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Benjamin Qi 2020-06-25 11:52:19 -04:00
parent 4b9f134fbd
commit cfc7891f99
16 changed files with 267 additions and 5 deletions
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10
content/6_Plat/Aliens.mdx Normal file
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---
id: aliens
title: "Aliens Trick"
author: Benjamin Qi
description: "?"
prerequisites:
- Plat - Convex Hull
---
IOI 2016 Aliens

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content/6_Plat/DP_Bitmasks.mdx
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@ -14,7 +14,8 @@ export const metadata = {
problems: {
general: [
new Problem("CSES", "Hamiltonian Flights", "1690", "Easy", false, ["Bitmasks"], ""),
new Problem("CSES", "Elevator Rides", "1653", "Normal", false, ["LCA"], ""),
new Problem("CSES", "Elevator Rides", "1653", "Normal", false, ["Bitmasks"], ""),
new Problem("YS", "Max Indep Set", "maximum_independent_set", "Hard", false, ["Bitmasks", "Meet in Middle"], ""),
],
}
};

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---
id: eulers-formula
title: "Euler's Formula"
author: Benjamin Qi
description: "?"
prerequisites:
- "?"
---
import { Problem } from "../models";
export const metadata = {
problems: {
e1: [
new Problem("DMOJ", "Rainbow Gold", "apio17p1", "Hard", false, [],""),
],
e2: [
new Problem("Plat", "Valleys", "950", "Hard", false, [], ""),
],
other: [
new Problem("Kattis", "Island Archipelago", "https://utipc20s.kattis.com/problems/utipc20s.islandarchipelago", "Very Hard", false, [],""),
],
}
};
## Example 1
<problems-list problems={metadata.problems.e1} />
Land of Rainbow Gold
## Example 2
<problems-list problems={metadata.problems.e2} />
<problems-list problems={metadata.problems.other} />

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content/6_Plat/Flows.mdx
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@ -1,5 +1,5 @@
---
id: flows
id: max-flow
title: "Maximum Flow"
author: Benjamin Qi
prerequisites:
@ -47,3 +47,10 @@ Has not been the solution to any platinum problem, but appeared in old gold.
- [Incorrect Flow](https://codeforces.com/contest/708/problem/D)
- [Multi-Path Story](https://atcoder.jp/contests/jag2013summer-day4/tasks/icpc2013summer_day4_i)
- [WAC 4 - Hungry Squirrels](https://dmoj.ca/problem/wac4p6)
* Faster Max Flow
* Hopcroft-Karp Bipartite Matching
* Dinic's Algorithm
* Push-Relabel
* [Fast Flow Implementation - Chilli](https://codeforces.com/blog/entry/66006)

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content/6_Plat/Hull.mdx
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@ -33,3 +33,9 @@ prerequisites:
- Generalization of "Balance Beam"
Minkowski addition?
## With DP
cbarn
mowing

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content/6_Plat/String_Search.mdx
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@ -35,3 +35,5 @@ description: Knuth-Morris-Pratt and Z Algorithms (and a few more related topics)
- Tutorial
- [adamant](http://codeforces.com/blog/entry/14854)
- [GeeksForGeeks](http://www.geeksforgeeks.org/aho-corasick-algorithm-pattern-searching/)
## Palindromic Tree (Intro)

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(likely restricted to camp)
* Treap
* Notes
* [Quora](https://threads-iiith.quora.com/Treaps-One-Tree-to-Rule-em-all-Part-1)
* [PPT](https://docs.google.com/presentation/d/14xgtdDWnIBwmJRAuIdZ8FvLZcX9uRxnNoGOGAQRDIvc/edit?usp=sharing)
* Samuel Hsiang Guide (see resources)
* [Euler Tour Tree](https://codeforces.com/blog/entry/18369)
* Problems
* [Strings](https://csacademy.com/contest/archive/task/strings/) [](181)
* [Points & Distances](https://www.hackerearth.com/problem/algorithm/septembereasy-points-and-distances-d30d0e6b/description/) [](185)
* [Tree Rotations 2](https://szkopul.edu.pl/problemset/problem/b0BM0al2crQBt6zovEtJfOc6/site/?key=statement) [](193)
* [A2OJ](https://a2oj.com/category?ID=14)

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content/6_Plat/FFT.mdx → content/7_Advanced/FFT.mdx
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* Game Theory
* Tutorial
* [HackerRank](https://www.hackerrank.com/topics/game-theory-and-grundy-numbers)
* [TopCoder](https://www.topcoder.com/community/data-science/data-science-tutorials/algorithm-games/)
* Books (thanks mnbvmar!)
* "On Numbers and Games" - Conway
* "Winning Ways for Your Mathematical Plays" (Berlekamp, Conway, Guy)
* Topics
* Nim
* Grundy Numbers
* Sprague-Grundy Theorem
* Problem(s)
* [Division Game](https://uva.onlinejudge.org/index.php?option=onlinejudge&page=show_problem&problem=2959)
* [Game of Stones](http://codeforces.com/problemset/problem/768/E) [](59)
* [Factorization Game](https://www.hackerearth.com/problem/algorithm/mancunian-and-factorization-game-b8794702/) [](61)
* [Arpa & Game](http://codeforces.com/contest/850/problem/C) [](66)
* [Apple Tree](http://codeforces.com/contest/812/problem/E) [](67)

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(restricted to camp)
* Splay Tree
* Notes
* [Splay Tree Paper](https://www.cs.cmu.edu/~sleator/papers/self-adjusting.pdf)
* [Splay Tree Presentation](https://web.stanford.edu/class/archive/cs/cs166/cs166.1146/lectures/08/Slides08.pdf)
* Link Cut Tree
* Notes
* [Link-Cut Tree](http://courses.csail.mit.edu/6.851/spring12/scribe/L19.pdf)
* [CTSC 2014 Translation](https://www.overleaf.com/read/zbbwngftkrkx?fbclid=IwAR1VJmGscfSZJHejVqU5_2Nlm8-R09pFlU7PpEg_i3CXEd0Qw-dzliSn5RI)
* [Subtree Queries Tutorial](https://codeforces.com/blog/entry/67637)
* Problems
* SPOJ
* [DYNACON1](https://www.spoj.com/problems/DYNACON1/)
* technically, LCT isn't needed because the queries are offline
* [DYNALCA](https://www.spoj.com/problems/DYNALCA/)
* CF
* [Silence's Sounds](https://codeforces.com/contest/1109/problem/F)
* test connectivity
* [Train Tracking](https://codeforces.com/contest/1344/problem/E)
* switching can be done with LCT access
* set min on path with lazy prop
* [Solution](https://codeforces.com/contest/1344/submission/79212522)
* [Tree or not Tree](https://codeforces.com/contest/117/problem/E)
* tree + one edge
* [Old Driver Tree](https://codeforces.com/contest/1172/problem/E)
* [Pastoral Oddities](https://codeforces.com/contest/603/problem/E)
* path + subtree queries
* USACO Camp (not public)
* [The Applicant](https://probgate.org/viewproblem.php?pid=578)
* tree + one edge
* [Cows Play on a Tree](https://probgate.org/viewproblem.php?pid=259)
* reverse tree paths
* HLD + Treap
* or two LCTs, one for real tree labels and one for query labels
* Other
* [Balanced Tokens (Eric Zhang)](https://www.hackerrank.com/contests/pwshpc-online-round/challenges/pwsh-tokens/problem)
* [Dynamic Tree Test (Easy)](https://dmoj.ca/problem/ds5easy)
* [Dynamic Tree Test](https://dmoj.ca/problem/ds5)
* Requires operations on subtrees in addition to those from the easy version
* [CEOI Treasure Hunt](https://cses.fi/174/list/)
* get k-th parent
* [CERC 17 D](https://codeforces.com/gym/101620)
* LCT not needed, but can directly apply solution from "The Applicant"

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* Matroid Intersection
* Tutorial
* [CF Tutorial](https://codeforces.com/blog/entry/69287)
* [Parametrized Algorithms Ch 12](http://parameterized-algorithms.mimuw.edu.pl/parameterized-algorithms.pdf)
* [Illinois Lecture Notes](https://courses.engr.illinois.edu/cs598csc/sp2010/Lectures/Lecture17.pdf)
* [Goemans](https://math.mit.edu/~goemans/18438F09/lec13.pdf)
* describes partition matroid
* Problems
* [Honesty](https://www.urionlinejudge.com.br/judge/en/problems/view/2128)
* Max Size Graphic + Colorful
* [Coins](https://www.spoj.com/problems/COIN/)
* Max Size Graphic + Colorful
* [SERVERS](https://www.codechef.com/problems/SERVERS)
* Max Size Graphic + Colorful
* [Seollal](https://codeforces.com/contest/1284/problem/G)
* Max Size Graphic + Colorful
* [Pick Your Own Nim](https://codeforces.com/gym/102156/problem/D)
* Max Size Linear + Colorful
* [CCNCT2](https://www.codechef.com/problems/CNNCT2)
* Max Size Graphic + Graphic
* [Ambiguous Forest](https://onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=3080)
* Max Size Graphic + Graphic
* [Rainbow Graph](https://open.kattis.com/problems/rainbowgraph)
* Min Weight Graphic + Colorful
* [NAIPC 2018 Sols](http://serjudging.vanb.org/?p=1165)
* [Arup Guha Sol](http://www.cs.ucf.edu/~dmarino/progcontests/mysols/northamerica/2018/g.java)
* [HAMEL](https://www.codechef.com/problems/HAMEL)
* Partition into 2 MST's, then construct
* [TST](https://dmoj.ca/problem/dmopc19c3p6)
* Partition into 3 MST's

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* Minimum Cost Flow
* Tutorial
* [TopCoder](https://www.topcoder.com/community/data-science/data-science-tutorials/minimum-cost-flow-part-two-algorithms/)
* [Johnson's Algorithm](https://en.wikipedia.org/wiki/Johnson%27s_algorithm)
* Problems
* [April Fool's Problem](http://codeforces.com/contest/802/problem/N)
* [Cow & Exercise](https://codeforces.com/contest/1307/problem/G)
* consider LP dual

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---
id: multiplicative
title: "Summing Multiplicative Functions"
author: Benjamin Qi
description: ?
---
(doesn't appear on USACO)
https://codeforces.com/blog/entry/54150
## Counting Primes
https://judge.yosupo.jp/problem/counting_primes
## Totient Function
https://judge.yosupo.jp/problem/sum_of_totient_function
```cpp
template<int SZ> struct Sieve {
vi pr;
int sp[SZ], phi[SZ]; // smallest prime that divides
Sieve() { // above is faster
memset(sp,0,sizeof sp);
phi[1] = 1;
FOR(i,2,SZ) {
if (sp[i] == 0) {
sp[i] = i, pr.pb(i); phi[i] = i-1;
} trav(p,pr) {
if (p > sp[i] || i*p >= SZ) break;
sp[i*p] = p;
phi[i*p] = (p == sp[i] ? p : p-1)*phi[i];
}
}
}
};
const int HI = 5000000;
Sieve<HI> S;
ll N;
vmi small(HI), big;
int main() {
setIO(); re(N); big.rsz(N/HI+2);
FOR(i,1,HI) small[i] = small[i-1]+S.phi[i];
ROF(i,1,sz(big)) {
ll mx = N/i; big[i] = mi(mx)*(mx+1)/2; // dbg("HUH",i,big[i]);
for (ll fac = 2, nex; fac <= mx; fac = nex) {
ll quo = mx/fac; nex = mx/quo+1;
big[i] -= (nex-fac)*(quo < HI ? small[quo] : big[i*fac]);
}
}
ps(big[1]);
}
```
(project euler)
(topcoder problem)

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(likely restricted to camp)
* Persistent Segment Tree
* Tutorial
* [Anudeep2011](https://blog.anudeep2011.com/persistent-segment-trees-explained-with-spoj-problems/)
* [oml1111](https://drive.google.com/file/d/0BwGLW04WRv0ITEZjRWlMSFc2bk0/view)
* [Lazy Propogation](http://codeforces.com/blog/entry/47108?#comment-315047)
* Problems
* [A2OJ](https://a2oj.com/category?ID=651)
(WAC problem)

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(restricted to camp)
* String Suffix Structures
* [Suffix Automata](http://codeforces.com/blog/entry/20861)
* Suffix Tree
* [CF](http://codeforces.com/blog/entry/16780)
* [CP-Algo](https://cp-algorithms.com/string/suffix-tree-ukkonen.html)
* O(nlogn) suffix array usually suffices
* [Palindromic Tree](http://codeforces.com/blog/entry/13959)
* [Palindrome Partition](https://codeforces.com/contest/932/problem/G)
* [Partial Solution](https://codeforces.com/blog/entry/19193)
* [Palindromic Magic (HARD)](https://codeforces.com/contest/1081/problem/H)

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content/ordering.ts
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@ -122,7 +122,6 @@ const ModuleOrdering = {
items: [
"dp-bitmasks",
"dp-ranges",
"slope",
]
},
{
@ -131,7 +130,8 @@ const ModuleOrdering = {
"sp-neg",
"more-dfs",
"eulerian-tours",
"flows",
"euler",
"max-flow",
]
},
{
@ -148,11 +148,12 @@ const ModuleOrdering = {
"geo-pri",
"hull",
"LC",
"aliens",
"slope",
]
},
"bitsets",
"fracture",
"fft",
]
};