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competitive.txt
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competitive.txt
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List of Topics for programming Competitions -
Basic Geometry/Euclidean Geometry/Coordinate Geometry/ [3-D variants of everything].
Computational Geometry.
Graham Scan algorithm for Convex Hull O(n * log(n)).
Online construction of 3-D convex hull in O(n^2).
Bentley Ottmann algorithm to list all intersection points of n line segments in O((n + I) * logn).
Suggested Reading -
http://softsurfer.com/Archive/algorithm_0108/algorithm_0108.htm
Rotating Calipers Technique.
Suggested Reading - http://cgm.cs.mcgill.ca/~orm/rotcal.html
Problems - Refer the article for a list of problems which can be solved using Rotating Calipers technique.
Line Sweep/Plane Sweep algorithms -
Area/Perimeter of Union of Rectangles.
Closest pair of points.
Suggested Reading -
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=lineSweep
Problems - Follow the tutorial for list of problems.
Area of Union of Circles.
Delayunay Triangulation of n points in O(n * logn).
Voronoi Diagrams of n points in O(n * logn) using Fortunes algorithm.
Point in a polygon problem -
O(n) solution without preprocessing.
O(logn) algorithm with O(n * logn) preprocessing for convex polygons.
Problems on computational geometry -
BSHEEP, BULK, SEGVIS, CONDUIT, RUNAWAY, DIRVS, RAIN1, SHAMAN, TCUTTER, LITEPIPE, RHOMBS, FSHEEP, FLBRKLIN, CERC07P, BAC, ALTARS, CERC07C, NECKLACE, CH3D, RECTANGL, POLYSSQ, FOREST2, KPPOLY, RAIN2, SEGMENTS, ARCHPLG, BALLOON, CIRCLES, COMPASS, EOWAMRT, ICERINK on SPOJ.
CultureGrowth, PolygonCover on Topcoder.
Suggested Reading -
Computational Geometry: Algorithms and applications. Mark De Burg.
String Algorithm.
KnuthMorrisPratt algorithm.
Problems - NHAY, PERIOD on SPOJ.
Suggested Reading -
Cormen chapter on Strings.
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=stringSearching
Aho Corasick algorithm.
Problems - WPUZZLES on SPOJ.
Suffix Arrays
O(n^2 * logn) Naive method of suffix array construction
O(n * logn^2) method of suffix array construction
O(n * logn) method of suffix array construction.
O(n) method of suffix array construction
O(n) LCA preprocess on Suffix Arrays to solve a variety of string problems.
Suffix Trees
O(n) construction of Suffix trees using Ukkenon’s algorithm.
O(n) construction of Suffix Trees if provided with Suffix Arrays using Farach’s algorithm.
Suffix Automata
O(n) Suffix Automaton construction.
Dictionary Of Basic Factors
O(n * logn) method of DBF construction using Radix Sort.
Manachar’s algorithm to find Lengh of palindromic substring of a string centered at a position for each position in the string. Runtime -> O(n).
Searching and preprocessing Regular Expressions consisting of ‘?’, ‘*’.
Multi-dimentional pattern matching.
Problems on Strings [can be solved with a variety of techniques] -
DISUBSTR, PLD, MSTRING, REPEATS, JEWELS, ARCHIVER, PROPKEY, LITELANG, EMOTICON, WORDS, AMCODES, UCODES, PT07H, MINSEQ, TOPALIN, BWHEELER, BEADS, SARRAY, LCS, LCS2, SUBST1, PHRASES, PRETILE on SPOJ
http://www.algorithmist.com/index.php/Category:String_algorithms
Basic Graphs [beginner].
Representation of graphs as adjacency list, adjacency matrix, incidence matrix and edge list and uses of different representations in different scenarios.
Breadth First Search.
problems -
PPATH, ONEZERO, WATER on SPOJ
Depth First Search.
Strongly Connected Components.
problems -
TOUR and BOTTOM on SPOJ.
Biconnected Components, Finding articulation points and bridges].
problems -
RELINETS, PT07A on SPOJ.
Dijkstra algorithm -
problems -
SHPATH on SPOJ.
Floyd Warshall algorithm -
problems -
COURIER on SPOJ.
Minimum Spanning Tree
problems -
BLINNET on SPOJ.
Flood-fill algorithm
Topological sort
Bellman-Ford algorithm.
Euler Tour/Path.
problems - WORDS1 on SPOJ.
Suggested reading for most of the topics in Graph algorithms -
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=graphsDataStrucs1.
Also refer to the tutorial for problems concerning these techniques.
Cormen chapter 22 to 24.
Flow networks/ matching etc etc. [Interdiate/Advanced].
Maximum flow using Ford Fulkerson Method.
Suggested Reading -
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=maxFlow
problems - TAXI, POTHOLE, IM, QUEST4, MUDDY, EN, CABLETV, STEAD, NETADMIN, COCONUTS, OPTM on SPOJ.
Maximum flow using Dinics Algorithm.
Problems - PROFIT on spoj.
Minimum Cost Maximum Flow.
Successive Shortest path algorithm.
Cycle Cancelling algorithm.
Suggested Reading -
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=minimumCostFlow1
Maximum weighted Bipartite Matching (Kuhn Munkras algorithm/Hungarian Method)
problems - GREED, SCITIES, TOURS on SPOJ | http://www.topcoder.com/stat?c=problem_statement&pm=8143
Stoer Wagner min-cut algorithm.
Hopcroft Karp bipartite matching algorithm.
problems - ANGELS on SPOJ.
Maximum matching in general graph (blossom shrinking)
Gomory-Hu Trees.
i) Problems - MCQUERY on Spoj.
Chinese Postman Problem.
problems - http://acm.uva.es/archive/nuevoportal/data/problem.php?p=4039
Suggested Reading - http://eie507.eie.polyu.edu.hk/ss-submission/B7a/
Suggested Reading for the full category ->
Network flow - Algorithms and Applications by Ahuja
Cormen book chapter 25.
Dynamic Programming.
Suggested Reading - Dynamic Programming(DP) as a tabulation method
Cormen chapter on DP
Standard problems (you should really feel comfortable with these types)
http://www.topcoder.com/stat?c=problem_statement&pm=8570&rd=12012&rm=269199&cr=7581406
http://www.topcoder.com/stat?c=problem_statement&pm=10765&rd=14183
State space reduction
http://www.topcoder.com/stat?c=problem_statement&pm=10902
http://www.topcoder.com/stat?c=problem_statement&pm=3001
http://www.topcoder.com/stat?c=problem_statement&pm=8605&rd=12012&rm=269199&cr=7581406
Solving in the reverse - easier characterizations looking from the end
http://www.spoj.pl/problems/MUSKET/
http://www.topcoder.com/stat?c=problem_statement&pm=5908
Counting/optimizing arrangements satisfying some specified properties
http://www.topcoder.com/stat?c=problem_statement&pm=8306
http://www.topcoder.com/stat?c=problem_statement&pm=7849
Strategies and expected values
http://www.topcoder.com/stat?c=problem_statement&pm=10765&rd=14183
http://www.topcoder.com/stat?c=problem_statement&pm=10806
http://www.topcoder.com/stat?c=problem_statement&pm=7828
http://www.topcoder.com/stat?c=problem_statement&pm=7316
DP on probability spaces
http://www.topcoder.com/stat?c=problem_statement&pm=7422
http://www.topcoder.com/stat?c=problem_statement&pm=2959
http://www.topcoder.com/stat?c=problem_statement&pm=10335
DP on trees
http://www.topcoder.com/stat?c=problem_statement&pm=10800
http://www.topcoder.com/stat?c=problem_statement&pm=10737
http://www.topcoder.com/stat?c=problem_solution&rm=266678&rd=10958&pm=8266&cr=7581406
DP with datastructures
http://www.spoj.pl/problems/INCSEQ/
http://www.spoj.pl/problems/INCDSEQ/
http://www.spoj.pl/problems/LIS2/
http://www.topcoder.com/stat?c=problem_statement&pm=1986
Symmetric characterization of DP state
http://www.topcoder.com/stat?c=problem_statement&pm=8610
A good collection of problems
http://codeforces.com/blog/entry/325
http://problemclassifier.appspot.com/index.jsp?search=dp&usr=
Greedy.
Suggested Reading -
Chapter on Greedy algorithms in Cormen.
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=greedyAlg
problems - refer to the topcoder tutorial.
Number Theory.
Modulus arithmetic - basic postulates [Including modular linear equations , Continued fraction and Pell's equation]
Suggested Reading -
Chapter 1 from Number Theory for Computing by SY Yan [ Recommended ]
31.1, 31.3 and 31.4 from Cormen
www.topcoder.com/tc?module=Static&d1=tutorials&d2=primeNumbers
Problems
http://projecteuler.net/index.php?section=problems&id=64
http://projecteuler.net/index.php?section=problems&id=65
http://projecteuler.net/index.php?section=problems&id=66
http://www.topcoder.com/stat?c=problem_statement&pm=6408&rd=9826
http://www.topcoder.com/stat?c=problem_statement&pm=2342
Fermat's theorem, Euler Totient theorem ( totient function, order , primitive roots )
Suggested Reading
1.6, 2.2 from Number Theory by SY Yan
31.6 , 31.7 from Cormen
Problems
http://projecteuler.net/index.php?section=problems&id=70
http://www.spoj.pl/problems/NDIVPHI/
Chinese remainder theorem
Suggested Reading
31.5 from Cormen
1.6 from Number Theory by SY Yan
Problems
Project Euler 271
http://www.topcoder.com/stat?c=problem_statement&pm=10551&rd=13903
Primality tests -
Deterministic O(sqrt(n) ) approach
Probabilistic primality tests - Fermat primality test, Miller-Rabin Primality test
Suggested Reading -
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=primalityTesting
Cormen 31.8
2.2 from Number Theory by SY Yan
Problems -
PON, PRIC, SOLSTRAS on SPOJ
http://www.topcoder.com/stat?c=problem_statement&pm=4515
Prime generation techniques - Sieve of Erastothenes
Suggested Problems - PRIME1 on SPOJ
GCD using euclidean method
Suggested Reading
31.2 Cormen
Problems -
GCD on SPOJ
http://uva.onlinejudge.org/external/114/11424.html
Logarithmic Exponentiation
Suggested Reading -
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=primalityTesting
Integer Factorization
Naive O(sqrt(n)) method
Pollard Rho factorization
Suggested Reading
2.3 from Number Theory SY Yan
31.9 Cormen
Problems -
http://www.topcoder.com/stat?c=problem_statement&pm=2986&rd=5862
http://www.spoj.pl/problems/DIVSUM2/
http://www.topcoder.com/stat?c=problem_statement&pm=4481&rd=6538
Stirling numbers
Wilson theorem
nCr % p in O(p) preprocess and O(log n ) query
Lucas Theorem
Suggested Reading for Number Theory -
Number theory for computing by Song Y Yan [ Simple book describing concepts in details ]
Concepts are also superficially covered in Chapter 31 of Introduction to Algorithms by Cormen
http://www.codechef.com/wiki/tutorial-number-theory
http://www.algorithmist.com/index.php/Category:Number_Theory
Problems on Number Theory -
http://www.algorithmist.com/index.php/Category:Number_Theory
http://problemclassifier.appspot.com/index.jsp?search=number&usr=
Math (Probability, Counting, Game Theory, Group Theory, Generating functions, Permutation Cycles, Linear Algebra)
Probability.
Syllabus
Basic probability and Conditional probability
Suggested problems
http://www.spoj.pl/problems/CT16E/
http://www.spoj.pl/problems/CHICAGO/
Random variables, probability generating functions
Mathematical expectation + Linearity of expectation
Suggested problems
http://www.spoj.pl/problems/FAVDICE/
http://www.topcoder.com/stat?c=problem_statement&pm=10744
Special discrete and continuous probability distributions
Bernoulli, Binomial, Poisson, normal distribution
Suggested Problem
http://acm.sgu.ru/problem.php?contest=0&problem=498
Suggested Readings
Cormen appendix C (very basic)
Topcoder probabilty tutorial http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=probabilities
http://en.wikipedia.org/wiki/Random_variable
http://en.wikipedia.org/wiki/Expected_value
William Feller, An introduction to probability theory and its applications
Counting
Syllabus
Basic principles - Pigeon hole principle, addition, multiplication rules
Suggested problems
http://acm.timus.ru/problem.aspx?space=1&num=1690
http://www.topcoder.com/stat?c=problem_statement&pm=10805
Suggested readings
http://en.wikipedia.org/wiki/Combinatorial_principles
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=combinatorics
http://www.maa.org/editorial/knot/pigeonhole.html
Inclusion-exclusion
Suggested readings
http://en.wikipedia.org/wiki/Inclusion–exclusion_principle
Suggested problems
http://www.topcoder.com/stat?c=problem_statement&pm=4463&rd=6536
http://www.topcoder.com/stat?c=problem_statement&pm=10238
Special numbers
Suggested reading - Stirling, eurlerian, harmonic, bernoulli, fibonnacci numbers
http://en.wikipedia.org/wiki/Stirling_number
http://en.wikipedia.org/wiki/Eulerian_numbers
http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
http://en.wikipedia.org/wiki/Bernoulli_number
http://en.wikipedia.org/wiki/Fibonnaci_numbers
Concrete mathematics by Knuth
Suggested problems
http://www.topcoder.com/stat?c=problem_statement&pm=1643
http://www.topcoder.com/stat?c=problem_statement&pm=8202&rd=11125
http://www.topcoder.com/stat?c=problem_statement&pm=8725
http://www.topcoder.com/stat?c=problem_statement&pm=2292&rd=10709
Advanced counting techniques - Polya counting, burnsides lemma
Suggested reading
http://en.wikipedia.org/wiki/Burnside's_lemma
http://petr-mitrichev.blogspot.com/2008/11/burnsides-lemma.html
Suggested Problems
http://www.topcoder.com/stat?c=problem_statement&pm=9975
http://www.spoj.pl/problems/TRANSP/
c. Game theory
Syllabus
Basic principles and Nim game
Sprague grundy theorem, grundy numbers
Suggested readings
http://en.wikipedia.org/wiki/Sprague%E2%80%93Grundy_theorem
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=algorithmGames
http://www.ams.org/samplings/feature-column/fcarc-games1
http://www.codechef.com/wiki/tutorial-game-theory
Suggested problems
http://www.topcoder.com/stat?c=problem_statement&pm=3491&rd=6517
http://www.topcoder.com/stat?c=problem_statement&pm=3491&rd=6517
Hackenbush
Suggested readings
http://en.wikipedia.org/wiki/Hackenbush
http://www.ams.org/samplings/feature-column/fcarc-partizan1
Suggested problems
http://www.cs.caltech.edu/ipsc/problems/g.html
http://www.spoj.pl/problems/PT07A/
d. Linear Algebra
Syllabus
Matrix Operations
Addition and subtraction of matrices
Suggested Reading
Cormen 28.1
Multiplication ( Strassen's algorithm ), logarithmic exponentiation
Suggested reading
Cormen 28.2
Linear Algebra by Kenneth Hoffman Section 1.6
Problems
http://uva.onlinejudge.org/external/111/11149.html
Matrix transformations [ Transpose, Rotation of Matrix, Representing Linear transformations using matrix ]
Suggested Reading
Linear Algebra By Kenneth Hoffman Section 3.1,3.2,3.4,3.7
Problems
http://www.topcoder.com/stat?c=problem_statement&pm=6877
JPIX on Spoj
Determinant , Rank and Inverse of Matrix [ Gaussean Elimination , Gauss Jordan Elimination]
Suggested Reading
28.4 Cormen
Linear Algebra by Kenneth Chapter 1
Problems
http://www.topcoder.com/stat?c=problem_statement&pm=8174
http://www.topcoder.com/stat?c=problem_statement&pm=6407&rd=9986
http://www.topcoder.com/stat?c=problem_statement&pm=8587
HIGH on Spoj
Solving system of linear equations
Suggested Reading
28.3 Cormen
Linear Algebra by Kenneth Chapter 1
Problems -
http://www.topcoder.com/stat?c=problem_statement&pm=3942&rd=6520
Using matrix exponentiation to solve recurrences
Suggested Reading
http://www.topcoder.com/tc?module=Static&d1=features&d2=010408
Problems
REC, RABBIT1 , PLHOP on spoj
http://www.topcoder.com/stat?c=problem_statement&pm=6386 , http://www.topcoder.com/stat?c=problem_statement&pm=7262, http://www.topcoder.com/stat?c=problem_statement&pm=6877
Eigen values and Eigen vectors
Problems
http://www.topcoder.com/stat?c=problem_statement&pm=2423&rd=4780
Polynomials
Roots of a polynomial [ Prime factorization of a polynomial, Integer roots of a polynomial, All real roots of a polynomial ]
Problems
http://www.topcoder.com/stat?c=problem_statement&pm=8273&rd=10798
POLYEQ , ROOTCIPH on Spoj
Lagrange Interpolation
Problems
http://www.topcoder.com/stat?c=problem_statement&pm=10239
http://www.topcoder.com/stat?c=problem_statement&pm=8725
e. Permutation cycles
Suggested Reading
Art of Computer Programming by Knuth Vol. 3
Problems
ShuffleMethod, Permutation and WordGame on topcoder.
f. Group Theory
Bernside Lemma, Polias theorem
Suggested Reading
Hernstein's topics in algebra
http://petr-mitrichev.blogspot.com/2008/11/burnsides-lemma.html
Problems
TRANSP on spoj
http://www.topcoder.com/stat?c=problem_statement&pm=9975
Generating functions
Suggested Reading
Herbert Wilf's generating functionology
Robert Sedgewick and Flajoulet's Combinatorial analysis
Data Structures.
Basic
Arrays/Stacks/Queues :
Problems
https://www.spoj.pl/problems/STPAR/
https://www.spoj.pl/problems/SHOP/
https://www.spoj.pl/problems/WATER/
Reading:
CLRS: section 10.1
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=dataStructures
b. Singly/Doubly Linked List :
Problems
https://www.spoj.pl/problems/POSTERS/
Reading: CLRS: section 10.2, Mark Allen Weies Chapter 3
c. Hash Tables :
Problems
https://www.spoj.pl/problems/HASHIT/
https://www.spoj.pl/problems/CUCKOO/
Reading: CLRS: Chapter 11, Mark Allen Weies Chapter 5
d. Circular linked list / queue
Problems
https://www.spoj.pl/problems/CTRICK/
e. Binary/nary Trees
Reading
CLRS: section 10.4
CLRS: Chapter 12
Mark Allen Weies Chapter 4
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=binarySearchRedBlack
f. Heaps
Problems
https://www.spoj.pl/problems/PRO/
https://www.spoj.pl/problems/EXPEDI/
Reading : Mark Allen Weies Chapter 6
ii. Advanced
Trie (Keyword tree)
Problems
https://www.spoj.pl/problems/MORSE/
https://www.spoj.pl/problems/EMOTICON/
Reading
Interval trees / Segment Trees
Problems
https://www.spoj.pl/problems/ORDERS/
https://www.spoj.pl/problems/FREQUENT/
Reading
Fenwick(Binary Indexed) trees
Problems
https://www.spoj.pl/problems/MATSUM/
Reading: http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=binaryIndexedTrees
Disjoint data structures
Problems
https://www.spoj.pl/problems/BLINNET/
https://www.spoj.pl/problems/CHAIN/
Reading:
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=disjointDataStructure
Mark Allen Weies Chapter 8
Range minimum Query(RMQ)
Problems
https://www.spoj.pl/problems/GSS1/
Reading http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=lowestCommonAncestor
Customized interval/segment trees (Augmented DS)
Problems
https://www.spoj.pl/problems/GSS3/
https://www.spoj.pl/problems/RRSCHED/
Reading: CLRS: Chapter 14 (augmented DS)
g. AVL Trees
Problems
1. https://www.spoj.pl/problems/ORDERS/
Reading
iii. Miscellaneous (Not to be covered)
Splay Trees
B/B+ Trees
k-d Trees
Red-black Trees
Skip List
Binomial/ Fibonacci heaps
iv. Exercices
https://www.spoj.pl/problems/LAZYPROG/ (Hint: Heaps)t
https://www.spoj.pl/problems/HELPR2D2/ (Hint: Interval Trees)
https://www.spoj.pl/problems/SAM/ (Hint: Heaps)
https://www.spoj.pl/problems/PRHYME/ (Hint: Trie)
https://www.spoj.pl/problems/HEAPULM/ (Hint: Interval Trees)
https://www.spoj.pl/problems/CORNET/ (Hint: Disjoint )
https://www.spoj.pl/problems/EXPAND/
https://www.spoj.pl/problems/WPUZZLES/
https://www.spoj.pl/problems/LIS2/
Search Techniques/Bruteforce writing techniques/Randomized algorithms.
Backtracking - [Beginner].
problems ->
N queens problems
Knights Tour
Sudoku Problem
Tiling Problem.
15 puzzle.
Dancing Links and Algorithm X given by Knuth - [Advanced]
problems - PRLGAME, SUDOKU, NQUEEN on SPOJ
Suggested reading -
http://www-cs-faculty.stanford.edu/~uno/papers/dancing-color.ps.gz
Binary Search - [Beginner].
poblems - AGGRCOW on SPOJ. Refer the tutorial for more problems.
finding all real roots of a polynomial using binary search. [intermediate].
Suggested Reading -
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=binarySearch
Ternary Search - [Intermediate].
problems -
http://www.spoj.pl/problems/KPPOLY/
http://www.codechef.com/DEC09/problems/K1/
http://www.topcoder.com/stat?c=problem_statement&pm=4705&rd=7993
http://www.topcoder.com/stat?c=problem_statement&pm=7741&rd=10671
http://www.topcoder.com/stat?c=problem_statement&pm=6464&rd=9994
http://www.topcoder.com/stat?c=problem_statement&pm=3501&rd=6529
http://www.topcoder.com/stat?c=problem_statement&pm=4567&rd=6539
Meet in the middle [Intermediate].
problems -
http://www.spoj.pl/problems/MAXISET/
http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=2868
Hill Climbing [Advanced].
Regular Iteration to reach a fixed point [Advanced].
Newton-Raphson method to find root of a mathematical function.
Iterations to solve linear non-homogeneous system of equations.
Randomized Algorithms [Intermediate]-
Quick-Sort.
General programming issues in contests ->
Arithmetic Precision - [Beginner].
Suggested Reading -
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=integersReals
Representing sets with bitmasks and manipulating bitmasks - [Beginner].
Suggested Reading -
http://www.topcoder.com/tc?module=Static&d1=tutorials&d2=bitManipulation
problems - refer to the tutorial link in Suggested reading section.