diff --git a/output/book.aux b/output/book.aux
new file mode 100644
index 0000000..83a1747
--- /dev/null
+++ b/output/book.aux
@@ -0,0 +1,58 @@
+\relax 
+\providecommand\hyper@newdestlabel[2]{}
+\providecommand\babel@aux[2]{}
+\@nameuse{bbl@beforestart}
+\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
+\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
+\global\let\oldcontentsline\contentsline
+\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global\let\oldnewlabel\newlabel
+\gdef\newlabel#1#2{\newlabelxx{#1}#2}
+\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\ifx\hyper@anchor\@undefined
+\let\contentsline\oldcontentsline
+\let\newlabel\oldnewlabel
+\fi}
+\fi}
+\global\let\hyper@last\relax 
+\gdef\HyperFirstAtBeginDocument#1{#1}
+\providecommand\HyField@AuxAddToFields[1]{}
+\providecommand\HyField@AuxAddToCoFields[2]{}
+\babel@aux{english}{}
+\@input{preface.aux}
+\@writefile{toc}{\contentsline {part}{I\hspace  {1em}Basic techniques}{1}{part.1}\protected@file@percent }
+\@input{chapter01.aux}
+\@input{chapter02.aux}
+\@input{chapter03.aux}
+\@input{chapter04.aux}
+\@input{chapter05.aux}
+\@input{chapter06.aux}
+\@input{chapter07.aux}
+\@input{chapter08.aux}
+\@input{chapter09.aux}
+\@input{chapter10.aux}
+\@writefile{toc}{\contentsline {part}{II\hspace  {1em}Graph algorithms}{107}{part.2}\protected@file@percent }
+\@input{chapter11.aux}
+\@input{chapter12.aux}
+\@input{chapter13.aux}
+\@input{chapter14.aux}
+\@input{chapter15.aux}
+\@input{chapter16.aux}
+\@input{chapter17.aux}
+\@input{chapter18.aux}
+\@input{chapter19.aux}
+\@input{chapter20.aux}
+\@writefile{toc}{\contentsline {part}{III\hspace  {1em}Advanced topics}{195}{part.3}\protected@file@percent }
+\@input{chapter21.aux}
+\@input{chapter22.aux}
+\@input{chapter23.aux}
+\@input{chapter24.aux}
+\@input{chapter25.aux}
+\@input{chapter26.aux}
+\@input{chapter27.aux}
+\@input{chapter28.aux}
+\@input{chapter29.aux}
+\@input{chapter30.aux}
+\@input{list.aux}
+\@writefile{toc}{\contentsline {chapter}{Bibliography}{281}{section*.3}\protected@file@percent }
+\@writefile{toc}{\contentsline {chapter}{Index}{287}{chapter*.5}\protected@file@percent }
diff --git a/output/book.dvi b/output/book.dvi
new file mode 100644
index 0000000..7a71d44
Binary files /dev/null and b/output/book.dvi differ
diff --git a/output/book.fdb_latexmk b/output/book.fdb_latexmk
new file mode 100644
index 0000000..0e34e52
--- /dev/null
+++ b/output/book.fdb_latexmk
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+# Fdb version 3
+["makeindex output/book.idx"] 1612133277 "output/book.idx" "output/book.ind" "output/book" 1612133640
+  "output/book.idx" 1612133640 14726 a4f79dc0584fe9e391a7573780c527ed "pdflatex"
+  (generated)
+  "output/book.ind"
+  "output/book.ilg"
+["pdflatex"] 1612133616 "book.tex" "output/book.pdf" "book" 1612133640
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diff --git a/output/book.idx b/output/book.idx
new file mode 100644
index 0000000..9edccb5
--- /dev/null
+++ b/output/book.idx
@@ -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}
diff --git a/output/book.ilg b/output/book.ilg
new file mode 100644
index 0000000..511b999
--- /dev/null
+++ b/output/book.ilg
@@ -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.
diff --git a/output/book.ind b/output/book.ind
new file mode 100644
index 0000000..f3c505d
--- /dev/null
+++ b/output/book.ind
@@ -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
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+\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
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+\BOOKMARK [1][-]{section.14.2}{Diameter}{chapter.14}% 74
+\BOOKMARK [1][-]{section.14.3}{All longest paths}{chapter.14}% 75
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+\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
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+\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
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+\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
diff --git a/output/book.pdf b/output/book.pdf
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index 0000000..8a092cc
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diff --git a/output/book.toc b/output/book.toc
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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}%
+\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}%
+\contentsline {subsubsection}{Pick's theorem}{272}{section.29.3}%
+\contentsline {section}{\numberline {29.4}Distance functions}{272}{section.29.4}%
+\contentsline {subsubsection}{Rotating coordinates}{273}{section.29.4}%
+\contentsline {chapter}{\numberline {30}Sweep line algorithms}{275}{chapter.30}%
+\contentsline {section}{\numberline {30.1}Intersection points}{276}{section.30.1}%
+\contentsline {section}{\numberline {30.2}Closest pair problem}{277}{section.30.2}%
+\contentsline {section}{\numberline {30.3}Convex hull problem}{278}{section.30.3}%
+\contentsline {chapter}{Bibliography}{281}{section*.3}%
+\contentsline {chapter}{Index}{287}{chapter*.5}%
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diff --git a/output/test.out b/output/test.out
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+\BOOKMARK [0][-]{chapter.1}{Tree algorithms}{}% 1
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diff --git a/output/test.toc b/output/test.toc
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index 0000000..2554dd9
--- /dev/null
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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}%
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+\contentsline {chapter}{Bibliography}{11}{section*.2}%
+\contentsline {chapter}{Index}{17}{chapter*.4}%
diff --git a/test.tex b/test.tex
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--- /dev/null
+++ b/test.tex
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+\documentclass[twoside,12pt,a4paper,english]{book}
+
+%\includeonly{chapter04,list}
+
+\usepackage[english]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage{listings}
+\usepackage[table]{xcolor}
+\usepackage{tikz}
+\usepackage{multicol}
+\usepackage{hyperref}
+\usepackage{array}
+\usepackage{microtype}
+
+\usepackage{fouriernc}
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+
+\usepackage{graphicx}
+\usepackage{framed}
+\usepackage{amssymb}
+\usepackage{amsmath}
+
+\usepackage{pifont}
+\usepackage{ifthen}
+\usepackage{makeidx}
+\usepackage{enumitem}
+
+\usepackage{titlesec}
+
+\usepackage{skak}
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+
+
+\usetikzlibrary{patterns,snakes}
+\pagestyle{plain}
+
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+\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
+}
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+
+\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}
\ No newline at end of file