() {
|
|||
</spoiler>
|
||||
|
||||
|
||||
## [USACO Robotic Cow Herd](http://www.usaco.org/index.php?page=viewproblem2&cpid=674)
|
||||
## Robotic Cow Herd
|
||||
|
||||
<problems-list problems={metadata.problems.sample} />
|
||||
|
||||
As with the analysis, for each location you should
|
||||
|
||||
|
|
@ -134,7 +157,7 @@ As with the analysis, for each location you should
|
|||
|
||||
Importantly, we should then sort the locations by their respective second-minimum controller costs.
|
||||
|
||||
## Approach 1
|
||||
### Approach 1
|
||||
|
||||
Binary search on the cost $c$ of the $K$-th robot. If we can compute the costs of all robots with cost at most $c$ or say that there are more than $K$ in $O(K)$ time, then we can solve this problem in $O(N\log N+K\log \max(c))$ time (similar to "Approach 2" above). This is the approach that the first analysis solution takes, although it includes an extra $\log N$ factor due to `upper_bound`. I have removed this in my solution below.
|
||||
|
||||
|
|
@ -199,7 +222,7 @@ int main() {
|
|||
|
||||
</spoiler>
|
||||
|
||||
## Approach 2
|
||||
### Approach 2
|
||||
|
||||
There's also an $O(N\log N+K\log K)$ time solution with a priority queue that constructs the robots in increasing order of cost. As before, we want each robot to have a bounded number of "child" robots. However, if you look at my DFS function above, it seems that every robot can have up to $N$ children! Nevertheless, the DFS takes $O(K)$ rather than $O(KN)$ time due to the break statement, which works since we sorted by second-cheapest robot.
|
||||
|
||||
|
|
@ -285,11 +308,4 @@ int main() {
|
|||
|
||||
## Other Problems
|
||||
|
||||
- [Baltic OI 2019 - Olympiads](https://cses.fi/248/list/)
|
||||
- Each state has $\le K$ children.
|
||||
- [CCO 20 Shopping Plans](https://dmoj.ca/problem/cco20p6)
|
||||
- Generalization of RoboHerd
|
||||
- [K-th Shortest Walk](https://judge.yosupo.jp/problem/k_shortest_walk)
|
||||
- (english description?)
|
||||
- [Relevant Paper](https://www.ics.uci.edu/~eppstein/pubs/Epp-SJC-98.pdf)
|
||||
- Can use to solve RoboHerd!
|
||||
<problems-list problems={metadata.problems.general} />
|
||||
|
|
@ -6,6 +6,7 @@ prerequisites:
|
|||
- Gold - Euler Tour on Tree
|
||||
- Platinum - Range Update Range Query
|
||||
description: Path and subtree updates and queries.
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
|
|||
|
|
@ -5,11 +5,38 @@ author: Benjamin Qi
|
|||
description: Smallest convex polygon containing a set of points on a grid.
|
||||
prerequisites:
|
||||
- Platinum - Geometry Primitives
|
||||
frequency: 2
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
||||
export const metadata = {
|
||||
problems: {
|
||||
sample: [
|
||||
new Problem("Kattis", "Convex Hull", "convexhull", "Intro", false, ["convex"], ""),
|
||||
],
|
||||
sample2: [
|
||||
new Problem("Kattis","Robert Hood", "roberthood", "Intro", false, ["convex"], "doesn't require convex hull since coordinates are small"),
|
||||
],
|
||||
general: [
|
||||
new Problem("Plat", "Balance Beam", "864", "Easy", false, ["convex"], ""),
|
||||
new Problem("CF", "Geometers Anonymous", "problemset/problem/1195/F", "Normal", false, ["convex", "PURS"], ""),
|
||||
new Problem("Old Gold", "Cow Curling", "382", "Normal", false, ["convex"], "testing whether points are inside hull"),
|
||||
new Problem("AC", "AGC E - Random Pawn", "https://atcoder.jp/contests/agc044/tasks/agc044_e", "Very Hard", false, ["convex"], ""),
|
||||
],
|
||||
rotating: [
|
||||
new Problem("Kattis", "Fence Orthogonality", "fenceortho", "Normal", false, ["convex"], "enclosing rectangle"),
|
||||
],
|
||||
cht: [
|
||||
new Problem("Plat", "Circular Barn", "626", "Normal", false, ["DP", "convex"], ""),
|
||||
new Problem("Plat", "Falling Portals", "998", "Hard", false, ["convex"], ""),
|
||||
],
|
||||
}
|
||||
};
|
||||
|
||||
## [Convex Hull](https://en.wikipedia.org/wiki/Convex_hull_algorithms)
|
||||
|
||||
- [Kattis Convex Hull](https://open.kattis.com/problems/convexhull)
|
||||
<problems-list problems={metadata.problems.sample} />
|
||||
|
||||
### Tutorial
|
||||
|
||||
|
|
@ -21,21 +48,21 @@ prerequisites:
|
|||
- [Wikipedia](https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain)
|
||||
- [My Implementation](https://github.com/bqi343/USACO/blob/master/Implementations/content/geometry%20(13)/Polygons/ConvexHull%20(13.2).h)
|
||||
|
||||
### Problems
|
||||
<problems-list problems={metadata.problems.general} />
|
||||
|
||||
- [USACO Plat - Balance Beam](http://www.usaco.org/index.php?page=viewproblem2&cpid=864)
|
||||
- quite easy (but make sure to avoid precision issues)
|
||||
- [USACO Plat - Falling Portals](http://www.usaco.org/index.php?page=viewproblem2&cpid=998)
|
||||
- [USACO Old Gold - Fencing](http://www.usaco.org/index.php?page=viewproblem2&cpid=534)
|
||||
- [USACO Old Gold - Cow Curling](http://www.usaco.org/index.php?page=viewproblem2&cpid=382)
|
||||
- [Kattis Fence Orthogonality](https://open.kattis.com/problems/fenceortho)
|
||||
- [AGC 44 Random Pawn](https://atcoder.jp/contests/agc044/tasks/agc044_e)
|
||||
- Generalization of "Balance Beam"
|
||||
## Rotating Caliphers
|
||||
|
||||
Minkowski addition?
|
||||
|
||||
## With DP
|
||||
<problems-list problems={metadata.problems.sample2} />
|
||||
|
||||
cbarn
|
||||
diameter of point set:
|
||||
|
||||
mowing
|
||||
- [CF Comment](https://codeforces.com/blog/entry/46162)
|
||||
|
||||
<problems-list problems={metadata.problems.rotating} />
|
||||
|
||||
## Convex Hull Trick
|
||||
|
||||
- [CF Tutorial](https://codeforces.com/blog/entry/63823)
|
||||
|
||||
<problems-list problems={metadata.problems.cht} />
|
||||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
description: Convex Container
|
||||
prerequisites:
|
||||
- Platinum - Convex Hull
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
## Half-Plane Intersection / Convex Stuff
|
||||
|
|
@ -22,5 +23,7 @@ prerequisites:
|
|||
- [Bridges](https://csacademy.com/contest/archive/task/building-bridges/)
|
||||
- direct application of LineContainer
|
||||
|
||||
- [USACO Old Gold - Fencing](http://www.usaco.org/index.php?page=viewproblem2&cpid=534)
|
||||
|
||||
(add ICPC probs)
|
||||
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
prerequisites:
|
||||
- Gold - Topological Sort
|
||||
description: Includes 2-edge-connected components, strongly connected components, and biconnected components.
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
*Some problems sourced from [here](http://codeforces.com/blog/entry/54526?#comment-385354).*
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
prerequisites:
|
||||
- Gold - Point Update Range Query
|
||||
description: Lazy updates on segment trees and two binary indexed trees in conjunction.
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
prerequisites:
|
||||
- Gold - Shortest Paths with Non-Negative Edge Weights
|
||||
description: Applications of Bellman-Ford.
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
- Hasn't appeared in recent USACO Gold as far as I know.
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
prerequisites:
|
||||
- Platinum - Convex Hull
|
||||
description: Ways to manipulate piecewise linear convex functions.
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
prerequisites:
|
||||
- Silver - Depth First Search
|
||||
description: Knuth-Morris-Pratt and Z Algorithms (and a few more related topics).
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
## General Resources
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
description: Sorting Suffixes of a String
|
||||
prerequisites:
|
||||
- Gold - Hashing
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
https://judge.yosupo.jp/problem/suffixarray
|
||||
|
|
|
|||
|
|
@ -3,6 +3,7 @@ id: tries
|
|||
title: "Tries"
|
||||
author: Benjamin Qi
|
||||
description: ?
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
|
|||
|
|
@ -5,12 +5,9 @@ author: Benjamin Qi
|
|||
description: "CSES Critical Cities and Extensions"
|
||||
prerequisites:
|
||||
- Gold - Cycle Finding
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
<info-block title="Pro Tip">
|
||||
Historically restricted to USACO Camp.
|
||||
</info-block>
|
||||
|
||||
## Paths
|
||||
|
||||
CSES Critical Cities https://cses.fi/problemset/task/1703/
|
||||
|
|
|
|||
|
|
@ -4,6 +4,7 @@ title: "Fast Fourier Transform and Applications"
|
|||
author: Benjamin Qi
|
||||
prerequisites:
|
||||
description: "?"
|
||||
frequency: 0
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
|
|||
|
|
@ -3,6 +3,7 @@ id: game-theory
|
|||
title: "Game Theory"
|
||||
author: Benjamin Qi
|
||||
description: "?"
|
||||
frequency: 0
|
||||
---
|
||||
|
||||
<info-block title="Pro Tip">
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
description: "?"
|
||||
prerequisites:
|
||||
- Advanced - Treaps
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
import { Problem } from "../models";
|
||||
|
|
|
|||
|
|
@ -4,12 +4,9 @@ title: "Matroid Intersection"
|
|||
author: Benjamin Qi
|
||||
description: "?"
|
||||
prerequisites:
|
||||
frequency: 0
|
||||
---
|
||||
|
||||
<info-block title="Pro Tip">
|
||||
Does not appear on USACO.
|
||||
</info-block>
|
||||
|
||||
* Tutorial
|
||||
* [CF Tutorial](https://codeforces.com/blog/entry/69287)
|
||||
* [Parametrized Algorithms Ch 12](http://parameterized-algorithms.mimuw.edu.pl/parameterized-algorithms.pdf)
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
description: "?"
|
||||
prerequisites:
|
||||
- Platinum - Maximum Flow
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
<info-block title="Pro Tip">
|
||||
|
|
|
|||
|
|
@ -2,13 +2,10 @@
|
|||
id: multiplicative
|
||||
title: "Prefix Sums of Multiplicative Functions"
|
||||
author: Benjamin Qi
|
||||
description: ?
|
||||
description: "?"
|
||||
frequency: 0
|
||||
---
|
||||
|
||||
<info-block title="Pro Tip">
|
||||
Does not appear on USACO.
|
||||
</info-block>
|
||||
|
||||
https://codeforces.com/blog/entry/54150
|
||||
|
||||
## Linear Time Sieve
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
description: "?"
|
||||
prerequisites:
|
||||
- Platinum - Range Update Range Query
|
||||
frequency: 1
|
||||
---
|
||||
|
||||
<info-block title="Pro Tip">
|
||||
|
|
|
|||
|
|
@ -5,12 +5,9 @@ author: Benjamin Qi
|
|||
description: "?"
|
||||
prerequisites:
|
||||
- Platinum - String Searching
|
||||
frequency: 0
|
||||
---
|
||||
|
||||
<info-block title="Pro Tip">
|
||||
Does not appear on USACO.
|
||||
</info-block>
|
||||
|
||||
* String Suffix Structures
|
||||
* [Suffix Automata](http://codeforces.com/blog/entry/20861)
|
||||
* Suffix Tree
|
||||
|
|
|
|||
|
|
@ -5,6 +5,7 @@ author: Benjamin Qi
|
|||
description: "?"
|
||||
prerequisites:
|
||||
- Platinum - Range Update Range Query
|
||||
frequency: 2
|
||||
---
|
||||
|
||||
<info-block title="Pro Tip">
|
||||
|
|
|
|||
|
|
@ -10,7 +10,7 @@ export class ModuleLinkInfo {
|
|||
}
|
||||
}
|
||||
|
||||
export type ModuleFrequency = null | 1 | 2 | 3 | 4;
|
||||
export type ModuleFrequency = null | 0 | 1 | 2 | 3 | 4;
|
||||
|
||||
// there's probably a way to do this without the duplicated types...
|
||||
export class ModuleInfo extends ModuleLinkInfo {
|
||||
|
|
|
|||
|
|
@ -293,20 +293,23 @@ const flattenNavLinks = (navLinks: NavLinkItem[]) => {
|
|||
|
||||
const Frequency = ({ frequency }: { frequency: ModuleFrequency }) => {
|
||||
const textColors = [
|
||||
'text-green-600',
|
||||
'text-red-600',
|
||||
'text-orange-600',
|
||||
'text-yellow-600',
|
||||
'text-teal-600',
|
||||
];
|
||||
const circleColors = [
|
||||
'text-green-500',
|
||||
'text-red-500',
|
||||
'text-orange-500',
|
||||
'text-yellow-500',
|
||||
'text-teal-500',
|
||||
];
|
||||
const labels = [
|
||||
'Rare (0-1 times)',
|
||||
'Not Frequent (2-3 times)',
|
||||
'Has Not Appeared',
|
||||
'Rare (1-2 times)',
|
||||
'Not Frequent (3-4 times)',
|
||||
'Somewhat Frequent',
|
||||
'Very Frequent (historically ~ once per contest)',
|
||||
];
|
||||
|
|
@ -314,14 +317,12 @@ const Frequency = ({ frequency }: { frequency: ModuleFrequency }) => {
|
|||
|
||||
return (
|
||||
<span
|
||||
className={`inline-flex items-center font-medium ${
|
||||
textColors[frequency - 1]
|
||||
}`}
|
||||
className={`inline-flex items-center font-medium ${textColors[frequency]}`}
|
||||
>
|
||||
{new Array(4).fill(null).map((_, idx) => (
|
||||
<svg
|
||||
className={`-ml-1 mr-1.5 h-2.5 w-2.5 ${
|
||||
idx >= frequency ? emptyCircle : circleColors[frequency - 1]
|
||||
idx >= frequency ? emptyCircle : circleColors[frequency]
|
||||
}`}
|
||||
fill="currentColor"
|
||||
viewBox="0 0 8 8"
|
||||
|
|
@ -329,7 +330,7 @@ const Frequency = ({ frequency }: { frequency: ModuleFrequency }) => {
|
|||
<circle cx="4" cy="4" r="3" />
|
||||
</svg>
|
||||
))}
|
||||
{labels[frequency - 1]}
|
||||
{labels[frequency]}
|
||||
</span>
|
||||
);
|
||||
};
|
||||
|
|
|
|||
Reference in a new issue