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 Bibin Muttappillil
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Bibin Muttappillil
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README.md
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README.md
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# Competitive Programmer's Handbook
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# Competitive Programmer's Handbook -- SOI Edition
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Competitive Programmer's Handbook is a modern introduction to competitive programming.
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Competitive Programmer's Handbook is a modern introduction to competitive programming.
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The book discusses programming tricks and algorithm design techniques relevant in competitive programming.
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The book discusses programming tricks and algorithm design techniques relevant in competitive programming.
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## CSES Problem Set
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We adapted it to fit our SOI training.
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The CSES Problem Set contains a collection of competitive programming problems.
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## Credits
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You can practice the techniques presented in the book by solving the problems.
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https://cses.fi/problemset/
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All credits belong to Antti Laaksonen.
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See original: https://github.com/pllk/cphb
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## License
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## License
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The license of the book is Creative Commons BY-NC-SA.
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The license of the book is Creative Commons BY-NC-SA.
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## Other books
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Guide to Competitive Programming is a printed book, published by Springer, based on Competitive Programmer's Handbook.
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There is also a Russian edition Олимпиадное программирование (Olympiad Programming) and a Korean edition 알고리즘 트레이닝: 프로그래밍 대회 입문 가이드.
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https://cses.fi/book/
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@ -0,0 +1,345 @@
|
||||||
|
\indexentry{programming language|hyperpage}{3}
|
||||||
|
\indexentry{input and output|hyperpage}{4}
|
||||||
|
\indexentry{integer|hyperpage}{6}
|
||||||
|
\indexentry{remainder|hyperpage}{6}
|
||||||
|
\indexentry{modular arithmetic|hyperpage}{6}
|
||||||
|
\indexentry{floating point number|hyperpage}{7}
|
||||||
|
\indexentry{tuppdef@\texttt{typedef}|hyperpage}{8}
|
||||||
|
\indexentry{macro|hyperpage}{9}
|
||||||
|
\indexentry{arithmetic progression|hyperpage}{10}
|
||||||
|
\indexentry{Faulhaber's formula|hyperpage}{10}
|
||||||
|
\indexentry{geometric progression|hyperpage}{11}
|
||||||
|
\indexentry{harmonic sum|hyperpage}{11}
|
||||||
|
\indexentry{set theory|hyperpage}{12}
|
||||||
|
\indexentry{set|hyperpage}{12}
|
||||||
|
\indexentry{intersection|hyperpage}{12}
|
||||||
|
\indexentry{union|hyperpage}{12}
|
||||||
|
\indexentry{difference|hyperpage}{12}
|
||||||
|
\indexentry{subset|hyperpage}{12}
|
||||||
|
\indexentry{universal set|hyperpage}{12}
|
||||||
|
\indexentry{complement|hyperpage}{12}
|
||||||
|
\indexentry{logic|hyperpage}{13}
|
||||||
|
\indexentry{negation|hyperpage}{13}
|
||||||
|
\indexentry{conjuction|hyperpage}{13}
|
||||||
|
\indexentry{disjunction|hyperpage}{13}
|
||||||
|
\indexentry{implication|hyperpage}{13}
|
||||||
|
\indexentry{equivalence|hyperpage}{13}
|
||||||
|
\indexentry{predicate|hyperpage}{13}
|
||||||
|
\indexentry{quantifier|hyperpage}{13}
|
||||||
|
\indexentry{factorial|hyperpage}{14}
|
||||||
|
\indexentry{Fibonacci number|hyperpage}{14}
|
||||||
|
\indexentry{Binet's formula|hyperpage}{14}
|
||||||
|
\indexentry{logarithm|hyperpage}{14}
|
||||||
|
\indexentry{natural logarithm|hyperpage}{15}
|
||||||
|
\indexentry{time complexity|hyperpage}{17}
|
||||||
|
\indexentry{complexity classes|hyperpage}{20}
|
||||||
|
\indexentry{constant-time algorithm|hyperpage}{20}
|
||||||
|
\indexentry{logarithmic algorithm|hyperpage}{20}
|
||||||
|
\indexentry{linear algorithm|hyperpage}{20}
|
||||||
|
\indexentry{quadratic algorithm|hyperpage}{20}
|
||||||
|
\indexentry{cubic algorithm|hyperpage}{20}
|
||||||
|
\indexentry{polynomial algorithm|hyperpage}{20}
|
||||||
|
\indexentry{NP-hard problem|hyperpage}{20}
|
||||||
|
\indexentry{constant factor|hyperpage}{21}
|
||||||
|
\indexentry{maximum subarray sum|hyperpage}{21}
|
||||||
|
\indexentry{Kadane's algorithm|hyperpage}{23}
|
||||||
|
\indexentry{sorting|hyperpage}{25}
|
||||||
|
\indexentry{bubble sort|hyperpage}{25}
|
||||||
|
\indexentry{inversion|hyperpage}{26}
|
||||||
|
\indexentry{merge sort|hyperpage}{27}
|
||||||
|
\indexentry{counting sort|hyperpage}{28}
|
||||||
|
\indexentry{sort@\texttt{sort}|hyperpage}{29}
|
||||||
|
\indexentry{comparison operator|hyperpage}{30}
|
||||||
|
\indexentry{pair@\texttt{pair}|hyperpage}{30}
|
||||||
|
\indexentry{tuple@\texttt{tuple}|hyperpage}{30}
|
||||||
|
\indexentry{comparison function|hyperpage}{31}
|
||||||
|
\indexentry{binary search|hyperpage}{31}
|
||||||
|
\indexentry{data structure|hyperpage}{35}
|
||||||
|
\indexentry{dynamic array|hyperpage}{35}
|
||||||
|
\indexentry{vector|hyperpage}{35}
|
||||||
|
\indexentry{string|hyperpage}{36}
|
||||||
|
\indexentry{set|hyperpage}{37}
|
||||||
|
\indexentry{map|hyperpage}{38}
|
||||||
|
\indexentry{iterator|hyperpage}{39}
|
||||||
|
\indexentry{sort@\texttt{sort}|hyperpage}{39}
|
||||||
|
\indexentry{reverse@\texttt{reverse}|hyperpage}{39}
|
||||||
|
\indexentry{random\_shuffle@\texttt{random\_shuffle}|hyperpage}{39}
|
||||||
|
\indexentry{bitset|hyperpage}{41}
|
||||||
|
\indexentry{deque|hyperpage}{42}
|
||||||
|
\indexentry{stack|hyperpage}{42}
|
||||||
|
\indexentry{queue|hyperpage}{43}
|
||||||
|
\indexentry{priority queue|hyperpage}{43}
|
||||||
|
\indexentry{heap|hyperpage}{43}
|
||||||
|
\indexentry{subset|hyperpage}{47}
|
||||||
|
\indexentry{permutation|hyperpage}{49}
|
||||||
|
\indexentry{next\_permutation@\texttt{next\_permutation}|hyperpage}{49}
|
||||||
|
\indexentry{backtracking|hyperpage}{50}
|
||||||
|
\indexentry{queen problem|hyperpage}{50}
|
||||||
|
\indexentry{meet in the middle|hyperpage}{54}
|
||||||
|
\indexentry{greedy algorithm|hyperpage}{57}
|
||||||
|
\indexentry{data compression|hyperpage}{62}
|
||||||
|
\indexentry{binary code|hyperpage}{62}
|
||||||
|
\indexentry{codeword|hyperpage}{62}
|
||||||
|
\indexentry{Huffman coding|hyperpage}{63}
|
||||||
|
\indexentry{dynamic programming|hyperpage}{65}
|
||||||
|
\indexentry{memoization|hyperpage}{67}
|
||||||
|
\indexentry{longest increasing subsequence|hyperpage}{70}
|
||||||
|
\indexentry{knapsack|hyperpage}{72}
|
||||||
|
\indexentry{edit distance|hyperpage}{74}
|
||||||
|
\indexentry{Levenshtein distance|hyperpage}{74}
|
||||||
|
\indexentry{amortized analysis|hyperpage}{77}
|
||||||
|
\indexentry{two pointers method|hyperpage}{77}
|
||||||
|
\indexentry{2SUM problem|hyperpage}{78}
|
||||||
|
\indexentry{3SUM problem|hyperpage}{79}
|
||||||
|
\indexentry{nearest smaller elements|hyperpage}{79}
|
||||||
|
\indexentry{sliding window|hyperpage}{81}
|
||||||
|
\indexentry{sliding window minimum|hyperpage}{81}
|
||||||
|
\indexentry{range query|hyperpage}{83}
|
||||||
|
\indexentry{sum query|hyperpage}{83}
|
||||||
|
\indexentry{minimum query|hyperpage}{83}
|
||||||
|
\indexentry{maximum query|hyperpage}{83}
|
||||||
|
\indexentry{prefix sum array|hyperpage}{84}
|
||||||
|
\indexentry{sparse table|hyperpage}{85}
|
||||||
|
\indexentry{binary indexed tree|hyperpage}{86}
|
||||||
|
\indexentry{Fenwick tree|hyperpage}{86}
|
||||||
|
\indexentry{segment tree|hyperpage}{89}
|
||||||
|
\indexentry{index compression|hyperpage}{93}
|
||||||
|
\indexentry{difference array|hyperpage}{93}
|
||||||
|
\indexentry{bit representation|hyperpage}{95}
|
||||||
|
\indexentry{and operation|hyperpage}{96}
|
||||||
|
\indexentry{or operation|hyperpage}{96}
|
||||||
|
\indexentry{xor operation|hyperpage}{97}
|
||||||
|
\indexentry{not operation|hyperpage}{97}
|
||||||
|
\indexentry{bit shift|hyperpage}{97}
|
||||||
|
\indexentry{Hamming distance|hyperpage}{100}
|
||||||
|
\indexentry{graph|hyperpage}{109}
|
||||||
|
\indexentry{node|hyperpage}{109}
|
||||||
|
\indexentry{edge|hyperpage}{109}
|
||||||
|
\indexentry{path|hyperpage}{109}
|
||||||
|
\indexentry{cycle|hyperpage}{109}
|
||||||
|
\indexentry{connected graph|hyperpage}{110}
|
||||||
|
\indexentry{component|hyperpage}{110}
|
||||||
|
\indexentry{tree|hyperpage}{110}
|
||||||
|
\indexentry{directed graph|hyperpage}{110}
|
||||||
|
\indexentry{weighted graph|hyperpage}{111}
|
||||||
|
\indexentry{neighbor|hyperpage}{111}
|
||||||
|
\indexentry{degree|hyperpage}{111}
|
||||||
|
\indexentry{regular graph|hyperpage}{111}
|
||||||
|
\indexentry{complete graph|hyperpage}{111}
|
||||||
|
\indexentry{indegree|hyperpage}{111}
|
||||||
|
\indexentry{outdegree|hyperpage}{111}
|
||||||
|
\indexentry{coloring|hyperpage}{112}
|
||||||
|
\indexentry{bipartite graph|hyperpage}{112}
|
||||||
|
\indexentry{simple graph|hyperpage}{112}
|
||||||
|
\indexentry{adjacency list|hyperpage}{113}
|
||||||
|
\indexentry{adjacency matrix|hyperpage}{114}
|
||||||
|
\indexentry{edge list|hyperpage}{115}
|
||||||
|
\indexentry{depth-first search|hyperpage}{117}
|
||||||
|
\indexentry{breadth-first search|hyperpage}{119}
|
||||||
|
\indexentry{connected graph|hyperpage}{121}
|
||||||
|
\indexentry{cycle|hyperpage}{121}
|
||||||
|
\indexentry{bipartite graph|hyperpage}{122}
|
||||||
|
\indexentry{shortest path|hyperpage}{123}
|
||||||
|
\indexentry{Bellman–Ford algorithm|hyperpage}{123}
|
||||||
|
\indexentry{negative cycle|hyperpage}{125}
|
||||||
|
\indexentry{SPFA algorithm|hyperpage}{126}
|
||||||
|
\indexentry{Dijkstra's algorithm|hyperpage}{126}
|
||||||
|
\indexentry{Floyd–Warshall algorithm|hyperpage}{129}
|
||||||
|
\indexentry{tree|hyperpage}{133}
|
||||||
|
\indexentry{leaf|hyperpage}{133}
|
||||||
|
\indexentry{root|hyperpage}{133}
|
||||||
|
\indexentry{rooted tree|hyperpage}{133}
|
||||||
|
\indexentry{child|hyperpage}{133}
|
||||||
|
\indexentry{parent|hyperpage}{133}
|
||||||
|
\indexentry{subtree|hyperpage}{133}
|
||||||
|
\indexentry{diameter|hyperpage}{135}
|
||||||
|
\indexentry{binary tree|hyperpage}{139}
|
||||||
|
\indexentry{pre-order|hyperpage}{139}
|
||||||
|
\indexentry{in-order|hyperpage}{139}
|
||||||
|
\indexentry{post-order|hyperpage}{139}
|
||||||
|
\indexentry{spanning tree|hyperpage}{141}
|
||||||
|
\indexentry{minimum spanning tree|hyperpage}{141}
|
||||||
|
\indexentry{maximum spanning tree|hyperpage}{142}
|
||||||
|
\indexentry{Kruskal's algorithm|hyperpage}{142}
|
||||||
|
\indexentry{union-find structure|hyperpage}{145}
|
||||||
|
\indexentry{Prim's algorithm|hyperpage}{147}
|
||||||
|
\indexentry{topological sorting|hyperpage}{149}
|
||||||
|
\indexentry{cycle|hyperpage}{149}
|
||||||
|
\indexentry{Dijkstra's algorithm|hyperpage}{153}
|
||||||
|
\indexentry{successor graph|hyperpage}{154}
|
||||||
|
\indexentry{functional graph|hyperpage}{154}
|
||||||
|
\indexentry{cycle|hyperpage}{155}
|
||||||
|
\indexentry{cycle detection|hyperpage}{155}
|
||||||
|
\indexentry{Floyd's algorithm|hyperpage}{156}
|
||||||
|
\indexentry{strongly connected graph|hyperpage}{157}
|
||||||
|
\indexentry{strongly connected component|hyperpage}{157}
|
||||||
|
\indexentry{component graph|hyperpage}{157}
|
||||||
|
\indexentry{Kosaraju's algorithm|hyperpage}{158}
|
||||||
|
\indexentry{2SAT problem|hyperpage}{160}
|
||||||
|
\indexentry{3SAT problem|hyperpage}{162}
|
||||||
|
\indexentry{tree query|hyperpage}{163}
|
||||||
|
\indexentry{ancestor|hyperpage}{163}
|
||||||
|
\indexentry{tree traversal array|hyperpage}{164}
|
||||||
|
\indexentry{lowest common ancestor|hyperpage}{167}
|
||||||
|
\indexentry{Euler tour technique|hyperpage}{168}
|
||||||
|
\indexentry{Eulerian path|hyperpage}{173}
|
||||||
|
\indexentry{Eulerian circuit|hyperpage}{174}
|
||||||
|
\indexentry{Hierholzer's algorithm|hyperpage}{175}
|
||||||
|
\indexentry{Hamiltonian path|hyperpage}{177}
|
||||||
|
\indexentry{Hamiltonian circuit|hyperpage}{177}
|
||||||
|
\indexentry{Dirac's theorem|hyperpage}{177}
|
||||||
|
\indexentry{Ore's theorem|hyperpage}{177}
|
||||||
|
\indexentry{De Bruijn sequence|hyperpage}{178}
|
||||||
|
\indexentry{knight's tour|hyperpage}{179}
|
||||||
|
\indexentry{heuristic|hyperpage}{179}
|
||||||
|
\indexentry{Warnsdorf's rule|hyperpage}{179}
|
||||||
|
\indexentry{flow|hyperpage}{181}
|
||||||
|
\indexentry{maximum flow|hyperpage}{181}
|
||||||
|
\indexentry{cut|hyperpage}{182}
|
||||||
|
\indexentry{minimum cut|hyperpage}{182}
|
||||||
|
\indexentry{Ford–Fulkerson algorithm|hyperpage}{182}
|
||||||
|
\indexentry{Edmonds–Karp algorithm|hyperpage}{184}
|
||||||
|
\indexentry{scaling algorithm|hyperpage}{185}
|
||||||
|
\indexentry{minimum cut|hyperpage}{185}
|
||||||
|
\indexentry{matching|hyperpage}{187}
|
||||||
|
\indexentry{maximum matching|hyperpage}{187}
|
||||||
|
\indexentry{Hall's theorem|hyperpage}{189}
|
||||||
|
\indexentry{perfect matching|hyperpage}{189}
|
||||||
|
\indexentry{Kőnig's theorem|hyperpage}{189}
|
||||||
|
\indexentry{node cover|hyperpage}{189}
|
||||||
|
\indexentry{minimum node cover|hyperpage}{189}
|
||||||
|
\indexentry{independent set|hyperpage}{190}
|
||||||
|
\indexentry{maximum independent set|hyperpage}{190}
|
||||||
|
\indexentry{path cover|hyperpage}{190}
|
||||||
|
\indexentry{Dilworth's theorem|hyperpage}{193}
|
||||||
|
\indexentry{antichain|hyperpage}{193}
|
||||||
|
\indexentry{number theory|hyperpage}{197}
|
||||||
|
\indexentry{divisibility|hyperpage}{197}
|
||||||
|
\indexentry{factor|hyperpage}{197}
|
||||||
|
\indexentry{divisor|hyperpage}{197}
|
||||||
|
\indexentry{prime|hyperpage}{197}
|
||||||
|
\indexentry{prime decomposition|hyperpage}{197}
|
||||||
|
\indexentry{perfect number|hyperpage}{198}
|
||||||
|
\indexentry{Goldbach's conjecture|hyperpage}{199}
|
||||||
|
\indexentry{twin prime|hyperpage}{199}
|
||||||
|
\indexentry{Legendre's conjecture|hyperpage}{199}
|
||||||
|
\indexentry{sieve of Eratosthenes|hyperpage}{200}
|
||||||
|
\indexentry{harmonic sum|hyperpage}{200}
|
||||||
|
\indexentry{greatest common divisor|hyperpage}{200}
|
||||||
|
\indexentry{least common multiple|hyperpage}{200}
|
||||||
|
\indexentry{Euclid's algorithm|hyperpage}{200}
|
||||||
|
\indexentry{coprime|hyperpage}{201}
|
||||||
|
\indexentry{Euler's totient function|hyperpage}{201}
|
||||||
|
\indexentry{modular arithmetic|hyperpage}{201}
|
||||||
|
\indexentry{Fermat's theorem|hyperpage}{202}
|
||||||
|
\indexentry{Euler's theorem|hyperpage}{202}
|
||||||
|
\indexentry{modular inverse|hyperpage}{202}
|
||||||
|
\indexentry{Diophantine equation|hyperpage}{204}
|
||||||
|
\indexentry{extended Euclid's algorithm|hyperpage}{204}
|
||||||
|
\indexentry{Chinese remainder theorem|hyperpage}{205}
|
||||||
|
\indexentry{Lagrange's theorem|hyperpage}{205}
|
||||||
|
\indexentry{Zeckendorf's theorem|hyperpage}{206}
|
||||||
|
\indexentry{Fibonacci number|hyperpage}{206}
|
||||||
|
\indexentry{Pythagorean triple|hyperpage}{206}
|
||||||
|
\indexentry{Euclid's formula|hyperpage}{206}
|
||||||
|
\indexentry{Wilson's theorem|hyperpage}{206}
|
||||||
|
\indexentry{combinatorics|hyperpage}{207}
|
||||||
|
\indexentry{binomial coefficient|hyperpage}{208}
|
||||||
|
\indexentry{Pascal's triangle|hyperpage}{209}
|
||||||
|
\indexentry{multinomial coefficient|hyperpage}{210}
|
||||||
|
\indexentry{Catalan number|hyperpage}{210}
|
||||||
|
\indexentry{parenthesis expression|hyperpage}{211}
|
||||||
|
\indexentry{inclusion-exclusion|hyperpage}{212}
|
||||||
|
\indexentry{derangement|hyperpage}{213}
|
||||||
|
\indexentry{Burnside's lemma|hyperpage}{214}
|
||||||
|
\indexentry{Cayley's formula|hyperpage}{215}
|
||||||
|
\indexentry{Prüfer code|hyperpage}{216}
|
||||||
|
\indexentry{matrix|hyperpage}{217}
|
||||||
|
\indexentry{vector|hyperpage}{217}
|
||||||
|
\indexentry{transpose|hyperpage}{217}
|
||||||
|
\indexentry{square matrix|hyperpage}{217}
|
||||||
|
\indexentry{matrix multiplication|hyperpage}{218}
|
||||||
|
\indexentry{identity matrix|hyperpage}{218}
|
||||||
|
\indexentry{matrix power|hyperpage}{219}
|
||||||
|
\indexentry{determinant|hyperpage}{219}
|
||||||
|
\indexentry{cofactor|hyperpage}{219}
|
||||||
|
\indexentry{inverse matrix|hyperpage}{220}
|
||||||
|
\indexentry{linear recurrence|hyperpage}{220}
|
||||||
|
\indexentry{Fibonacci number|hyperpage}{220}
|
||||||
|
\indexentry{Kirchhoff's theorem|hyperpage}{223}
|
||||||
|
\indexentry{spanning tree|hyperpage}{223}
|
||||||
|
\indexentry{Laplacean matrix|hyperpage}{224}
|
||||||
|
\indexentry{probability|hyperpage}{225}
|
||||||
|
\indexentry{conditional probability|hyperpage}{227}
|
||||||
|
\indexentry{independence|hyperpage}{228}
|
||||||
|
\indexentry{random variable|hyperpage}{228}
|
||||||
|
\indexentry{expected value|hyperpage}{229}
|
||||||
|
\indexentry{distribution|hyperpage}{229}
|
||||||
|
\indexentry{uniform distribution|hyperpage}{230}
|
||||||
|
\indexentry{binomial distribution|hyperpage}{230}
|
||||||
|
\indexentry{geometric distribution|hyperpage}{230}
|
||||||
|
\indexentry{Markov chain|hyperpage}{230}
|
||||||
|
\indexentry{randomized algorithm|hyperpage}{231}
|
||||||
|
\indexentry{Monte Carlo algorithm|hyperpage}{231}
|
||||||
|
\indexentry{Las Vegas algorithm|hyperpage}{231}
|
||||||
|
\indexentry{order statistic|hyperpage}{232}
|
||||||
|
\indexentry{matrix multiplication|hyperpage}{232}
|
||||||
|
\indexentry{quicksort|hyperpage}{232}
|
||||||
|
\indexentry{quickselect|hyperpage}{232}
|
||||||
|
\indexentry{Freivalds' algoritm|hyperpage}{232}
|
||||||
|
\indexentry{coloring|hyperpage}{233}
|
||||||
|
\indexentry{winning state|hyperpage}{235}
|
||||||
|
\indexentry{losing state|hyperpage}{235}
|
||||||
|
\indexentry{nim game|hyperpage}{237}
|
||||||
|
\indexentry{nim sum|hyperpage}{237}
|
||||||
|
\indexentry{misère game|hyperpage}{238}
|
||||||
|
\indexentry{Sprague–Grundy theorem|hyperpage}{238}
|
||||||
|
\indexentry{Grundy number|hyperpage}{238}
|
||||||
|
\indexentry{mex function|hyperpage}{238}
|
||||||
|
\indexentry{Grundy's game|hyperpage}{241}
|
||||||
|
\indexentry{pattern matching|hyperpage}{243}
|
||||||
|
\indexentry{string|hyperpage}{243}
|
||||||
|
\indexentry{alphabet|hyperpage}{243}
|
||||||
|
\indexentry{substring|hyperpage}{243}
|
||||||
|
\indexentry{subsequence|hyperpage}{243}
|
||||||
|
\indexentry{prefix|hyperpage}{243}
|
||||||
|
\indexentry{suffix|hyperpage}{243}
|
||||||
|
\indexentry{rotation|hyperpage}{243}
|
||||||
|
\indexentry{period|hyperpage}{243}
|
||||||
|
\indexentry{border|hyperpage}{244}
|
||||||
|
\indexentry{lexicographical order|hyperpage}{244}
|
||||||
|
\indexentry{trie|hyperpage}{244}
|
||||||
|
\indexentry{hashing|hyperpage}{245}
|
||||||
|
\indexentry{string hashing|hyperpage}{245}
|
||||||
|
\indexentry{hash value|hyperpage}{245}
|
||||||
|
\indexentry{polynomial hashing|hyperpage}{245}
|
||||||
|
\indexentry{collision|hyperpage}{246}
|
||||||
|
\indexentry{birthday paradox|hyperpage}{247}
|
||||||
|
\indexentry{Z-algorithm|hyperpage}{247}
|
||||||
|
\indexentry{Z-array|hyperpage}{247}
|
||||||
|
\indexentry{square root algorithm|hyperpage}{251}
|
||||||
|
\indexentry{Mo's algorithm|hyperpage}{255}
|
||||||
|
\indexentry{segment tree|hyperpage}{257}
|
||||||
|
\indexentry{lazy propagation|hyperpage}{258}
|
||||||
|
\indexentry{lazy segment tree|hyperpage}{258}
|
||||||
|
\indexentry{dynamic segment tree|hyperpage}{261}
|
||||||
|
\indexentry{sparse segment tree|hyperpage}{261}
|
||||||
|
\indexentry{persistent segment tree|hyperpage}{262}
|
||||||
|
\indexentry{two-dimensional segment tree|hyperpage}{264}
|
||||||
|
\indexentry{geometry|hyperpage}{265}
|
||||||
|
\indexentry{Heron's formula|hyperpage}{265}
|
||||||
|
\indexentry{complex number|hyperpage}{266}
|
||||||
|
\indexentry{point|hyperpage}{266}
|
||||||
|
\indexentry{vector|hyperpage}{266}
|
||||||
|
\indexentry{complex@\texttt{complex}|hyperpage}{266}
|
||||||
|
\indexentry{cross product|hyperpage}{268}
|
||||||
|
\indexentry{line segment intersection|hyperpage}{269}
|
||||||
|
\indexentry{shoelace formula|hyperpage}{271}
|
||||||
|
\indexentry{Pick's theorem|hyperpage}{272}
|
||||||
|
\indexentry{distance function|hyperpage}{272}
|
||||||
|
\indexentry{Euclidean distance|hyperpage}{272}
|
||||||
|
\indexentry{Manhattan distance|hyperpage}{272}
|
||||||
|
\indexentry{sweep line|hyperpage}{275}
|
||||||
|
\indexentry{intersection point|hyperpage}{276}
|
||||||
|
\indexentry{closest pair|hyperpage}{277}
|
||||||
|
\indexentry{Andrew's algorithm|hyperpage}{279}
|
||||||
|
|
@ -0,0 +1,6 @@
|
||||||
|
This is makeindex, version 2.15 [TeX Live 2020] (kpathsea + Thai support).
|
||||||
|
Scanning input file output/book.idx....done (345 entries accepted, 0 rejected).
|
||||||
|
Sorting entries......done (3076 comparisons).
|
||||||
|
Generating output file output/book.ind....done (401 lines written, 0 warnings).
|
||||||
|
Output written in output/book.ind.
|
||||||
|
Transcript written in output/book.ilg.
|
||||||
|
|
@ -0,0 +1,401 @@
|
||||||
|
\begin{theindex}
|
||||||
|
|
||||||
|
\item 2SAT problem, \hyperpage{160}
|
||||||
|
\item 2SUM problem, \hyperpage{78}
|
||||||
|
\item 3SAT problem, \hyperpage{162}
|
||||||
|
\item 3SUM problem, \hyperpage{79}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item adjacency list, \hyperpage{113}
|
||||||
|
\item adjacency matrix, \hyperpage{114}
|
||||||
|
\item alphabet, \hyperpage{243}
|
||||||
|
\item amortized analysis, \hyperpage{77}
|
||||||
|
\item ancestor, \hyperpage{163}
|
||||||
|
\item and operation, \hyperpage{96}
|
||||||
|
\item Andrew's algorithm, \hyperpage{279}
|
||||||
|
\item antichain, \hyperpage{193}
|
||||||
|
\item arithmetic progression, \hyperpage{10}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item backtracking, \hyperpage{50}
|
||||||
|
\item Bellman–Ford algorithm, \hyperpage{123}
|
||||||
|
\item binary code, \hyperpage{62}
|
||||||
|
\item binary indexed tree, \hyperpage{86}
|
||||||
|
\item binary search, \hyperpage{31}
|
||||||
|
\item binary tree, \hyperpage{139}
|
||||||
|
\item Binet's formula, \hyperpage{14}
|
||||||
|
\item binomial coefficient, \hyperpage{208}
|
||||||
|
\item binomial distribution, \hyperpage{230}
|
||||||
|
\item bipartite graph, \hyperpage{112}, \hyperpage{122}
|
||||||
|
\item birthday paradox, \hyperpage{247}
|
||||||
|
\item bit representation, \hyperpage{95}
|
||||||
|
\item bit shift, \hyperpage{97}
|
||||||
|
\item bitset, \hyperpage{41}
|
||||||
|
\item border, \hyperpage{244}
|
||||||
|
\item breadth-first search, \hyperpage{119}
|
||||||
|
\item bubble sort, \hyperpage{25}
|
||||||
|
\item Burnside's lemma, \hyperpage{214}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item Catalan number, \hyperpage{210}
|
||||||
|
\item Cayley's formula, \hyperpage{215}
|
||||||
|
\item child, \hyperpage{133}
|
||||||
|
\item Chinese remainder theorem, \hyperpage{205}
|
||||||
|
\item closest pair, \hyperpage{277}
|
||||||
|
\item codeword, \hyperpage{62}
|
||||||
|
\item cofactor, \hyperpage{219}
|
||||||
|
\item collision, \hyperpage{246}
|
||||||
|
\item coloring, \hyperpage{112}, \hyperpage{233}
|
||||||
|
\item combinatorics, \hyperpage{207}
|
||||||
|
\item comparison function, \hyperpage{31}
|
||||||
|
\item comparison operator, \hyperpage{30}
|
||||||
|
\item complement, \hyperpage{12}
|
||||||
|
\item complete graph, \hyperpage{111}
|
||||||
|
\item \texttt{complex}, \hyperpage{266}
|
||||||
|
\item complex number, \hyperpage{266}
|
||||||
|
\item complexity classes, \hyperpage{20}
|
||||||
|
\item component, \hyperpage{110}
|
||||||
|
\item component graph, \hyperpage{157}
|
||||||
|
\item conditional probability, \hyperpage{227}
|
||||||
|
\item conjuction, \hyperpage{13}
|
||||||
|
\item connected graph, \hyperpage{110}, \hyperpage{121}
|
||||||
|
\item constant factor, \hyperpage{21}
|
||||||
|
\item constant-time algorithm, \hyperpage{20}
|
||||||
|
\item coprime, \hyperpage{201}
|
||||||
|
\item counting sort, \hyperpage{28}
|
||||||
|
\item cross product, \hyperpage{268}
|
||||||
|
\item cubic algorithm, \hyperpage{20}
|
||||||
|
\item cut, \hyperpage{182}
|
||||||
|
\item cycle, \hyperpage{109}, \hyperpage{121}, \hyperpage{149},
|
||||||
|
\hyperpage{155}
|
||||||
|
\item cycle detection, \hyperpage{155}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item data compression, \hyperpage{62}
|
||||||
|
\item data structure, \hyperpage{35}
|
||||||
|
\item De Bruijn sequence, \hyperpage{178}
|
||||||
|
\item degree, \hyperpage{111}
|
||||||
|
\item depth-first search, \hyperpage{117}
|
||||||
|
\item deque, \hyperpage{42}
|
||||||
|
\item derangement, \hyperpage{213}
|
||||||
|
\item determinant, \hyperpage{219}
|
||||||
|
\item diameter, \hyperpage{135}
|
||||||
|
\item difference, \hyperpage{12}
|
||||||
|
\item difference array, \hyperpage{93}
|
||||||
|
\item Dijkstra's algorithm, \hyperpage{126}, \hyperpage{153}
|
||||||
|
\item Dilworth's theorem, \hyperpage{193}
|
||||||
|
\item Diophantine equation, \hyperpage{204}
|
||||||
|
\item Dirac's theorem, \hyperpage{177}
|
||||||
|
\item directed graph, \hyperpage{110}
|
||||||
|
\item disjunction, \hyperpage{13}
|
||||||
|
\item distance function, \hyperpage{272}
|
||||||
|
\item distribution, \hyperpage{229}
|
||||||
|
\item divisibility, \hyperpage{197}
|
||||||
|
\item divisor, \hyperpage{197}
|
||||||
|
\item dynamic array, \hyperpage{35}
|
||||||
|
\item dynamic programming, \hyperpage{65}
|
||||||
|
\item dynamic segment tree, \hyperpage{261}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item edge, \hyperpage{109}
|
||||||
|
\item edge list, \hyperpage{115}
|
||||||
|
\item edit distance, \hyperpage{74}
|
||||||
|
\item Edmonds–Karp algorithm, \hyperpage{184}
|
||||||
|
\item equivalence, \hyperpage{13}
|
||||||
|
\item Euclid's algorithm, \hyperpage{200}
|
||||||
|
\item Euclid's formula, \hyperpage{206}
|
||||||
|
\item Euclidean distance, \hyperpage{272}
|
||||||
|
\item Euler tour technique, \hyperpage{168}
|
||||||
|
\item Euler's theorem, \hyperpage{202}
|
||||||
|
\item Euler's totient function, \hyperpage{201}
|
||||||
|
\item Eulerian circuit, \hyperpage{174}
|
||||||
|
\item Eulerian path, \hyperpage{173}
|
||||||
|
\item expected value, \hyperpage{229}
|
||||||
|
\item extended Euclid's algorithm, \hyperpage{204}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item factor, \hyperpage{197}
|
||||||
|
\item factorial, \hyperpage{14}
|
||||||
|
\item Faulhaber's formula, \hyperpage{10}
|
||||||
|
\item Fenwick tree, \hyperpage{86}
|
||||||
|
\item Fermat's theorem, \hyperpage{202}
|
||||||
|
\item Fibonacci number, \hyperpage{14}, \hyperpage{206},
|
||||||
|
\hyperpage{220}
|
||||||
|
\item floating point number, \hyperpage{7}
|
||||||
|
\item flow, \hyperpage{181}
|
||||||
|
\item Floyd's algorithm, \hyperpage{156}
|
||||||
|
\item Floyd–Warshall algorithm, \hyperpage{129}
|
||||||
|
\item Ford–Fulkerson algorithm, \hyperpage{182}
|
||||||
|
\item Freivalds' algoritm, \hyperpage{232}
|
||||||
|
\item functional graph, \hyperpage{154}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item geometric distribution, \hyperpage{230}
|
||||||
|
\item geometric progression, \hyperpage{11}
|
||||||
|
\item geometry, \hyperpage{265}
|
||||||
|
\item Goldbach's conjecture, \hyperpage{199}
|
||||||
|
\item graph, \hyperpage{109}
|
||||||
|
\item greatest common divisor, \hyperpage{200}
|
||||||
|
\item greedy algorithm, \hyperpage{57}
|
||||||
|
\item Grundy number, \hyperpage{238}
|
||||||
|
\item Grundy's game, \hyperpage{241}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item Hall's theorem, \hyperpage{189}
|
||||||
|
\item Hamiltonian circuit, \hyperpage{177}
|
||||||
|
\item Hamiltonian path, \hyperpage{177}
|
||||||
|
\item Hamming distance, \hyperpage{100}
|
||||||
|
\item harmonic sum, \hyperpage{11}, \hyperpage{200}
|
||||||
|
\item hash value, \hyperpage{245}
|
||||||
|
\item hashing, \hyperpage{245}
|
||||||
|
\item heap, \hyperpage{43}
|
||||||
|
\item Heron's formula, \hyperpage{265}
|
||||||
|
\item heuristic, \hyperpage{179}
|
||||||
|
\item Hierholzer's algorithm, \hyperpage{175}
|
||||||
|
\item Huffman coding, \hyperpage{63}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item identity matrix, \hyperpage{218}
|
||||||
|
\item implication, \hyperpage{13}
|
||||||
|
\item in-order, \hyperpage{139}
|
||||||
|
\item inclusion-exclusion, \hyperpage{212}
|
||||||
|
\item indegree, \hyperpage{111}
|
||||||
|
\item independence, \hyperpage{228}
|
||||||
|
\item independent set, \hyperpage{190}
|
||||||
|
\item index compression, \hyperpage{93}
|
||||||
|
\item input and output, \hyperpage{4}
|
||||||
|
\item integer, \hyperpage{6}
|
||||||
|
\item intersection, \hyperpage{12}
|
||||||
|
\item intersection point, \hyperpage{276}
|
||||||
|
\item inverse matrix, \hyperpage{220}
|
||||||
|
\item inversion, \hyperpage{26}
|
||||||
|
\item iterator, \hyperpage{39}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item Kadane's algorithm, \hyperpage{23}
|
||||||
|
\item Kirchhoff's theorem, \hyperpage{223}
|
||||||
|
\item knapsack, \hyperpage{72}
|
||||||
|
\item knight's tour, \hyperpage{179}
|
||||||
|
\item Kosaraju's algorithm, \hyperpage{158}
|
||||||
|
\item Kruskal's algorithm, \hyperpage{142}
|
||||||
|
\item Kőnig's theorem, \hyperpage{189}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item Lagrange's theorem, \hyperpage{205}
|
||||||
|
\item Laplacean matrix, \hyperpage{224}
|
||||||
|
\item Las Vegas algorithm, \hyperpage{231}
|
||||||
|
\item lazy propagation, \hyperpage{258}
|
||||||
|
\item lazy segment tree, \hyperpage{258}
|
||||||
|
\item leaf, \hyperpage{133}
|
||||||
|
\item least common multiple, \hyperpage{200}
|
||||||
|
\item Legendre's conjecture, \hyperpage{199}
|
||||||
|
\item Levenshtein distance, \hyperpage{74}
|
||||||
|
\item lexicographical order, \hyperpage{244}
|
||||||
|
\item line segment intersection, \hyperpage{269}
|
||||||
|
\item linear algorithm, \hyperpage{20}
|
||||||
|
\item linear recurrence, \hyperpage{220}
|
||||||
|
\item logarithm, \hyperpage{14}
|
||||||
|
\item logarithmic algorithm, \hyperpage{20}
|
||||||
|
\item logic, \hyperpage{13}
|
||||||
|
\item longest increasing subsequence, \hyperpage{70}
|
||||||
|
\item losing state, \hyperpage{235}
|
||||||
|
\item lowest common ancestor, \hyperpage{167}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item macro, \hyperpage{9}
|
||||||
|
\item Manhattan distance, \hyperpage{272}
|
||||||
|
\item map, \hyperpage{38}
|
||||||
|
\item Markov chain, \hyperpage{230}
|
||||||
|
\item matching, \hyperpage{187}
|
||||||
|
\item matrix, \hyperpage{217}
|
||||||
|
\item matrix multiplication, \hyperpage{218}, \hyperpage{232}
|
||||||
|
\item matrix power, \hyperpage{219}
|
||||||
|
\item maximum flow, \hyperpage{181}
|
||||||
|
\item maximum independent set, \hyperpage{190}
|
||||||
|
\item maximum matching, \hyperpage{187}
|
||||||
|
\item maximum query, \hyperpage{83}
|
||||||
|
\item maximum spanning tree, \hyperpage{142}
|
||||||
|
\item maximum subarray sum, \hyperpage{21}
|
||||||
|
\item meet in the middle, \hyperpage{54}
|
||||||
|
\item memoization, \hyperpage{67}
|
||||||
|
\item merge sort, \hyperpage{27}
|
||||||
|
\item mex function, \hyperpage{238}
|
||||||
|
\item minimum cut, \hyperpage{182}, \hyperpage{185}
|
||||||
|
\item minimum node cover, \hyperpage{189}
|
||||||
|
\item minimum query, \hyperpage{83}
|
||||||
|
\item minimum spanning tree, \hyperpage{141}
|
||||||
|
\item misère game, \hyperpage{238}
|
||||||
|
\item Mo's algorithm, \hyperpage{255}
|
||||||
|
\item modular arithmetic, \hyperpage{6}, \hyperpage{201}
|
||||||
|
\item modular inverse, \hyperpage{202}
|
||||||
|
\item Monte Carlo algorithm, \hyperpage{231}
|
||||||
|
\item multinomial coefficient, \hyperpage{210}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item natural logarithm, \hyperpage{15}
|
||||||
|
\item nearest smaller elements, \hyperpage{79}
|
||||||
|
\item negation, \hyperpage{13}
|
||||||
|
\item negative cycle, \hyperpage{125}
|
||||||
|
\item neighbor, \hyperpage{111}
|
||||||
|
\item \texttt{next\_permutation}, \hyperpage{49}
|
||||||
|
\item nim game, \hyperpage{237}
|
||||||
|
\item nim sum, \hyperpage{237}
|
||||||
|
\item node, \hyperpage{109}
|
||||||
|
\item node cover, \hyperpage{189}
|
||||||
|
\item not operation, \hyperpage{97}
|
||||||
|
\item NP-hard problem, \hyperpage{20}
|
||||||
|
\item number theory, \hyperpage{197}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item or operation, \hyperpage{96}
|
||||||
|
\item order statistic, \hyperpage{232}
|
||||||
|
\item Ore's theorem, \hyperpage{177}
|
||||||
|
\item outdegree, \hyperpage{111}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item \texttt{pair}, \hyperpage{30}
|
||||||
|
\item parent, \hyperpage{133}
|
||||||
|
\item parenthesis expression, \hyperpage{211}
|
||||||
|
\item Pascal's triangle, \hyperpage{209}
|
||||||
|
\item path, \hyperpage{109}
|
||||||
|
\item path cover, \hyperpage{190}
|
||||||
|
\item pattern matching, \hyperpage{243}
|
||||||
|
\item perfect matching, \hyperpage{189}
|
||||||
|
\item perfect number, \hyperpage{198}
|
||||||
|
\item period, \hyperpage{243}
|
||||||
|
\item permutation, \hyperpage{49}
|
||||||
|
\item persistent segment tree, \hyperpage{262}
|
||||||
|
\item Pick's theorem, \hyperpage{272}
|
||||||
|
\item point, \hyperpage{266}
|
||||||
|
\item polynomial algorithm, \hyperpage{20}
|
||||||
|
\item polynomial hashing, \hyperpage{245}
|
||||||
|
\item post-order, \hyperpage{139}
|
||||||
|
\item pre-order, \hyperpage{139}
|
||||||
|
\item predicate, \hyperpage{13}
|
||||||
|
\item prefix, \hyperpage{243}
|
||||||
|
\item prefix sum array, \hyperpage{84}
|
||||||
|
\item Prim's algorithm, \hyperpage{147}
|
||||||
|
\item prime, \hyperpage{197}
|
||||||
|
\item prime decomposition, \hyperpage{197}
|
||||||
|
\item priority queue, \hyperpage{43}
|
||||||
|
\item probability, \hyperpage{225}
|
||||||
|
\item programming language, \hyperpage{3}
|
||||||
|
\item Prüfer code, \hyperpage{216}
|
||||||
|
\item Pythagorean triple, \hyperpage{206}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item quadratic algorithm, \hyperpage{20}
|
||||||
|
\item quantifier, \hyperpage{13}
|
||||||
|
\item queen problem, \hyperpage{50}
|
||||||
|
\item queue, \hyperpage{43}
|
||||||
|
\item quickselect, \hyperpage{232}
|
||||||
|
\item quicksort, \hyperpage{232}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item random variable, \hyperpage{228}
|
||||||
|
\item \texttt{random\_shuffle}, \hyperpage{39}
|
||||||
|
\item randomized algorithm, \hyperpage{231}
|
||||||
|
\item range query, \hyperpage{83}
|
||||||
|
\item regular graph, \hyperpage{111}
|
||||||
|
\item remainder, \hyperpage{6}
|
||||||
|
\item \texttt{reverse}, \hyperpage{39}
|
||||||
|
\item root, \hyperpage{133}
|
||||||
|
\item rooted tree, \hyperpage{133}
|
||||||
|
\item rotation, \hyperpage{243}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item scaling algorithm, \hyperpage{185}
|
||||||
|
\item segment tree, \hyperpage{89}, \hyperpage{257}
|
||||||
|
\item set, \hyperpage{12}, \hyperpage{37}
|
||||||
|
\item set theory, \hyperpage{12}
|
||||||
|
\item shoelace formula, \hyperpage{271}
|
||||||
|
\item shortest path, \hyperpage{123}
|
||||||
|
\item sieve of Eratosthenes, \hyperpage{200}
|
||||||
|
\item simple graph, \hyperpage{112}
|
||||||
|
\item sliding window, \hyperpage{81}
|
||||||
|
\item sliding window minimum, \hyperpage{81}
|
||||||
|
\item \texttt{sort}, \hyperpage{29}, \hyperpage{39}
|
||||||
|
\item sorting, \hyperpage{25}
|
||||||
|
\item spanning tree, \hyperpage{141}, \hyperpage{223}
|
||||||
|
\item sparse segment tree, \hyperpage{261}
|
||||||
|
\item sparse table, \hyperpage{85}
|
||||||
|
\item SPFA algorithm, \hyperpage{126}
|
||||||
|
\item Sprague–Grundy theorem, \hyperpage{238}
|
||||||
|
\item square matrix, \hyperpage{217}
|
||||||
|
\item square root algorithm, \hyperpage{251}
|
||||||
|
\item stack, \hyperpage{42}
|
||||||
|
\item string, \hyperpage{36}, \hyperpage{243}
|
||||||
|
\item string hashing, \hyperpage{245}
|
||||||
|
\item strongly connected component, \hyperpage{157}
|
||||||
|
\item strongly connected graph, \hyperpage{157}
|
||||||
|
\item subsequence, \hyperpage{243}
|
||||||
|
\item subset, \hyperpage{12}, \hyperpage{47}
|
||||||
|
\item substring, \hyperpage{243}
|
||||||
|
\item subtree, \hyperpage{133}
|
||||||
|
\item successor graph, \hyperpage{154}
|
||||||
|
\item suffix, \hyperpage{243}
|
||||||
|
\item sum query, \hyperpage{83}
|
||||||
|
\item sweep line, \hyperpage{275}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item time complexity, \hyperpage{17}
|
||||||
|
\item topological sorting, \hyperpage{149}
|
||||||
|
\item transpose, \hyperpage{217}
|
||||||
|
\item tree, \hyperpage{110}, \hyperpage{133}
|
||||||
|
\item tree query, \hyperpage{163}
|
||||||
|
\item tree traversal array, \hyperpage{164}
|
||||||
|
\item trie, \hyperpage{244}
|
||||||
|
\item \texttt{tuple}, \hyperpage{30}
|
||||||
|
\item \texttt{typedef}, \hyperpage{8}
|
||||||
|
\item twin prime, \hyperpage{199}
|
||||||
|
\item two pointers method, \hyperpage{77}
|
||||||
|
\item two-dimensional segment tree, \hyperpage{264}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item uniform distribution, \hyperpage{230}
|
||||||
|
\item union, \hyperpage{12}
|
||||||
|
\item union-find structure, \hyperpage{145}
|
||||||
|
\item universal set, \hyperpage{12}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item vector, \hyperpage{35}, \hyperpage{217}, \hyperpage{266}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item Warnsdorf's rule, \hyperpage{179}
|
||||||
|
\item weighted graph, \hyperpage{111}
|
||||||
|
\item Wilson's theorem, \hyperpage{206}
|
||||||
|
\item winning state, \hyperpage{235}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item xor operation, \hyperpage{97}
|
||||||
|
|
||||||
|
\indexspace
|
||||||
|
|
||||||
|
\item Z-algorithm, \hyperpage{247}
|
||||||
|
\item Z-array, \hyperpage{247}
|
||||||
|
\item Zeckendorf's theorem, \hyperpage{206}
|
||||||
|
|
||||||
|
\end{theindex}
|
||||||
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|
|
@ -0,0 +1,154 @@
|
||||||
|
\BOOKMARK [0][-]{chapter*.2}{Preface}{}% 1
|
||||||
|
\BOOKMARK [-1][-]{part.1}{I Basic techniques}{}% 2
|
||||||
|
\BOOKMARK [0][-]{chapter.1}{Introduction}{part.1}% 3
|
||||||
|
\BOOKMARK [1][-]{section.1.1}{Programming languages}{chapter.1}% 4
|
||||||
|
\BOOKMARK [1][-]{section.1.2}{Input and output}{chapter.1}% 5
|
||||||
|
\BOOKMARK [1][-]{section.1.3}{Working with numbers}{chapter.1}% 6
|
||||||
|
\BOOKMARK [1][-]{section.1.4}{Shortening code}{chapter.1}% 7
|
||||||
|
\BOOKMARK [1][-]{section.1.5}{Mathematics}{chapter.1}% 8
|
||||||
|
\BOOKMARK [1][-]{section.1.6}{Contests and resources}{chapter.1}% 9
|
||||||
|
\BOOKMARK [0][-]{chapter.2}{Time complexity}{part.1}% 10
|
||||||
|
\BOOKMARK [1][-]{section.2.1}{Calculation rules}{chapter.2}% 11
|
||||||
|
\BOOKMARK [1][-]{section.2.2}{Complexity classes}{chapter.2}% 12
|
||||||
|
\BOOKMARK [1][-]{section.2.3}{Estimating efficiency}{chapter.2}% 13
|
||||||
|
\BOOKMARK [1][-]{section.2.4}{Maximum subarray sum}{chapter.2}% 14
|
||||||
|
\BOOKMARK [0][-]{chapter.3}{Sorting}{part.1}% 15
|
||||||
|
\BOOKMARK [1][-]{section.3.1}{Sorting theory}{chapter.3}% 16
|
||||||
|
\BOOKMARK [1][-]{section.3.2}{Sorting in C++}{chapter.3}% 17
|
||||||
|
\BOOKMARK [1][-]{section.3.3}{Binary search}{chapter.3}% 18
|
||||||
|
\BOOKMARK [0][-]{chapter.4}{Data structures}{part.1}% 19
|
||||||
|
\BOOKMARK [1][-]{section.4.1}{Dynamic arrays}{chapter.4}% 20
|
||||||
|
\BOOKMARK [1][-]{section.4.2}{Set structures}{chapter.4}% 21
|
||||||
|
\BOOKMARK [1][-]{section.4.3}{Map structures}{chapter.4}% 22
|
||||||
|
\BOOKMARK [1][-]{section.4.4}{Iterators and ranges}{chapter.4}% 23
|
||||||
|
\BOOKMARK [1][-]{section.4.5}{Other structures}{chapter.4}% 24
|
||||||
|
\BOOKMARK [1][-]{section.4.6}{Comparison to sorting}{chapter.4}% 25
|
||||||
|
\BOOKMARK [0][-]{chapter.5}{Complete search}{part.1}% 26
|
||||||
|
\BOOKMARK [1][-]{section.5.1}{Generating subsets}{chapter.5}% 27
|
||||||
|
\BOOKMARK [1][-]{section.5.2}{Generating permutations}{chapter.5}% 28
|
||||||
|
\BOOKMARK [1][-]{section.5.3}{Backtracking}{chapter.5}% 29
|
||||||
|
\BOOKMARK [1][-]{section.5.4}{Pruning the search}{chapter.5}% 30
|
||||||
|
\BOOKMARK [1][-]{section.5.5}{Meet in the middle}{chapter.5}% 31
|
||||||
|
\BOOKMARK [0][-]{chapter.6}{Greedy algorithms}{part.1}% 32
|
||||||
|
\BOOKMARK [1][-]{section.6.1}{Coin problem}{chapter.6}% 33
|
||||||
|
\BOOKMARK [1][-]{section.6.2}{Scheduling}{chapter.6}% 34
|
||||||
|
\BOOKMARK [1][-]{section.6.3}{Tasks and deadlines}{chapter.6}% 35
|
||||||
|
\BOOKMARK [1][-]{section.6.4}{Minimizing sums}{chapter.6}% 36
|
||||||
|
\BOOKMARK [1][-]{section.6.5}{Data compression}{chapter.6}% 37
|
||||||
|
\BOOKMARK [0][-]{chapter.7}{Dynamic programming}{part.1}% 38
|
||||||
|
\BOOKMARK [1][-]{section.7.1}{Coin problem}{chapter.7}% 39
|
||||||
|
\BOOKMARK [1][-]{section.7.2}{Longest increasing subsequence}{chapter.7}% 40
|
||||||
|
\BOOKMARK [1][-]{section.7.3}{Paths in a grid}{chapter.7}% 41
|
||||||
|
\BOOKMARK [1][-]{section.7.4}{Knapsack problems}{chapter.7}% 42
|
||||||
|
\BOOKMARK [1][-]{section.7.5}{Edit distance}{chapter.7}% 43
|
||||||
|
\BOOKMARK [1][-]{section.7.6}{Counting tilings}{chapter.7}% 44
|
||||||
|
\BOOKMARK [0][-]{chapter.8}{Amortized analysis}{part.1}% 45
|
||||||
|
\BOOKMARK [1][-]{section.8.1}{Two pointers method}{chapter.8}% 46
|
||||||
|
\BOOKMARK [1][-]{section.8.2}{Nearest smaller elements}{chapter.8}% 47
|
||||||
|
\BOOKMARK [1][-]{section.8.3}{Sliding window minimum}{chapter.8}% 48
|
||||||
|
\BOOKMARK [0][-]{chapter.9}{Range queries}{part.1}% 49
|
||||||
|
\BOOKMARK [1][-]{section.9.1}{Static array queries}{chapter.9}% 50
|
||||||
|
\BOOKMARK [1][-]{section.9.2}{Binary indexed tree}{chapter.9}% 51
|
||||||
|
\BOOKMARK [1][-]{section.9.3}{Segment tree}{chapter.9}% 52
|
||||||
|
\BOOKMARK [1][-]{section.9.4}{Additional techniques}{chapter.9}% 53
|
||||||
|
\BOOKMARK [0][-]{chapter.10}{Bit manipulation}{part.1}% 54
|
||||||
|
\BOOKMARK [1][-]{section.10.1}{Bit representation}{chapter.10}% 55
|
||||||
|
\BOOKMARK [1][-]{section.10.2}{Bit operations}{chapter.10}% 56
|
||||||
|
\BOOKMARK [1][-]{section.10.3}{Representing sets}{chapter.10}% 57
|
||||||
|
\BOOKMARK [1][-]{section.10.4}{Bit optimizations}{chapter.10}% 58
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||||||
|
\BOOKMARK [1][-]{section.10.5}{Dynamic programming}{chapter.10}% 59
|
||||||
|
\BOOKMARK [-1][-]{part.2}{II Graph algorithms}{}% 60
|
||||||
|
\BOOKMARK [0][-]{chapter.11}{Basics of graphs}{part.2}% 61
|
||||||
|
\BOOKMARK [1][-]{section.11.1}{Graph terminology}{chapter.11}% 62
|
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|
\BOOKMARK [1][-]{section.11.2}{Graph representation}{chapter.11}% 63
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||||||
|
\BOOKMARK [0][-]{chapter.12}{Graph traversal}{part.2}% 64
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||||||
|
\BOOKMARK [1][-]{section.12.1}{Depth-first search}{chapter.12}% 65
|
||||||
|
\BOOKMARK [1][-]{section.12.2}{Breadth-first search}{chapter.12}% 66
|
||||||
|
\BOOKMARK [1][-]{section.12.3}{Applications}{chapter.12}% 67
|
||||||
|
\BOOKMARK [0][-]{chapter.13}{Shortest paths}{part.2}% 68
|
||||||
|
\BOOKMARK [1][-]{section.13.1}{Bellman\205Ford algorithm}{chapter.13}% 69
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||||||
|
\BOOKMARK [1][-]{section.13.2}{Dijkstra's algorithm}{chapter.13}% 70
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||||||
|
\BOOKMARK [1][-]{section.13.3}{Floyd\205Warshall algorithm}{chapter.13}% 71
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||||||
|
\BOOKMARK [0][-]{chapter.14}{Tree algorithms}{part.2}% 72
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||||||
|
\BOOKMARK [1][-]{section.14.1}{Tree traversal}{chapter.14}% 73
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||||||
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\BOOKMARK [1][-]{section.14.2}{Diameter}{chapter.14}% 74
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\BOOKMARK [1][-]{section.14.3}{All longest paths}{chapter.14}% 75
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\BOOKMARK [1][-]{section.14.4}{Binary trees}{chapter.14}% 76
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\BOOKMARK [0][-]{chapter.15}{Spanning trees}{part.2}% 77
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||||||
|
\BOOKMARK [1][-]{section.15.1}{Kruskal's algorithm}{chapter.15}% 78
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||||||
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\BOOKMARK [1][-]{section.15.2}{Union-find structure}{chapter.15}% 79
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||||||
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\BOOKMARK [1][-]{section.15.3}{Prim's algorithm}{chapter.15}% 80
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||||||
|
\BOOKMARK [0][-]{chapter.16}{Directed graphs}{part.2}% 81
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||||||
|
\BOOKMARK [1][-]{section.16.1}{Topological sorting}{chapter.16}% 82
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\BOOKMARK [1][-]{section.16.2}{Dynamic programming}{chapter.16}% 83
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|
\BOOKMARK [1][-]{section.16.3}{Successor paths}{chapter.16}% 84
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|
\BOOKMARK [1][-]{section.16.4}{Cycle detection}{chapter.16}% 85
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||||||
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\BOOKMARK [0][-]{chapter.17}{Strong connectivity}{part.2}% 86
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||||||
|
\BOOKMARK [1][-]{section.17.1}{Kosaraju's algorithm}{chapter.17}% 87
|
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|
\BOOKMARK [1][-]{section.17.2}{2SAT problem}{chapter.17}% 88
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||||||
|
\BOOKMARK [0][-]{chapter.18}{Tree queries}{part.2}% 89
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||||||
|
\BOOKMARK [1][-]{section.18.1}{Finding ancestors}{chapter.18}% 90
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||||||
|
\BOOKMARK [1][-]{section.18.2}{Subtrees and paths}{chapter.18}% 91
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||||||
|
\BOOKMARK [1][-]{section.18.3}{Lowest common ancestor}{chapter.18}% 92
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|
\BOOKMARK [1][-]{section.18.4}{Offline algorithms}{chapter.18}% 93
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|
\BOOKMARK [0][-]{chapter.19}{Paths and circuits}{part.2}% 94
|
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|
\BOOKMARK [1][-]{section.19.1}{Eulerian paths}{chapter.19}% 95
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|
\BOOKMARK [1][-]{section.19.2}{Hamiltonian paths}{chapter.19}% 96
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|
\BOOKMARK [1][-]{section.19.3}{De Bruijn sequences}{chapter.19}% 97
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|
\BOOKMARK [1][-]{section.19.4}{Knight's tours}{chapter.19}% 98
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\BOOKMARK [0][-]{chapter.20}{Flows and cuts}{part.2}% 99
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|
\BOOKMARK [1][-]{section.20.1}{Ford\205Fulkerson algorithm}{chapter.20}% 100
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|
\BOOKMARK [1][-]{section.20.2}{Disjoint paths}{chapter.20}% 101
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|
\BOOKMARK [1][-]{section.20.3}{Maximum matchings}{chapter.20}% 102
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\BOOKMARK [1][-]{section.20.4}{Path covers}{chapter.20}% 103
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|
\BOOKMARK [-1][-]{part.3}{III Advanced topics}{}% 104
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\BOOKMARK [0][-]{chapter.21}{Number theory}{part.3}% 105
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\BOOKMARK [1][-]{section.21.1}{Primes and factors}{chapter.21}% 106
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\BOOKMARK [1][-]{section.21.2}{Modular arithmetic}{chapter.21}% 107
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||||||
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\BOOKMARK [1][-]{section.21.3}{Solving equations}{chapter.21}% 108
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||||||
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\BOOKMARK [1][-]{section.21.4}{Other results}{chapter.21}% 109
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||||||
|
\BOOKMARK [0][-]{chapter.22}{Combinatorics}{part.3}% 110
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||||||
|
\BOOKMARK [1][-]{section.22.1}{Binomial coefficients}{chapter.22}% 111
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||||||
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\BOOKMARK [1][-]{section.22.2}{Catalan numbers}{chapter.22}% 112
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||||||
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\BOOKMARK [1][-]{section.22.3}{Inclusion-exclusion}{chapter.22}% 113
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||||||
|
\BOOKMARK [1][-]{section.22.4}{Burnside's lemma}{chapter.22}% 114
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||||||
|
\BOOKMARK [1][-]{section.22.5}{Cayley's formula}{chapter.22}% 115
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||||||
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\BOOKMARK [0][-]{chapter.23}{Matrices}{part.3}% 116
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||||||
|
\BOOKMARK [1][-]{section.23.1}{Operations}{chapter.23}% 117
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||||||
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\BOOKMARK [1][-]{section.23.2}{Linear recurrences}{chapter.23}% 118
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||||||
|
\BOOKMARK [1][-]{section.23.3}{Graphs and matrices}{chapter.23}% 119
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||||||
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\BOOKMARK [0][-]{chapter.24}{Probability}{part.3}% 120
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||||||
|
\BOOKMARK [1][-]{section.24.1}{Calculation}{chapter.24}% 121
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||||||
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\BOOKMARK [1][-]{section.24.2}{Events}{chapter.24}% 122
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\BOOKMARK [1][-]{section.24.3}{Random variables}{chapter.24}% 123
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||||||
|
\BOOKMARK [1][-]{section.24.4}{Markov chains}{chapter.24}% 124
|
||||||
|
\BOOKMARK [1][-]{section.24.5}{Randomized algorithms}{chapter.24}% 125
|
||||||
|
\BOOKMARK [0][-]{chapter.25}{Game theory}{part.3}% 126
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||||||
|
\BOOKMARK [1][-]{section.25.1}{Game states}{chapter.25}% 127
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||||||
|
\BOOKMARK [1][-]{section.25.2}{Nim game}{chapter.25}% 128
|
||||||
|
\BOOKMARK [1][-]{section.25.3}{Sprague\205Grundy theorem}{chapter.25}% 129
|
||||||
|
\BOOKMARK [0][-]{chapter.26}{String algorithms}{part.3}% 130
|
||||||
|
\BOOKMARK [1][-]{section.26.1}{String terminology}{chapter.26}% 131
|
||||||
|
\BOOKMARK [1][-]{section.26.2}{Trie structure}{chapter.26}% 132
|
||||||
|
\BOOKMARK [1][-]{section.26.3}{String hashing}{chapter.26}% 133
|
||||||
|
\BOOKMARK [1][-]{section.26.4}{Z-algorithm}{chapter.26}% 134
|
||||||
|
\BOOKMARK [0][-]{chapter.27}{Square root algorithms}{part.3}% 135
|
||||||
|
\BOOKMARK [1][-]{section.27.1}{Combining algorithms}{chapter.27}% 136
|
||||||
|
\BOOKMARK [1][-]{section.27.2}{Integer partitions}{chapter.27}% 137
|
||||||
|
\BOOKMARK [1][-]{section.27.3}{Mo's algorithm}{chapter.27}% 138
|
||||||
|
\BOOKMARK [0][-]{chapter.28}{Segment trees revisited}{part.3}% 139
|
||||||
|
\BOOKMARK [1][-]{section.28.1}{Lazy propagation}{chapter.28}% 140
|
||||||
|
\BOOKMARK [1][-]{section.28.2}{Dynamic trees}{chapter.28}% 141
|
||||||
|
\BOOKMARK [1][-]{section.28.3}{Data structures}{chapter.28}% 142
|
||||||
|
\BOOKMARK [1][-]{section.28.4}{Two-dimensionality}{chapter.28}% 143
|
||||||
|
\BOOKMARK [0][-]{chapter.29}{Geometry}{part.3}% 144
|
||||||
|
\BOOKMARK [1][-]{section.29.1}{Complex numbers}{chapter.29}% 145
|
||||||
|
\BOOKMARK [1][-]{section.29.2}{Points and lines}{chapter.29}% 146
|
||||||
|
\BOOKMARK [1][-]{section.29.3}{Polygon area}{chapter.29}% 147
|
||||||
|
\BOOKMARK [1][-]{section.29.4}{Distance functions}{chapter.29}% 148
|
||||||
|
\BOOKMARK [0][-]{chapter.30}{Sweep line algorithms}{part.3}% 149
|
||||||
|
\BOOKMARK [1][-]{section.30.1}{Intersection points}{chapter.30}% 150
|
||||||
|
\BOOKMARK [1][-]{section.30.2}{Closest pair problem}{chapter.30}% 151
|
||||||
|
\BOOKMARK [1][-]{section.30.3}{Convex hull problem}{chapter.30}% 152
|
||||||
|
\BOOKMARK [0][-]{section*.3}{Bibliography}{part.3}% 153
|
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|
\BOOKMARK [0][-]{chapter*.5}{Index}{part.3}% 154
|
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\babel@toc {english}{}
|
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\contentsline {chapter}{Preface}{ix}{chapter*.2}%
|
||||||
|
\contentsline {part}{I\hspace {1em}Basic techniques}{1}{part.1}%
|
||||||
|
\contentsline {chapter}{\numberline {1}Introduction}{3}{chapter.1}%
|
||||||
|
\contentsline {section}{\numberline {1.1}Programming languages}{3}{section.1.1}%
|
||||||
|
\contentsline {subsubsection}{C++ code template}{4}{section.1.1}%
|
||||||
|
\contentsline {section}{\numberline {1.2}Input and output}{4}{section.1.2}%
|
||||||
|
\contentsline {section}{\numberline {1.3}Working with numbers}{6}{section.1.3}%
|
||||||
|
\contentsline {subsubsection}{Integers}{6}{section.1.3}%
|
||||||
|
\contentsline {subsubsection}{Modular arithmetic}{6}{lstnumber.-14.3}%
|
||||||
|
\contentsline {subsubsection}{Floating point numbers}{7}{lstnumber.-16.2}%
|
||||||
|
\contentsline {section}{\numberline {1.4}Shortening code}{8}{section.1.4}%
|
||||||
|
\contentsline {subsubsection}{Type names}{8}{section.1.4}%
|
||||||
|
\contentsline {subsubsection}{Macros}{9}{lstnumber.-23.2}%
|
||||||
|
\contentsline {section}{\numberline {1.5}Mathematics}{10}{section.1.5}%
|
||||||
|
\contentsline {subsubsection}{Sum formulas}{10}{section.1.5}%
|
||||||
|
\contentsline {subsubsection}{Set theory}{12}{section.1.5}%
|
||||||
|
\contentsline {subsubsection}{Logic}{13}{section.1.5}%
|
||||||
|
\contentsline {subsubsection}{Functions}{13}{section.1.5}%
|
||||||
|
\contentsline {subsubsection}{Logarithms}{14}{section.1.5}%
|
||||||
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\contentsline {section}{\numberline {1.6}Contests and resources}{15}{section.1.6}%
|
||||||
|
\contentsline {subsubsection}{IOI}{15}{section.1.6}%
|
||||||
|
\contentsline {subsubsection}{ICPC}{15}{section.1.6}%
|
||||||
|
\contentsline {subsubsection}{Online contests}{16}{section.1.6}%
|
||||||
|
\contentsline {subsubsection}{Books}{16}{section.1.6}%
|
||||||
|
\contentsline {chapter}{\numberline {2}Time complexity}{17}{chapter.2}%
|
||||||
|
\contentsline {section}{\numberline {2.1}Calculation rules}{17}{section.2.1}%
|
||||||
|
\contentsline {section}{\numberline {2.2}Complexity classes}{20}{section.2.2}%
|
||||||
|
\contentsline {section}{\numberline {2.3}Estimating efficiency}{21}{section.2.3}%
|
||||||
|
\contentsline {section}{\numberline {2.4}Maximum subarray sum}{21}{section.2.4}%
|
||||||
|
\contentsline {subsubsection}{Algorithm 1}{22}{section.2.4}%
|
||||||
|
\contentsline {subsubsection}{Algorithm 2}{22}{lstnumber.-46.11}%
|
||||||
|
\contentsline {subsubsection}{Algorithm 3}{23}{lstnumber.-47.9}%
|
||||||
|
\contentsline {subsubsection}{Efficiency comparison}{23}{lstnumber.-48.6}%
|
||||||
|
\contentsline {chapter}{\numberline {3}Sorting}{25}{chapter.3}%
|
||||||
|
\contentsline {section}{\numberline {3.1}Sorting theory}{25}{section.3.1}%
|
||||||
|
\contentsline {subsubsection}{$O(n^2)$ algorithms}{25}{section.3.1}%
|
||||||
|
\contentsline {subsubsection}{Inversions}{26}{lstnumber.-49.7}%
|
||||||
|
\contentsline {subsubsection}{$O(n \qopname \relax o{log}n)$ algorithms}{27}{lstnumber.-49.7}%
|
||||||
|
\contentsline {subsubsection}{Sorting lower bound}{28}{Item.7}%
|
||||||
|
\contentsline {subsubsection}{Counting sort}{28}{Item.7}%
|
||||||
|
\contentsline {section}{\numberline {3.2}Sorting in C++}{29}{section.3.2}%
|
||||||
|
\contentsline {subsubsection}{Comparison operators}{30}{lstnumber.-53.2}%
|
||||||
|
\contentsline {subsubsection}{User-defined structs}{30}{lstnumber.-55.5}%
|
||||||
|
\contentsline {subsubsection}{Comparison functions}{31}{lstnumber.-56.7}%
|
||||||
|
\contentsline {section}{\numberline {3.3}Binary search}{31}{section.3.3}%
|
||||||
|
\contentsline {subsubsection}{Method 1}{32}{lstnumber.-59.5}%
|
||||||
|
\contentsline {subsubsection}{Method 2}{32}{lstnumber.-60.9}%
|
||||||
|
\contentsline {subsubsection}{C++ functions}{33}{lstnumber.-61.7}%
|
||||||
|
\contentsline {subsubsection}{Finding the smallest solution}{33}{lstnumber.-64.2}%
|
||||||
|
\contentsline {subsubsection}{Finding the maximum value}{34}{lstnumber.-65.5}%
|
||||||
|
\contentsline {chapter}{\numberline {4}Data structures}{35}{chapter.4}%
|
||||||
|
\contentsline {section}{\numberline {4.1}Dynamic arrays}{35}{section.4.1}%
|
||||||
|
\contentsline {section}{\numberline {4.2}Set structures}{37}{section.4.2}%
|
||||||
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\contentsline {section}{\numberline {4.3}Map structures}{38}{section.4.3}%
|
||||||
|
\contentsline {section}{\numberline {4.4}Iterators and ranges}{39}{section.4.4}%
|
||||||
|
\contentsline {subsubsection}{Working with ranges}{39}{section.4.4}%
|
||||||
|
\contentsline {subsubsection}{Set iterators}{40}{lstnumber.-87.3}%
|
||||||
|
\contentsline {section}{\numberline {4.5}Other structures}{41}{section.4.5}%
|
||||||
|
\contentsline {subsubsection}{Bitset}{41}{section.4.5}%
|
||||||
|
\contentsline {subsubsection}{Deque}{42}{lstnumber.-98.5}%
|
||||||
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\contentsline {subsubsection}{Stack}{42}{lstnumber.-99.6}%
|
||||||
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\contentsline {subsubsection}{Queue}{43}{lstnumber.-100.7}%
|
||||||
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\contentsline {subsubsection}{Priority queue}{43}{lstnumber.-101.7}%
|
||||||
|
\contentsline {subsubsection}{Policy-based data structures}{44}{lstnumber.-103.1}%
|
||||||
|
\contentsline {section}{\numberline {4.6}Comparison to sorting}{44}{section.4.6}%
|
||||||
|
\contentsline {subsubsection}{Algorithm 1}{45}{section.4.6}%
|
||||||
|
\contentsline {subsubsection}{Algorithm 2}{45}{section.4.6}%
|
||||||
|
\contentsline {subsubsection}{Algorithm 3}{45}{section.4.6}%
|
||||||
|
\contentsline {subsubsection}{Efficiency comparison}{45}{section.4.6}%
|
||||||
|
\contentsline {chapter}{\numberline {5}Complete search}{47}{chapter.5}%
|
||||||
|
\contentsline {section}{\numberline {5.1}Generating subsets}{47}{section.5.1}%
|
||||||
|
\contentsline {subsubsection}{Method 1}{47}{section.5.1}%
|
||||||
|
\contentsline {subsubsection}{Method 2}{48}{lstnumber.-110.10}%
|
||||||
|
\contentsline {section}{\numberline {5.2}Generating permutations}{49}{section.5.2}%
|
||||||
|
\contentsline {subsubsection}{Method 1}{49}{section.5.2}%
|
||||||
|
\contentsline {subsubsection}{Method 2}{49}{lstnumber.-113.14}%
|
||||||
|
\contentsline {section}{\numberline {5.3}Backtracking}{50}{section.5.3}%
|
||||||
|
\contentsline {section}{\numberline {5.4}Pruning the search}{51}{section.5.4}%
|
||||||
|
\contentsline {subsubsection}{Basic algorithm}{52}{section.5.4}%
|
||||||
|
\contentsline {subsubsection}{Optimization 1}{52}{section.5.4}%
|
||||||
|
\contentsline {subsubsection}{Optimization 2}{53}{section.5.4}%
|
||||||
|
\contentsline {subsubsection}{Optimization 3}{53}{section.5.4}%
|
||||||
|
\contentsline {subsubsection}{Optimization 4}{53}{section.5.4}%
|
||||||
|
\contentsline {section}{\numberline {5.5}Meet in the middle}{54}{section.5.5}%
|
||||||
|
\contentsline {chapter}{\numberline {6}Greedy algorithms}{57}{chapter.6}%
|
||||||
|
\contentsline {section}{\numberline {6.1}Coin problem}{57}{section.6.1}%
|
||||||
|
\contentsline {subsubsection}{Greedy algorithm}{57}{section.6.1}%
|
||||||
|
\contentsline {subsubsection}{General case}{58}{section.6.1}%
|
||||||
|
\contentsline {section}{\numberline {6.2}Scheduling}{58}{section.6.2}%
|
||||||
|
\contentsline {section}{\numberline {6.3}Tasks and deadlines}{60}{section.6.3}%
|
||||||
|
\contentsline {section}{\numberline {6.4}Minimizing sums}{61}{section.6.4}%
|
||||||
|
\contentsline {subsubsection}{Case $c=1$}{61}{section.6.4}%
|
||||||
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\contentsline {subsubsection}{Case $c=2$}{61}{section.6.4}%
|
||||||
|
\contentsline {section}{\numberline {6.5}Data compression}{62}{section.6.5}%
|
||||||
|
\contentsline {subsubsection}{Huffman coding}{63}{section.6.5}%
|
||||||
|
\contentsline {chapter}{\numberline {7}Dynamic programming}{65}{chapter.7}%
|
||||||
|
\contentsline {section}{\numberline {7.1}Coin problem}{65}{section.7.1}%
|
||||||
|
\contentsline {subsubsection}{Recursive formulation}{66}{section.7.1}%
|
||||||
|
\contentsline {subsubsection}{Using memoization}{67}{lstnumber.-116.9}%
|
||||||
|
\contentsline {subsubsection}{Constructing a solution}{68}{lstnumber.-119.9}%
|
||||||
|
\contentsline {subsubsection}{Counting the number of solutions}{69}{lstnumber.-122.4}%
|
||||||
|
\contentsline {section}{\numberline {7.2}Longest increasing subsequence}{70}{section.7.2}%
|
||||||
|
\contentsline {section}{\numberline {7.3}Paths in a grid}{71}{section.7.3}%
|
||||||
|
\contentsline {section}{\numberline {7.4}Knapsack problems}{72}{section.7.4}%
|
||||||
|
\contentsline {section}{\numberline {7.5}Edit distance}{74}{section.7.5}%
|
||||||
|
\contentsline {section}{\numberline {7.6}Counting tilings}{75}{section.7.6}%
|
||||||
|
\contentsline {chapter}{\numberline {8}Amortized analysis}{77}{chapter.8}%
|
||||||
|
\contentsline {section}{\numberline {8.1}Two pointers method}{77}{section.8.1}%
|
||||||
|
\contentsline {subsubsection}{Subarray sum}{77}{section.8.1}%
|
||||||
|
\contentsline {subsubsection}{2SUM problem}{78}{section.8.1}%
|
||||||
|
\contentsline {section}{\numberline {8.2}Nearest smaller elements}{79}{section.8.2}%
|
||||||
|
\contentsline {section}{\numberline {8.3}Sliding window minimum}{81}{section.8.3}%
|
||||||
|
\contentsline {chapter}{\numberline {9}Range queries}{83}{chapter.9}%
|
||||||
|
\contentsline {section}{\numberline {9.1}Static array queries}{84}{section.9.1}%
|
||||||
|
\contentsline {subsubsection}{Sum queries}{84}{section.9.1}%
|
||||||
|
\contentsline {subsubsection}{Minimum queries}{85}{section.9.1}%
|
||||||
|
\contentsline {section}{\numberline {9.2}Binary indexed tree}{86}{section.9.2}%
|
||||||
|
\contentsline {subsubsection}{Structure}{86}{section.9.2}%
|
||||||
|
\contentsline {subsubsection}{Implementation}{88}{section.9.2}%
|
||||||
|
\contentsline {section}{\numberline {9.3}Segment tree}{89}{section.9.3}%
|
||||||
|
\contentsline {subsubsection}{Structure}{89}{section.9.3}%
|
||||||
|
\contentsline {subsubsection}{Implementation}{90}{section.9.3}%
|
||||||
|
\contentsline {subsubsection}{Other queries}{92}{lstnumber.-135.7}%
|
||||||
|
\contentsline {section}{\numberline {9.4}Additional techniques}{93}{section.9.4}%
|
||||||
|
\contentsline {subsubsection}{Index compression}{93}{section.9.4}%
|
||||||
|
\contentsline {subsubsection}{Range updates}{93}{section.9.4}%
|
||||||
|
\contentsline {chapter}{\numberline {10}Bit manipulation}{95}{chapter.10}%
|
||||||
|
\contentsline {section}{\numberline {10.1}Bit representation}{95}{section.10.1}%
|
||||||
|
\contentsline {section}{\numberline {10.2}Bit operations}{96}{section.10.2}%
|
||||||
|
\contentsline {subsubsection}{And operation}{96}{section.10.2}%
|
||||||
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\contentsline {subsubsection}{Or operation}{96}{section.10.2}%
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||||||
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\contentsline {subsubsection}{Xor operation}{97}{section.10.2}%
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||||||
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\contentsline {subsubsection}{Not operation}{97}{section.10.2}%
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||||||
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\contentsline {subsubsection}{Bit shifts}{97}{section.10.2}%
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||||||
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\contentsline {subsubsection}{Applications}{97}{section.10.2}%
|
||||||
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\contentsline {section}{\numberline {10.3}Representing sets}{98}{section.10.3}%
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||||||
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\contentsline {subsubsection}{Set implementation}{98}{section.10.3}%
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||||||
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\contentsline {subsubsection}{Set operations}{99}{lstnumber.-141.4}%
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||||||
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\contentsline {subsubsection}{Iterating through subsets}{99}{lstnumber.-142.4}%
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||||||
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\contentsline {section}{\numberline {10.4}Bit optimizations}{100}{section.10.4}%
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||||||
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\contentsline {subsubsection}{Hamming distances}{100}{section.10.4}%
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||||||
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\contentsline {subsubsection}{Counting subgrids}{101}{lstnumber.-147.3}%
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\contentsline {section}{\numberline {10.5}Dynamic programming}{102}{section.10.5}%
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\contentsline {subsubsection}{Optimal selection}{102}{section.10.5}%
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||||||
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\contentsline {subsubsection}{From permutations to subsets}{103}{lstnumber.-152.11}%
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||||||
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\contentsline {subsubsection}{Counting subsets}{105}{lstnumber.-155.18}%
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||||||
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\contentsline {part}{II\hspace {1em}Graph algorithms}{107}{part.2}%
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\contentsline {chapter}{\numberline {11}Basics of graphs}{109}{chapter.11}%
|
||||||
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\contentsline {section}{\numberline {11.1}Graph terminology}{109}{section.11.1}%
|
||||||
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\contentsline {subsubsection}{Connectivity}{110}{section.11.1}%
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||||||
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\contentsline {subsubsection}{Edge directions}{110}{section.11.1}%
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||||||
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\contentsline {subsubsection}{Edge weights}{111}{section.11.1}%
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||||||
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\contentsline {subsubsection}{Neighbors and degrees}{111}{section.11.1}%
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||||||
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\contentsline {subsubsection}{Colorings}{112}{section.11.1}%
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||||||
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\contentsline {subsubsection}{Simplicity}{112}{section.11.1}%
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\contentsline {section}{\numberline {11.2}Graph representation}{113}{section.11.2}%
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\contentsline {subsubsection}{Adjacency list representation}{113}{section.11.2}%
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\contentsline {subsubsection}{Adjacency matrix representation}{114}{lstnumber.-163.3}%
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\contentsline {subsubsection}{Edge list representation}{115}{lstnumber.-164.1}%
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\contentsline {chapter}{\numberline {12}Graph traversal}{117}{chapter.12}%
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\contentsline {section}{\numberline {12.1}Depth-first search}{117}{section.12.1}%
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\contentsline {section}{\numberline {12.2}Breadth-first search}{119}{section.12.2}%
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||||||
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\contentsline {section}{\numberline {12.3}Applications}{121}{section.12.3}%
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||||||
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\contentsline {subsubsection}{Connectivity check}{121}{section.12.3}%
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\contentsline {subsubsection}{Finding cycles}{121}{section.12.3}%
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\contentsline {subsubsection}{Bipartiteness check}{122}{section.12.3}%
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||||||
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\contentsline {chapter}{\numberline {13}Shortest paths}{123}{chapter.13}%
|
||||||
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\contentsline {section}{\numberline {13.1}Bellman–Ford algorithm}{123}{section.13.1}%
|
||||||
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\contentsline {subsubsection}{Example}{123}{section.13.1}%
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||||||
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\contentsline {subsubsection}{Implementation}{125}{section.13.1}%
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||||||
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\contentsline {subsubsection}{Negative cycles}{125}{lstnumber.-174.9}%
|
||||||
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\contentsline {subsubsection}{SPFA algorithm}{126}{lstnumber.-174.9}%
|
||||||
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\contentsline {section}{\numberline {13.2}Dijkstra's algorithm}{126}{section.13.2}%
|
||||||
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\contentsline {subsubsection}{Example}{126}{section.13.2}%
|
||||||
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\contentsline {subsubsection}{Negative edges}{128}{section.13.2}%
|
||||||
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\contentsline {subsubsection}{Implementation}{128}{section.13.2}%
|
||||||
|
\contentsline {section}{\numberline {13.3}Floyd–Warshall algorithm}{129}{section.13.3}%
|
||||||
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\contentsline {subsubsection}{Example}{129}{section.13.3}%
|
||||||
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\contentsline {subsubsection}{Implementation}{131}{section.13.3}%
|
||||||
|
\contentsline {chapter}{\numberline {14}Tree algorithms}{133}{chapter.14}%
|
||||||
|
\contentsline {section}{\numberline {14.1}Tree traversal}{134}{section.14.1}%
|
||||||
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\contentsline {subsubsection}{Dynamic programming}{134}{lstnumber.-179.1}%
|
||||||
|
\contentsline {section}{\numberline {14.2}Diameter}{135}{section.14.2}%
|
||||||
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\contentsline {subsubsection}{Algorithm 1}{135}{section.14.2}%
|
||||||
|
\contentsline {subsubsection}{Algorithm 2}{136}{section.14.2}%
|
||||||
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\contentsline {section}{\numberline {14.3}All longest paths}{137}{section.14.3}%
|
||||||
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\contentsline {section}{\numberline {14.4}Binary trees}{139}{section.14.4}%
|
||||||
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\contentsline {chapter}{\numberline {15}Spanning trees}{141}{chapter.15}%
|
||||||
|
\contentsline {section}{\numberline {15.1}Kruskal's algorithm}{142}{section.15.1}%
|
||||||
|
\contentsline {subsubsection}{Example}{142}{section.15.1}%
|
||||||
|
\contentsline {subsubsection}{Why does this work?}{144}{section.15.1}%
|
||||||
|
\contentsline {subsubsection}{Implementation}{145}{section.15.1}%
|
||||||
|
\contentsline {section}{\numberline {15.2}Union-find structure}{145}{section.15.2}%
|
||||||
|
\contentsline {subsubsection}{Structure}{145}{section.15.2}%
|
||||||
|
\contentsline {subsubsection}{Implementation}{146}{section.15.2}%
|
||||||
|
\contentsline {section}{\numberline {15.3}Prim's algorithm}{147}{section.15.3}%
|
||||||
|
\contentsline {subsubsection}{Example}{147}{section.15.3}%
|
||||||
|
\contentsline {subsubsection}{Implementation}{148}{section.15.3}%
|
||||||
|
\contentsline {chapter}{\numberline {16}Directed graphs}{149}{chapter.16}%
|
||||||
|
\contentsline {section}{\numberline {16.1}Topological sorting}{149}{section.16.1}%
|
||||||
|
\contentsline {subsubsection}{Algorithm}{150}{section.16.1}%
|
||||||
|
\contentsline {subsubsection}{Example 1}{150}{section.16.1}%
|
||||||
|
\contentsline {subsubsection}{Example 2}{151}{section.16.1}%
|
||||||
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\contentsline {section}{\numberline {16.2}Dynamic programming}{151}{section.16.2}%
|
||||||
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\contentsline {subsubsection}{Counting the number of paths}{152}{section.16.2}%
|
||||||
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\contentsline {subsubsection}{Extending Dijkstra's algorithm}{153}{section.16.2}%
|
||||||
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\contentsline {subsubsection}{Representing problems as graphs}{153}{section.16.2}%
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||||||
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\contentsline {section}{\numberline {16.3}Successor paths}{154}{section.16.3}%
|
||||||
|
\contentsline {section}{\numberline {16.4}Cycle detection}{155}{section.16.4}%
|
||||||
|
\contentsline {subsubsection}{Floyd's algorithm}{156}{section.16.4}%
|
||||||
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\contentsline {chapter}{\numberline {17}Strong connectivity}{157}{chapter.17}%
|
||||||
|
\contentsline {section}{\numberline {17.1}Kosaraju's algorithm}{158}{section.17.1}%
|
||||||
|
\contentsline {subsubsection}{Search 1}{158}{section.17.1}%
|
||||||
|
\contentsline {subsubsection}{Search 2}{159}{section.17.1}%
|
||||||
|
\contentsline {section}{\numberline {17.2}2SAT problem}{160}{section.17.2}%
|
||||||
|
\contentsline {chapter}{\numberline {18}Tree queries}{163}{chapter.18}%
|
||||||
|
\contentsline {section}{\numberline {18.1}Finding ancestors}{163}{section.18.1}%
|
||||||
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\contentsline {section}{\numberline {18.2}Subtrees and paths}{164}{section.18.2}%
|
||||||
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\contentsline {subsubsection}{Subtree queries}{165}{section.18.2}%
|
||||||
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\contentsline {subsubsection}{Path queries}{166}{section.18.2}%
|
||||||
|
\contentsline {section}{\numberline {18.3}Lowest common ancestor}{167}{section.18.3}%
|
||||||
|
\contentsline {subsubsection}{Method 1}{167}{section.18.3}%
|
||||||
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\contentsline {subsubsection}{Method 2}{168}{section.18.3}%
|
||||||
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\contentsline {subsubsection}{Distances of nodes}{169}{section.18.3}%
|
||||||
|
\contentsline {section}{\numberline {18.4}Offline algorithms}{170}{section.18.4}%
|
||||||
|
\contentsline {subsubsection}{Merging data structures}{170}{section.18.4}%
|
||||||
|
\contentsline {subsubsection}{Lowest common ancestors}{171}{lstnumber.-189.1}%
|
||||||
|
\contentsline {chapter}{\numberline {19}Paths and circuits}{173}{chapter.19}%
|
||||||
|
\contentsline {section}{\numberline {19.1}Eulerian paths}{173}{section.19.1}%
|
||||||
|
\contentsline {subsubsection}{Existence}{174}{section.19.1}%
|
||||||
|
\contentsline {subsubsection}{Hierholzer's algorithm}{175}{section.19.1}%
|
||||||
|
\contentsline {subsubsection}{Example}{176}{section.19.1}%
|
||||||
|
\contentsline {section}{\numberline {19.2}Hamiltonian paths}{177}{section.19.2}%
|
||||||
|
\contentsline {subsubsection}{Existence}{177}{section.19.2}%
|
||||||
|
\contentsline {subsubsection}{Construction}{178}{section.19.2}%
|
||||||
|
\contentsline {section}{\numberline {19.3}De Bruijn sequences}{178}{section.19.3}%
|
||||||
|
\contentsline {section}{\numberline {19.4}Knight's tours}{179}{section.19.4}%
|
||||||
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\contentsline {subsubsection}{Warnsdorf's rule}{179}{section.19.4}%
|
||||||
|
\contentsline {chapter}{\numberline {20}Flows and cuts}{181}{chapter.20}%
|
||||||
|
\contentsline {subsubsection}{Maximum flow}{181}{chapter.20}%
|
||||||
|
\contentsline {subsubsection}{Minimum cut}{182}{chapter.20}%
|
||||||
|
\contentsline {section}{\numberline {20.1}Ford–Fulkerson algorithm}{182}{section.20.1}%
|
||||||
|
\contentsline {subsubsection}{Algorithm description}{183}{section.20.1}%
|
||||||
|
\contentsline {subsubsection}{Finding paths}{184}{section.20.1}%
|
||||||
|
\contentsline {subsubsection}{Minimum cuts}{185}{section.20.1}%
|
||||||
|
\contentsline {section}{\numberline {20.2}Disjoint paths}{186}{section.20.2}%
|
||||||
|
\contentsline {subsubsection}{Edge-disjoint paths}{186}{section.20.2}%
|
||||||
|
\contentsline {subsubsection}{Node-disjoint paths}{186}{section.20.2}%
|
||||||
|
\contentsline {section}{\numberline {20.3}Maximum matchings}{187}{section.20.3}%
|
||||||
|
\contentsline {subsubsection}{Finding maximum matchings}{188}{section.20.3}%
|
||||||
|
\contentsline {subsubsection}{Hall's theorem}{189}{section.20.3}%
|
||||||
|
\contentsline {subsubsection}{Kőnig's theorem}{189}{section.20.3}%
|
||||||
|
\contentsline {section}{\numberline {20.4}Path covers}{190}{section.20.4}%
|
||||||
|
\contentsline {subsubsection}{Node-disjoint path cover}{191}{section.20.4}%
|
||||||
|
\contentsline {subsubsection}{General path cover}{192}{section.20.4}%
|
||||||
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\contentsline {subsubsection}{Dilworth's theorem}{193}{section.20.4}%
|
||||||
|
\contentsline {part}{III\hspace {1em}Advanced topics}{195}{part.3}%
|
||||||
|
\contentsline {chapter}{\numberline {21}Number theory}{197}{chapter.21}%
|
||||||
|
\contentsline {section}{\numberline {21.1}Primes and factors}{197}{section.21.1}%
|
||||||
|
\contentsline {subsubsection}{Number of primes}{198}{section.21.1}%
|
||||||
|
\contentsline {subsubsection}{Density of primes}{198}{section.21.1}%
|
||||||
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\contentsline {subsubsection}{Conjectures}{199}{section.21.1}%
|
||||||
|
\contentsline {subsubsection}{Basic algorithms}{199}{section.21.1}%
|
||||||
|
\contentsline {subsubsection}{Sieve of Eratosthenes}{200}{lstnumber.-191.11}%
|
||||||
|
\contentsline {subsubsection}{Euclid's algorithm}{200}{lstnumber.-192.6}%
|
||||||
|
\contentsline {subsubsection}{Euler's totient function}{201}{lstnumber.-193.4}%
|
||||||
|
\contentsline {section}{\numberline {21.2}Modular arithmetic}{201}{section.21.2}%
|
||||||
|
\contentsline {subsubsection}{Modular exponentiation}{202}{section.21.2}%
|
||||||
|
\contentsline {subsubsection}{Fermat's theorem and Euler's theorem}{202}{lstnumber.-194.7}%
|
||||||
|
\contentsline {subsubsection}{Modular inverse}{202}{lstnumber.-194.7}%
|
||||||
|
\contentsline {subsubsection}{Computer arithmetic}{203}{lstnumber.-194.7}%
|
||||||
|
\contentsline {section}{\numberline {21.3}Solving equations}{204}{section.21.3}%
|
||||||
|
\contentsline {subsubsection}{Chinese remainder theorem}{205}{section.21.3}%
|
||||||
|
\contentsline {section}{\numberline {21.4}Other results}{205}{section.21.4}%
|
||||||
|
\contentsline {subsubsection}{Lagrange's theorem}{205}{section.21.4}%
|
||||||
|
\contentsline {subsubsection}{Zeckendorf's theorem}{206}{section.21.4}%
|
||||||
|
\contentsline {subsubsection}{Pythagorean triples}{206}{section.21.4}%
|
||||||
|
\contentsline {subsubsection}{Wilson's theorem}{206}{section.21.4}%
|
||||||
|
\contentsline {chapter}{\numberline {22}Combinatorics}{207}{chapter.22}%
|
||||||
|
\contentsline {section}{\numberline {22.1}Binomial coefficients}{208}{section.22.1}%
|
||||||
|
\contentsline {subsubsection}{Formula 1}{208}{section.22.1}%
|
||||||
|
\contentsline {subsubsection}{Formula 2}{208}{section.22.1}%
|
||||||
|
\contentsline {subsubsection}{Properties}{208}{section.22.1}%
|
||||||
|
\contentsline {subsubsection}{Boxes and balls}{209}{section.22.1}%
|
||||||
|
\contentsline {subsubsection}{Multinomial coefficients}{210}{section.22.1}%
|
||||||
|
\contentsline {section}{\numberline {22.2}Catalan numbers}{210}{section.22.2}%
|
||||||
|
\contentsline {subsubsection}{Parenthesis expressions}{211}{section.22.2}%
|
||||||
|
\contentsline {subsubsection}{Formula 1}{211}{section.22.2}%
|
||||||
|
\contentsline {subsubsection}{Formula 2}{211}{section.22.2}%
|
||||||
|
\contentsline {subsubsection}{Counting trees}{212}{section.22.2}%
|
||||||
|
\contentsline {section}{\numberline {22.3}Inclusion-exclusion}{212}{section.22.3}%
|
||||||
|
\contentsline {subsubsection}{Derangements}{213}{section.22.3}%
|
||||||
|
\contentsline {section}{\numberline {22.4}Burnside's lemma}{214}{section.22.4}%
|
||||||
|
\contentsline {section}{\numberline {22.5}Cayley's formula}{215}{section.22.5}%
|
||||||
|
\contentsline {subsubsection}{Prüfer code}{216}{section.22.5}%
|
||||||
|
\contentsline {chapter}{\numberline {23}Matrices}{217}{chapter.23}%
|
||||||
|
\contentsline {section}{\numberline {23.1}Operations}{217}{section.23.1}%
|
||||||
|
\contentsline {subsubsection}{Matrix multiplication}{218}{section.23.1}%
|
||||||
|
\contentsline {subsubsection}{Matrix power}{219}{section.23.1}%
|
||||||
|
\contentsline {subsubsection}{Determinant}{219}{section.23.1}%
|
||||||
|
\contentsline {section}{\numberline {23.2}Linear recurrences}{220}{section.23.2}%
|
||||||
|
\contentsline {subsubsection}{Fibonacci numbers}{220}{section.23.2}%
|
||||||
|
\contentsline {subsubsection}{General case}{221}{section.23.2}%
|
||||||
|
\contentsline {section}{\numberline {23.3}Graphs and matrices}{222}{section.23.3}%
|
||||||
|
\contentsline {subsubsection}{Counting paths}{222}{section.23.3}%
|
||||||
|
\contentsline {subsubsection}{Shortest paths}{222}{section.23.3}%
|
||||||
|
\contentsline {subsubsection}{Kirchhoff's theorem}{223}{section.23.3}%
|
||||||
|
\contentsline {chapter}{\numberline {24}Probability}{225}{chapter.24}%
|
||||||
|
\contentsline {section}{\numberline {24.1}Calculation}{225}{section.24.1}%
|
||||||
|
\contentsline {section}{\numberline {24.2}Events}{226}{section.24.2}%
|
||||||
|
\contentsline {subsubsection}{Complement}{227}{section.24.2}%
|
||||||
|
\contentsline {subsubsection}{Union}{227}{section.24.2}%
|
||||||
|
\contentsline {subsubsection}{Conditional probability}{227}{section.24.2}%
|
||||||
|
\contentsline {subsubsection}{Intersection}{228}{section.24.2}%
|
||||||
|
\contentsline {section}{\numberline {24.3}Random variables}{228}{section.24.3}%
|
||||||
|
\contentsline {subsubsection}{Expected value}{229}{section.24.3}%
|
||||||
|
\contentsline {subsubsection}{Distributions}{229}{section.24.3}%
|
||||||
|
\contentsline {section}{\numberline {24.4}Markov chains}{230}{section.24.4}%
|
||||||
|
\contentsline {section}{\numberline {24.5}Randomized algorithms}{231}{section.24.5}%
|
||||||
|
\contentsline {subsubsection}{Order statistics}{232}{section.24.5}%
|
||||||
|
\contentsline {subsubsection}{Verifying matrix multiplication}{232}{section.24.5}%
|
||||||
|
\contentsline {subsubsection}{Graph coloring}{233}{section.24.5}%
|
||||||
|
\contentsline {chapter}{\numberline {25}Game theory}{235}{chapter.25}%
|
||||||
|
\contentsline {section}{\numberline {25.1}Game states}{235}{section.25.1}%
|
||||||
|
\contentsline {subsubsection}{Winning and losing states}{235}{section.25.1}%
|
||||||
|
\contentsline {subsubsection}{State graph}{236}{section.25.1}%
|
||||||
|
\contentsline {section}{\numberline {25.2}Nim game}{237}{section.25.2}%
|
||||||
|
\contentsline {subsubsection}{Analysis}{237}{section.25.2}%
|
||||||
|
\contentsline {subsubsection}{Misère game}{238}{section.25.2}%
|
||||||
|
\contentsline {section}{\numberline {25.3}Sprague–Grundy theorem}{238}{section.25.3}%
|
||||||
|
\contentsline {subsubsection}{Grundy numbers}{238}{section.25.3}%
|
||||||
|
\contentsline {subsubsection}{Subgames}{240}{section.25.3}%
|
||||||
|
\contentsline {subsubsection}{Grundy's game}{240}{section.25.3}%
|
||||||
|
\contentsline {chapter}{\numberline {26}String algorithms}{243}{chapter.26}%
|
||||||
|
\contentsline {section}{\numberline {26.1}String terminology}{243}{section.26.1}%
|
||||||
|
\contentsline {section}{\numberline {26.2}Trie structure}{244}{section.26.2}%
|
||||||
|
\contentsline {section}{\numberline {26.3}String hashing}{245}{section.26.3}%
|
||||||
|
\contentsline {section}{\numberline {26.4}Z-algorithm}{247}{section.26.4}%
|
||||||
|
\contentsline {subsubsection}{Using the Z-array}{250}{section.26.4}%
|
||||||
|
\contentsline {subsubsection}{Implementation}{250}{section.26.4}%
|
||||||
|
\contentsline {chapter}{\numberline {27}Square root algorithms}{251}{chapter.27}%
|
||||||
|
\contentsline {section}{\numberline {27.1}Combining algorithms}{252}{section.27.1}%
|
||||||
|
\contentsline {subsubsection}{Case processing}{252}{section.27.1}%
|
||||||
|
\contentsline {subsubsection}{Batch processing}{253}{section.27.1}%
|
||||||
|
\contentsline {section}{\numberline {27.2}Integer partitions}{254}{section.27.2}%
|
||||||
|
\contentsline {subsubsection}{Knapsack}{254}{section.27.2}%
|
||||||
|
\contentsline {subsubsection}{String construction}{255}{section.27.2}%
|
||||||
|
\contentsline {section}{\numberline {27.3}Mo's algorithm}{255}{section.27.3}%
|
||||||
|
\contentsline {chapter}{\numberline {28}Segment trees revisited}{257}{chapter.28}%
|
||||||
|
\contentsline {section}{\numberline {28.1}Lazy propagation}{258}{section.28.1}%
|
||||||
|
\contentsline {subsubsection}{Lazy segment trees}{258}{section.28.1}%
|
||||||
|
\contentsline {subsubsection}{Polynomial updates}{260}{section.28.1}%
|
||||||
|
\contentsline {section}{\numberline {28.2}Dynamic trees}{261}{section.28.2}%
|
||||||
|
\contentsline {subsubsection}{Sparse segment trees}{261}{lstnumber.-202.4}%
|
||||||
|
\contentsline {subsubsection}{Persistent segment trees}{262}{lstnumber.-202.4}%
|
||||||
|
\contentsline {section}{\numberline {28.3}Data structures}{263}{section.28.3}%
|
||||||
|
\contentsline {section}{\numberline {28.4}Two-dimensionality}{264}{section.28.4}%
|
||||||
|
\contentsline {chapter}{\numberline {29}Geometry}{265}{chapter.29}%
|
||||||
|
\contentsline {section}{\numberline {29.1}Complex numbers}{266}{section.29.1}%
|
||||||
|
\contentsline {section}{\numberline {29.2}Points and lines}{268}{section.29.2}%
|
||||||
|
\contentsline {subsubsection}{Point location}{268}{lstnumber.-208.3}%
|
||||||
|
\contentsline {subsubsection}{Line segment intersection}{269}{lstnumber.-208.3}%
|
||||||
|
\contentsline {subsubsection}{Point distance from a line}{269}{lstnumber.-208.3}%
|
||||||
|
\contentsline {subsubsection}{Point inside a polygon}{270}{lstnumber.-208.3}%
|
||||||
|
\contentsline {section}{\numberline {29.3}Polygon area}{271}{section.29.3}%
|
||||||
|
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(generated)
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"output/test.ilg"
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"output/test.ind"
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\BOOKMARK [0][-]{chapter.1}{Tree algorithms}{}% 1
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|
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|
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|
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\title{\Huge Competitive Programmer's Handbook}
|
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\author{\Large Antti Laaksonen}
|
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\makeindex
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
%\phantomsection
|
||||||
|
%\addcontentsline{toc}{chapter}{Bibliography}
|
||||||
|
%\include{list}
|
||||||
|
|
||||||
|
%\cleardoublepage
|
||||||
|
%\printindex
|
||||||
|
|
||||||
|
\end{document}
|
||||||
Loading…
Reference in New Issue