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| \relax  | ||||
| \providecommand\hyper@newdestlabel[2]{} | ||||
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| \@input{chapter04.aux} | ||||
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| \@input{chapter06.aux} | ||||
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| \@input{chapter14.aux} | ||||
| \@input{chapter15.aux} | ||||
| \@input{chapter16.aux} | ||||
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| \@input{chapter21.aux} | ||||
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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} | ||||
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| 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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| \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 | ||||
| \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 | ||||
| \BOOKMARK [1][-]{section.11.2}{Graph representation}{chapter.11}% 63 | ||||
| \BOOKMARK [0][-]{chapter.12}{Graph traversal}{part.2}% 64 | ||||
| \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 | ||||
| \BOOKMARK [1][-]{section.13.2}{Dijkstra's algorithm}{chapter.13}% 70 | ||||
| \BOOKMARK [1][-]{section.13.3}{Floyd\205Warshall algorithm}{chapter.13}% 71 | ||||
| \BOOKMARK [0][-]{chapter.14}{Tree algorithms}{part.2}% 72 | ||||
| \BOOKMARK [1][-]{section.14.1}{Tree traversal}{chapter.14}% 73 | ||||
| \BOOKMARK [1][-]{section.14.2}{Diameter}{chapter.14}% 74 | ||||
| \BOOKMARK [1][-]{section.14.3}{All longest paths}{chapter.14}% 75 | ||||
| \BOOKMARK [1][-]{section.14.4}{Binary trees}{chapter.14}% 76 | ||||
| \BOOKMARK [0][-]{chapter.15}{Spanning trees}{part.2}% 77 | ||||
| \BOOKMARK [1][-]{section.15.1}{Kruskal's algorithm}{chapter.15}% 78 | ||||
| \BOOKMARK [1][-]{section.15.2}{Union-find structure}{chapter.15}% 79 | ||||
| \BOOKMARK [1][-]{section.15.3}{Prim's algorithm}{chapter.15}% 80 | ||||
| \BOOKMARK [0][-]{chapter.16}{Directed graphs}{part.2}% 81 | ||||
| \BOOKMARK [1][-]{section.16.1}{Topological sorting}{chapter.16}% 82 | ||||
| \BOOKMARK [1][-]{section.16.2}{Dynamic programming}{chapter.16}% 83 | ||||
| \BOOKMARK [1][-]{section.16.3}{Successor paths}{chapter.16}% 84 | ||||
| \BOOKMARK [1][-]{section.16.4}{Cycle detection}{chapter.16}% 85 | ||||
| \BOOKMARK [0][-]{chapter.17}{Strong connectivity}{part.2}% 86 | ||||
| \BOOKMARK [1][-]{section.17.1}{Kosaraju's algorithm}{chapter.17}% 87 | ||||
| \BOOKMARK [1][-]{section.17.2}{2SAT problem}{chapter.17}% 88 | ||||
| \BOOKMARK [0][-]{chapter.18}{Tree queries}{part.2}% 89 | ||||
| \BOOKMARK [1][-]{section.18.1}{Finding ancestors}{chapter.18}% 90 | ||||
| \BOOKMARK [1][-]{section.18.2}{Subtrees and paths}{chapter.18}% 91 | ||||
| \BOOKMARK [1][-]{section.18.3}{Lowest common ancestor}{chapter.18}% 92 | ||||
| \BOOKMARK [1][-]{section.18.4}{Offline algorithms}{chapter.18}% 93 | ||||
| \BOOKMARK [0][-]{chapter.19}{Paths and circuits}{part.2}% 94 | ||||
| \BOOKMARK [1][-]{section.19.1}{Eulerian paths}{chapter.19}% 95 | ||||
| \BOOKMARK [1][-]{section.19.2}{Hamiltonian paths}{chapter.19}% 96 | ||||
| \BOOKMARK [1][-]{section.19.3}{De Bruijn sequences}{chapter.19}% 97 | ||||
| \BOOKMARK [1][-]{section.19.4}{Knight's tours}{chapter.19}% 98 | ||||
| \BOOKMARK [0][-]{chapter.20}{Flows and cuts}{part.2}% 99 | ||||
| \BOOKMARK [1][-]{section.20.1}{Ford\205Fulkerson algorithm}{chapter.20}% 100 | ||||
| \BOOKMARK [1][-]{section.20.2}{Disjoint paths}{chapter.20}% 101 | ||||
| \BOOKMARK [1][-]{section.20.3}{Maximum matchings}{chapter.20}% 102 | ||||
| \BOOKMARK [1][-]{section.20.4}{Path covers}{chapter.20}% 103 | ||||
| \BOOKMARK [-1][-]{part.3}{III Advanced topics}{}% 104 | ||||
| \BOOKMARK [0][-]{chapter.21}{Number theory}{part.3}% 105 | ||||
| \BOOKMARK [1][-]{section.21.1}{Primes and factors}{chapter.21}% 106 | ||||
| \BOOKMARK [1][-]{section.21.2}{Modular arithmetic}{chapter.21}% 107 | ||||
| \BOOKMARK [1][-]{section.21.3}{Solving equations}{chapter.21}% 108 | ||||
| \BOOKMARK [1][-]{section.21.4}{Other results}{chapter.21}% 109 | ||||
| \BOOKMARK [0][-]{chapter.22}{Combinatorics}{part.3}% 110 | ||||
| \BOOKMARK [1][-]{section.22.1}{Binomial coefficients}{chapter.22}% 111 | ||||
| \BOOKMARK [1][-]{section.22.2}{Catalan numbers}{chapter.22}% 112 | ||||
| \BOOKMARK [1][-]{section.22.3}{Inclusion-exclusion}{chapter.22}% 113 | ||||
| \BOOKMARK [1][-]{section.22.4}{Burnside's lemma}{chapter.22}% 114 | ||||
| \BOOKMARK [1][-]{section.22.5}{Cayley's formula}{chapter.22}% 115 | ||||
| \BOOKMARK [0][-]{chapter.23}{Matrices}{part.3}% 116 | ||||
| \BOOKMARK [1][-]{section.23.1}{Operations}{chapter.23}% 117 | ||||
| \BOOKMARK [1][-]{section.23.2}{Linear recurrences}{chapter.23}% 118 | ||||
| \BOOKMARK [1][-]{section.23.3}{Graphs and matrices}{chapter.23}% 119 | ||||
| \BOOKMARK [0][-]{chapter.24}{Probability}{part.3}% 120 | ||||
| \BOOKMARK [1][-]{section.24.1}{Calculation}{chapter.24}% 121 | ||||
| \BOOKMARK [1][-]{section.24.2}{Events}{chapter.24}% 122 | ||||
| \BOOKMARK [1][-]{section.24.3}{Random variables}{chapter.24}% 123 | ||||
| \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 | ||||
| \BOOKMARK [1][-]{section.25.1}{Game states}{chapter.25}% 127 | ||||
| \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 | ||||
| \BOOKMARK [0][-]{chapter*.5}{Index}{part.3}% 154 | ||||
										
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| \babel@toc {english}{} | ||||
| \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}% | ||||
| \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}% | ||||
| \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}% | ||||
| \contentsline {subsubsection}{Stack}{42}{lstnumber.-99.6}% | ||||
| \contentsline {subsubsection}{Queue}{43}{lstnumber.-100.7}% | ||||
| \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}% | ||||
| \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}% | ||||
| \contentsline {subsubsection}{Or operation}{96}{section.10.2}% | ||||
| \contentsline {subsubsection}{Xor operation}{97}{section.10.2}% | ||||
| \contentsline {subsubsection}{Not operation}{97}{section.10.2}% | ||||
| \contentsline {subsubsection}{Bit shifts}{97}{section.10.2}% | ||||
| \contentsline {subsubsection}{Applications}{97}{section.10.2}% | ||||
| \contentsline {section}{\numberline {10.3}Representing sets}{98}{section.10.3}% | ||||
| \contentsline {subsubsection}{Set implementation}{98}{section.10.3}% | ||||
| \contentsline {subsubsection}{Set operations}{99}{lstnumber.-141.4}% | ||||
| \contentsline {subsubsection}{Iterating through subsets}{99}{lstnumber.-142.4}% | ||||
| \contentsline {section}{\numberline {10.4}Bit optimizations}{100}{section.10.4}% | ||||
| \contentsline {subsubsection}{Hamming distances}{100}{section.10.4}% | ||||
| \contentsline {subsubsection}{Counting subgrids}{101}{lstnumber.-147.3}% | ||||
| \contentsline {section}{\numberline {10.5}Dynamic programming}{102}{section.10.5}% | ||||
| \contentsline {subsubsection}{Optimal selection}{102}{section.10.5}% | ||||
| \contentsline {subsubsection}{From permutations to subsets}{103}{lstnumber.-152.11}% | ||||
| \contentsline {subsubsection}{Counting subsets}{105}{lstnumber.-155.18}% | ||||
| \contentsline {part}{II\hspace {1em}Graph algorithms}{107}{part.2}% | ||||
| \contentsline {chapter}{\numberline {11}Basics of graphs}{109}{chapter.11}% | ||||
| \contentsline {section}{\numberline {11.1}Graph terminology}{109}{section.11.1}% | ||||
| \contentsline {subsubsection}{Connectivity}{110}{section.11.1}% | ||||
| \contentsline {subsubsection}{Edge directions}{110}{section.11.1}% | ||||
| \contentsline {subsubsection}{Edge weights}{111}{section.11.1}% | ||||
| \contentsline {subsubsection}{Neighbors and degrees}{111}{section.11.1}% | ||||
| \contentsline {subsubsection}{Colorings}{112}{section.11.1}% | ||||
| \contentsline {subsubsection}{Simplicity}{112}{section.11.1}% | ||||
| \contentsline {section}{\numberline {11.2}Graph representation}{113}{section.11.2}% | ||||
| \contentsline {subsubsection}{Adjacency list representation}{113}{section.11.2}% | ||||
| \contentsline {subsubsection}{Adjacency matrix representation}{114}{lstnumber.-163.3}% | ||||
| \contentsline {subsubsection}{Edge list representation}{115}{lstnumber.-164.1}% | ||||
| \contentsline {chapter}{\numberline {12}Graph traversal}{117}{chapter.12}% | ||||
| \contentsline {section}{\numberline {12.1}Depth-first search}{117}{section.12.1}% | ||||
| \contentsline {section}{\numberline {12.2}Breadth-first search}{119}{section.12.2}% | ||||
| \contentsline {section}{\numberline {12.3}Applications}{121}{section.12.3}% | ||||
| \contentsline {subsubsection}{Connectivity check}{121}{section.12.3}% | ||||
| \contentsline {subsubsection}{Finding cycles}{121}{section.12.3}% | ||||
| \contentsline {subsubsection}{Bipartiteness check}{122}{section.12.3}% | ||||
| \contentsline {chapter}{\numberline {13}Shortest paths}{123}{chapter.13}% | ||||
| \contentsline {section}{\numberline {13.1}Bellman–Ford algorithm}{123}{section.13.1}% | ||||
| \contentsline {subsubsection}{Example}{123}{section.13.1}% | ||||
| \contentsline {subsubsection}{Implementation}{125}{section.13.1}% | ||||
| \contentsline {subsubsection}{Negative cycles}{125}{lstnumber.-174.9}% | ||||
| \contentsline {subsubsection}{SPFA algorithm}{126}{lstnumber.-174.9}% | ||||
| \contentsline {section}{\numberline {13.2}Dijkstra's algorithm}{126}{section.13.2}% | ||||
| \contentsline {subsubsection}{Example}{126}{section.13.2}% | ||||
| \contentsline {subsubsection}{Negative edges}{128}{section.13.2}% | ||||
| \contentsline {subsubsection}{Implementation}{128}{section.13.2}% | ||||
| \contentsline {section}{\numberline {13.3}Floyd–Warshall algorithm}{129}{section.13.3}% | ||||
| \contentsline {subsubsection}{Example}{129}{section.13.3}% | ||||
| \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}% | ||||
| \contentsline {subsubsection}{Dynamic programming}{134}{lstnumber.-179.1}% | ||||
| \contentsline {section}{\numberline {14.2}Diameter}{135}{section.14.2}% | ||||
| \contentsline {subsubsection}{Algorithm 1}{135}{section.14.2}% | ||||
| \contentsline {subsubsection}{Algorithm 2}{136}{section.14.2}% | ||||
| \contentsline {section}{\numberline {14.3}All longest paths}{137}{section.14.3}% | ||||
| \contentsline {section}{\numberline {14.4}Binary trees}{139}{section.14.4}% | ||||
| \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}% | ||||
| \contentsline {section}{\numberline {16.2}Dynamic programming}{151}{section.16.2}% | ||||
| \contentsline {subsubsection}{Counting the number of paths}{152}{section.16.2}% | ||||
| \contentsline {subsubsection}{Extending Dijkstra's algorithm}{153}{section.16.2}% | ||||
| \contentsline {subsubsection}{Representing problems as graphs}{153}{section.16.2}% | ||||
| \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}% | ||||
| \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}% | ||||
| \contentsline {section}{\numberline {18.2}Subtrees and paths}{164}{section.18.2}% | ||||
| \contentsline {subsubsection}{Subtree queries}{165}{section.18.2}% | ||||
| \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}% | ||||
| \contentsline {subsubsection}{Method 2}{168}{section.18.3}% | ||||
| \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}% | ||||
| \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}% | ||||
| \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}% | ||||
| \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}% | ||||
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| \indexentry{tree|hyperpage}{1} | ||||
| \indexentry{leaf|hyperpage}{1} | ||||
| \indexentry{root|hyperpage}{1} | ||||
| \indexentry{rooted tree|hyperpage}{1} | ||||
| \indexentry{child|hyperpage}{1} | ||||
| \indexentry{parent|hyperpage}{1} | ||||
| \indexentry{subtree|hyperpage}{1} | ||||
| \indexentry{diameter|hyperpage}{3} | ||||
| \indexentry{binary tree|hyperpage}{7} | ||||
| \indexentry{pre-order|hyperpage}{7} | ||||
| \indexentry{in-order|hyperpage}{7} | ||||
| \indexentry{post-order|hyperpage}{7} | ||||
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| This is makeindex, version 2.15 [TeX Live 2020] (kpathsea + Thai support). | ||||
| Scanning input file output/test.idx....done (12 entries accepted, 0 rejected). | ||||
| Sorting entries....done (50 comparisons). | ||||
| Generating output file output/test.ind....done (40 lines written, 0 warnings). | ||||
| Output written in output/test.ind. | ||||
| Transcript written in output/test.ilg. | ||||
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| \begin{theindex} | ||||
| 
 | ||||
|   \item binary tree, \hyperpage{7} | ||||
| 
 | ||||
|   \indexspace | ||||
| 
 | ||||
|   \item child, \hyperpage{1} | ||||
| 
 | ||||
|   \indexspace | ||||
| 
 | ||||
|   \item diameter, \hyperpage{3} | ||||
| 
 | ||||
|   \indexspace | ||||
| 
 | ||||
|   \item in-order, \hyperpage{7} | ||||
| 
 | ||||
|   \indexspace | ||||
| 
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|   \item leaf, \hyperpage{1} | ||||
| 
 | ||||
|   \indexspace | ||||
| 
 | ||||
|   \item parent, \hyperpage{1} | ||||
|   \item post-order, \hyperpage{7} | ||||
|   \item pre-order, \hyperpage{7} | ||||
| 
 | ||||
|   \indexspace | ||||
| 
 | ||||
|   \item root, \hyperpage{1} | ||||
|   \item rooted tree, \hyperpage{1} | ||||
| 
 | ||||
|   \indexspace | ||||
| 
 | ||||
|   \item subtree, \hyperpage{1} | ||||
| 
 | ||||
|   \indexspace | ||||
| 
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|   \item tree, \hyperpage{1} | ||||
| 
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| \end{theindex} | ||||
										
											
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| \BOOKMARK [0][-]{chapter.1}{Tree algorithms}{}% 1 | ||||
| \BOOKMARK [1][-]{section.1.1}{Tree traversal}{chapter.1}% 2 | ||||
| \BOOKMARK [1][-]{section.1.2}{Diameter}{chapter.1}% 3 | ||||
| \BOOKMARK [1][-]{section.1.3}{All longest paths}{chapter.1}% 4 | ||||
| \BOOKMARK [1][-]{section.1.4}{Binary trees}{chapter.1}% 5 | ||||
										
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| \babel@toc {english}{} | ||||
| \contentsline {part}{I\hspace {1em}Graph algorithms}{1}{part.1}% | ||||
| \contentsline {chapter}{\numberline {1}Tree algorithms}{3}{chapter.1}% | ||||
| \contentsline {section}{\numberline {1.1}Tree traversal}{4}{section.1.1}% | ||||
| \contentsline {subsubsection}{Dynamic programming}{4}{lstnumber.-2.1}% | ||||
| \contentsline {section}{\numberline {1.2}Diameter}{5}{section.1.2}% | ||||
| \contentsline {subsubsection}{Algorithm 1}{5}{section.1.2}% | ||||
| \contentsline {subsubsection}{Algorithm 2}{6}{section.1.2}% | ||||
| \contentsline {section}{\numberline {1.3}All longest paths}{7}{section.1.3}% | ||||
| \contentsline {section}{\numberline {1.4}Binary trees}{9}{section.1.4}% | ||||
| \contentsline {chapter}{Bibliography}{11}{section*.2}% | ||||
| \contentsline {chapter}{Index}{17}{chapter*.4}% | ||||
|  | @ -0,0 +1,100 @@ | |||
| \documentclass[twoside,12pt,a4paper,english]{book} | ||||
| 
 | ||||
| %\includeonly{chapter04,list} | ||||
| 
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| \usepackage[english]{babel} | ||||
| \usepackage[utf8]{inputenc} | ||||
| \usepackage{listings} | ||||
| \usepackage[table]{xcolor} | ||||
| \usepackage{tikz} | ||||
| \usepackage{multicol} | ||||
| \usepackage{hyperref} | ||||
| \usepackage{array} | ||||
| \usepackage{microtype} | ||||
| 
 | ||||
| \usepackage{fouriernc} | ||||
| \usepackage[T1]{fontenc} | ||||
| 
 | ||||
| \usepackage{graphicx} | ||||
| \usepackage{framed} | ||||
| \usepackage{amssymb} | ||||
| \usepackage{amsmath} | ||||
| 
 | ||||
| \usepackage{pifont} | ||||
| \usepackage{ifthen} | ||||
| \usepackage{makeidx} | ||||
| \usepackage{enumitem} | ||||
| 
 | ||||
| \usepackage{titlesec} | ||||
| 
 | ||||
| \usepackage{skak} | ||||
| \usepackage[scaled=0.95]{inconsolata} | ||||
| 
 | ||||
| 
 | ||||
| \usetikzlibrary{patterns,snakes} | ||||
| \pagestyle{plain} | ||||
| 
 | ||||
| \definecolor{keywords}{HTML}{44548A} | ||||
| \definecolor{strings}{HTML}{00999A} | ||||
| \definecolor{comments}{HTML}{990000} | ||||
| 
 | ||||
| \lstset{language=C++,frame=single,basicstyle=\ttfamily \small,showstringspaces=false,columns=flexible} | ||||
| \lstset{ | ||||
|   literate={ö}{{\"o}}1 | ||||
|            {ä}{{\"a}}1 | ||||
|            {ü}{{\"u}}1 | ||||
| } | ||||
| \lstset{xleftmargin=20pt,xrightmargin=5pt} | ||||
| \lstset{aboveskip=12pt,belowskip=8pt} | ||||
| 
 | ||||
| \lstset{ | ||||
|     commentstyle=\color{comments}, | ||||
|     keywordstyle=\color{keywords}, | ||||
|     stringstyle=\color{strings} | ||||
| } | ||||
| 
 | ||||
| \date{Draft \today} | ||||
| 
 | ||||
| \usepackage[a4paper,vmargin=30mm,hmargin=33mm,footskip=15mm]{geometry} | ||||
| 
 | ||||
| \title{\Huge Competitive Programmer's Handbook} | ||||
| \author{\Large Antti Laaksonen} | ||||
| 
 | ||||
| \makeindex | ||||
| \usepackage[totoc]{idxlayout} | ||||
| 
 | ||||
| \titleformat{\subsubsection} | ||||
| {\normalfont\large\bfseries\sffamily}{\thesubsection}{1em}{} | ||||
| 
 | ||||
| \begin{document} | ||||
| 
 | ||||
| %\selectlanguage{finnish} | ||||
| 
 | ||||
| %\setcounter{page}{1} | ||||
| %\pagenumbering{roman} | ||||
| 
 | ||||
| %\frontmatter | ||||
| %\maketitle | ||||
| %\setcounter{tocdepth}{1} | ||||
| %\tableofcontents | ||||
| 
 | ||||
| %\include{preface} | ||||
| 
 | ||||
| \mainmatter | ||||
| \pagenumbering{arabic} | ||||
| \setcounter{page}{1} | ||||
| 
 | ||||
| \newcommand{\key}[1] {\textbf{#1}} | ||||
| 
 | ||||
| %\part{Graph algorithms} | ||||
| \include{chapter14} | ||||
| 
 | ||||
| %\cleardoublepage | ||||
| %\phantomsection | ||||
| %\addcontentsline{toc}{chapter}{Bibliography} | ||||
| %\include{list} | ||||
| 
 | ||||
| %\cleardoublepage | ||||
| %\printindex | ||||
| 
 | ||||
| \end{document} | ||||
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