Enable macros

Oleksandr Kulkov · adamant-pwn · commit b0c987e9301f · 2022-06-05T23:59:44.000+02:00
diff --git a/.github/workflows/deploy-prod.yml b/.github/workflows/deploy-prod.yml
@@ -18,7 +18,7 @@ jobs:
           python-version: '3.8'
       - name: Install mkdocs-material
         run: |
-          pip install mkdocs-material
+          pip install mkdocs-material mkdocs-macros-plugin
       - name: Build pages
         run: |
           mkdocs build --strict
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
@@ -14,7 +14,7 @@ jobs:
           python-version: '3.8'
       - name: Install mkdocs-material
         run: |
-          pip install mkdocs-material
+          pip install mkdocs-material mkdocs-macros-plugin
       - name: Set up C++
         run: |
           sudo apt install -y --no-install-recommends build-essential
diff --git a/README.md b/README.md
diff --git a/README.md b/README.md
@@ -0,0 +1 @@
+src/index_body
diff --git a/mkdocs.yml b/mkdocs.yml
@@ -46,13 +46,21 @@ markdown_extensions:
   - pymdownx.emoji:
       emoji_index: !!python/name:materialx.emoji.twemoji 
       emoji_generator: !!python/name:materialx.emoji.to_svg
+  - meta
+
+plugins:
+  - search
+  - macros
+  #- git-authors
+
 extra:
   analytics:
     provider: google
     property: UA-85220282-1
 nav:
   - 'Home':
     - 'index.md'
+    - 'navigation.md'
     - 'contrib.md'
     - 'preview.md'
   - 'Algebra':
diff --git a/src/algebra/module-inverse.md b/src/algebra/module-inverse.md
@@ -70,7 +70,7 @@ From these results, we can easily find the modular inverse using the [binary exp
 
 Even though this method is easier to understand than the method described in previous paragraph, in the case when $m$ is not a prime number, we need to calculate Euler phi function, which involves factorization of $m$, which might be very hard. If the prime factorization of $m$ is known, then the complexity of this method is $O(\log m)$.
 
-## Finding the modular inverse for every number modulo $m$ {#mod-inv-all-num data-toc-label="Finding the modular inverse for every number modulo m"}
+## Finding the modular inverse for every number modulo $m$ { #mod-inv-all-num data-toc-label="Finding the modular inverse for every number modulo m"}
 
 The problem is the following: 
 we want to compute the modular inverse for every number in the range $[1, m-1]$.
diff --git a/src/algebra/phi-function.md b/src/algebra/phi-function.md
@@ -89,7 +89,7 @@ void phi_1_to_n(int n) {
 ```
 
 
-## Divisor sum property {#divsum}
+## Divisor sum property { #divsum}
 
 This interesting property was established by Gauss:
 
diff --git a/src/combinatorics/binomial-coefficients.md b/src/combinatorics/binomial-coefficients.md
@@ -159,7 +159,7 @@ long long binomial_coefficient(int n, int k) {
 }
 ```
 
-### Binomial coefficient modulo prime power  {#mod-prime-pow}
+### Binomial coefficient modulo prime power  { #mod-prime-pow}
 
 Here we want to compute the binomial coefficient modulo some prime power, i.e. $m = p^b$ for some prime $p$.
 If $p > \max(k, n-k)$, then we can use the same method as described in the previous section.
diff --git a/src/data_structures/disjoint_set_union.md b/src/data_structures/disjoint_set_union.md
@@ -422,7 +422,7 @@ bool is_bipartite(int v) {
 }
 ```
 
-### Offline RMQ (range minimum query) in $O(\alpha(n))$ on average / Arpa's trick {#arpa data-toc-label="Offline RMQ / Arpa's trick"}
+### Offline RMQ (range minimum query) in $O(\alpha(n))$ on average / Arpa's trick { #arpa data-toc-label="Offline RMQ / Arpa's trick"}
 
 We are given an array `a[]` and we have to compute some minima in given segments of the array.
 
diff --git a/src/data_structures/segment_tree.md b/src/data_structures/segment_tree.md
@@ -148,7 +148,7 @@ The green vertices are the vertices that we visit and update.
 
 !["Sum Segment Tree Update"](sum-segment-tree-update.png)
 
-### Implementation ### {#implementation}
+### Implementation ### { #implementation}
 
 The main consideration is how to store the Segment Tree.
 Of course we can define a $\text{Vertex}$ struct and create objects, that store the boundaries of the segment, its sum and additionally also pointers to its child vertices.
@@ -325,7 +325,7 @@ This interesting variation of the Segment Tree can be solved in exactly the same
 it is enough to store the GCD / LCM of the corresponding vertex in each vertex of the tree. 
 Combining two vertices can be done by computing the GCD / LCM of both vertices.
 
-#### Counting the number of zeros, searching for the $k$-th zero {#counting-zero-search-kth data-toc-label="Counting the number of zeros, searching for the k-th zero"}
+#### Counting the number of zeros, searching for the $k$-th zero { #counting-zero-search-kth data-toc-label="Counting the number of zeros, searching for the k-th zero"}
 
 In this problem we want to find the number of zeros in a given range, and additionally find the index of the $k$-th zero using a second function.
 
diff --git a/src/graph/edmonds_karp.md b/src/graph/edmonds_karp.md
@@ -176,7 +176,7 @@ int maxflow(int s, int t) {
 }
 ```
 
-## Integral flow theorem ## {#integral-theorem}
+## Integral flow theorem ## { #integral-theorem}
 
 The theorem simply says, that if every capacity in the network is an integer, then the flow in each edge will be an integer in the maximal flow.
 
diff --git a/src/index.md b/src/index.md
@@ -1,251 +1,5 @@
 ---
 title: Main Page
 ---
-# Algorithms for Competitive Programming
 
-*The goal of this project is to translate the wonderful resource
-[http://e-maxx.ru/algo](http://e-maxx.ru/algo) which provides descriptions of many algorithms
-and data structures especially popular in field of competitive programming.
-Moreover we want to improve the collected knowledge by extending the articles
-and adding new articles to the collection.*
-
-## Changelog
-
-
-- June 5, 2022: Enabled content tabs and sidebar navigation. The navigation structure should be adjusted in [mkdocs.yml](https://github.com/e-maxx-eng/e-maxx-eng/blob/master/mkdocs.yml) whenever a new article is created or an old one is moved.
-- January 16, 2022: Switched to the [MkDocs](https://www.mkdocs.org/) site generator with the [Material for MkDocs](https://squidfunk.github.io/mkdocs-material/) theme, which give the website a more modern look, brings a couple of new features (dark mode, better search, ...), makes the website more stable (in terms of rendering math formulas), and makes it easier to contribute.
-
-## New articles
-
-- (12 May 2022) [Factoring Exponentiation](algebra/factoring-exp.md)
-- (7 May 2022) [Knuth's Optimization](dynamic_programming/knuth-optimization.md)
-- (31 March 2022) [Continued fractions](algebra/continued-fractions.md)
-
-Full list of updates: [Commit History](https://github.com/e-maxx-eng/e-maxx-eng/commits/master)
-
-## Contributing
-
-- [Information for contributors](contrib.md)
-- [Test-Your-Page form](preview.md)
-
----
-
-## Articles
-
-### Algebra
-
-- **Fundamentals**
-    - [Binary Exponentiation](algebra/binary-exp.md)
-    - [Factoring Exponentiation](algebra/factoring-exp.md)
-    - [Euclidean algorithm for computing the greatest common divisor](algebra/euclid-algorithm.md)
-    - [Extended Euclidean Algorithm](algebra/extended-euclid-algorithm.md)
-    - [Linear Diophantine Equations](algebra/linear-diophantine-equation.md)
-    - [Fibonacci Numbers](algebra/fibonacci-numbers.md)
-- **Prime numbers**
-    - [Sieve of Eratosthenes](algebra/sieve-of-eratosthenes.md)
-    - [Linear Sieve](algebra/prime-sieve-linear.md)
-    - [Primality tests](algebra/primality_tests.md)
-    - [Integer factorization](algebra/factorization.md)
-- **Number-theoretic functions**
-    - [Euler's totient function](algebra/phi-function.md)
-    - [Number of divisors / sum of divisors](algebra/divisors.md)
-- **Modular arithmetic**
-    - [Modular Inverse](algebra/module-inverse.md)
-    - [Linear Congruence Equation](algebra/linear_congruence_equation.md)
-    - [Chinese Remainder Theorem](algebra/chinese-remainder-theorem.md)
-    - [Factorial modulo $p$](algebra/factorial-modulo.md)
-    - [Discrete Log](algebra/discrete-log.md)
-    - [Primitive Root](algebra/primitive-root.md)
-    - [Discrete Root](algebra/discrete-root.md)
-    - [Montgomery Multiplication](algebra/montgomery_multiplication.md)
-- **Number systems**
-    - [Balanced Ternary](algebra/balanced-ternary.md)
-    - [Gray code](algebra/gray-code.md)
-- **Miscellaneous**
-    - [Enumerating submasks of a bitmask](algebra/all-submasks.md)
-    - [Arbitrary-Precision Arithmetic](algebra/big-integer.md)
-    - [Fast Fourier transform](algebra/fft.md)
-    - [Operations on polynomials and series](algebra/polynomial.md)
-    - [Continued fractions](algebra/continued-fractions.md)
-
-### Data Structures
-
-- **Fundamentals**
-    - [Minimum Stack / Minimum Queue](data_structures/stack_queue_modification.md)
-    - [Sparse Table](data_structures/sparse-table.md)
-- **Trees**
-    - [Disjoint Set Union](data_structures/disjoint_set_union.md)
-    - [Fenwick Tree](data_structures/fenwick.md)
-    - [Sqrt Decomposition](data_structures/sqrt_decomposition.md)
-    - [Segment Tree](data_structures/segment_tree.md)
-    - [Treap](data_structures/treap.md)
-    - [Sqrt Tree](data_structures/sqrt-tree.md)
-    - [Randomized Heap](data_structures/randomized_heap.md)
-- **Advanced**
-    - [Deleting from a data structure in O(T(n)log n)](data_structures/deleting_in_log_n.md)
-
-### Dynamic Programming
-
-- **DP optimizations**
-    - [Divide and Conquer DP](dynamic_programming/divide-and-conquer-dp.md)
-    - [Knuth's Optimization](dynamic_programming/knuth-optimization.md)
-- **Tasks**
-    - [Dynamic Programming on Broken Profile. Problem "Parquet"](dynamic_programming/profile-dynamics.md)
-    - [Finding the largest zero submatrix](dynamic_programming/zero_matrix.md)
-
-### String Processing
-
-- **Fundamentals**
-    - [String Hashing](string/string-hashing.md)
-    - [Rabin-Karp for String Matching](string/rabin-karp.md)
-    - [Prefix function - Knuth-Morris-Pratt](string/prefix-function.md)
-    - [Z-function](string/z-function.md)
-    - [Suffix Array](string/suffix-array.md)
-    - [Aho-Corasick algorithm](string/aho_corasick.md)
-- **Advanced**
-    - [Suffix Tree](string/suffix-tree-ukkonen.md)
-    - [Suffix Automaton](string/suffix-automaton.md)
-    - [Lyndon factorization](string/lyndon_factorization.md)
-- **Tasks**
-    - [Expression parsing](string/expression_parsing.md)
-    - [Manacher's Algorithm - Finding all sub-palindromes in O(N)](string/manacher.md)
-    - [Finding repetitions](string/main_lorentz.md)
-
-### Linear Algebra
-
-- **Matrices**
-    - [Gauss & System of Linear Equations](linear_algebra/linear-system-gauss.md)
-    - [Gauss & Determinant](linear_algebra/determinant-gauss.md)
-    - [Kraut & Determinant](linear_algebra/determinant-kraut.md)
-    - [Rank of a matrix](linear_algebra/rank-matrix.md)
-
-### Combinatorics
-
-- **Fundamentals**
-    - [Finding Power of Factorial Divisor](algebra/factorial-divisors.md)
-    - [Binomial Coefficients](combinatorics/binomial-coefficients.md)
-    - [Catalan Numbers](combinatorics/catalan-numbers.md)
-- **Techniques**
-    - [The Inclusion-Exclusion Principle](combinatorics/inclusion-exclusion.md)
-    - [Burnside's lemma / Pólya enumeration theorem](combinatorics/burnside.md)
-    - [Stars and bars](combinatorics/stars_and_bars.md)
-    - [Generating all $K$-combinations](combinatorics/generating_combinations.md)
-- **Tasks**
-    - [Placing Bishops on a Chessboard](combinatorics/bishops-on-chessboard.md)
-    - [Balanced bracket sequences](combinatorics/bracket_sequences.md)
-    - [Counting labeled graphs](combinatorics/counting_labeled_graphs.md)
-
-### Numerical Methods
-
-- **Search**
-    - [Ternary Search](num_methods/ternary_search.md)
-    - [Newton's method for finding roots](num_methods/roots_newton.md)
-- **Integration**
-    - [Integration by Simpson's formula](num_methods/simpson-integration.md)
-
-### Geometry
-
-- **Elementary operations**
-    - [Basic Geometry](geometry/basic-geometry.md)
-    - [Finding the equation of a line for a segment](geometry/segment-to-line.md)
-    - [Intersection Point of Lines](geometry/lines-intersection.md)
-    - [Check if two segments intersect](geometry/check-segments-intersection.md)
-    - [Intersection of Segments](geometry/segments-intersection.md)
-    - [Circle-Line Intersection](geometry/circle-line-intersection.md)
-    - [Circle-Circle Intersection](geometry/circle-circle-intersection.md)
-    - [Common tangents to two circles](geometry/tangents-to-two-circles.md)
-    - [Length of the union of segments](geometry/length-of-segments-union.md)
-- **Polygons**
-    - [Oriented area of a triangle](geometry/oriented-triangle-area.md)
-    - [Area of simple polygon](geometry/area-of-simple-polygon.md)
-    - [Check if points belong to the convex polygon in O(log N)](geometry/point-in-convex-polygon.md)
-    - [Minkowski sum of convex polygons](geometry/minkowski.md)
-    - [Pick's Theorem - area of lattice polygons](geometry/picks-theorem.md)
-    - [Lattice points of non-lattice polygon](geometry/lattice-points.md)
-- **Convex hull**
-    - [Convex hull construction](geometry/convex-hull.md)
-    - [Convex hull trick and Li Chao tree](geometry/convex_hull_trick.md)
-- **Sweep-line**
-    - [Search for a pair of intersecting segments](geometry/intersecting_segments.md)
-    - [Point location in O(log N)](geometry/point-location.md)
-- **Miscellaneous**
-    - [Finding the nearest pair of points](geometry/nearest_points.md)
-    - [Delaunay triangulation and Voronoi diagram](geometry/delaunay.md)
-    - [Vertical decomposition](geometry/vertical_decomposition.md)
-    - [Half-plane intersection - S&I Algorithm in O(Nlog N)](geometry/halfplane-intersection.md)
-
-### Graphs
-
-- **Graph traversal**
-    - [Breadth First Search](graph/breadth-first-search.md)
-    - [Depth First Search](graph/depth-first-search.md)
-- **Connected components, bridges, articulations points**
-    - [Finding Connected Components](graph/search-for-connected-components.md)
-    - [Finding Bridges in O(N+M)](graph/bridge-searching.md)
-    - [Finding Bridges Online](graph/bridge-searching-online.md)
-    - [Finding Articulation Points in O(N+M)](graph/cutpoints.md)
-    - [Strongly Connected Components and Condensation Graph](graph/strongly-connected-components.md)
-    - [Strong Orientation](graph/strong-orientation.md)
-- **Single-source shortest paths**
-    - [Dijkstra - finding shortest paths from given vertex](graph/dijkstra.md)
-    - [Dijkstra on sparse graphs](graph/dijkstra_sparse.md)
-    - [Bellman-Ford - finding shortest paths with negative weights](graph/bellman_ford.md)
-    - [0-1 BFS](graph/01_bfs.md)
-    - [D´Esopo-Pape algorithm](graph/desopo_pape.md)
-- **All-pairs shortest paths**
-    - [Floyd-Warshall - finding all shortest paths](graph/all-pair-shortest-path-floyd-warshall.md)
-    - [Number of paths of fixed length / Shortest paths of fixed length](graph/fixed_length_paths.md)
-- **Spanning trees**
-    - [Minimum Spanning Tree - Prim's Algorithm](graph/mst_prim.md)
-    - [Minimum Spanning Tree - Kruskal](graph/mst_kruskal.md)
-    - [Minimum Spanning Tree - Kruskal with Disjoint Set Union](graph/mst_kruskal_with_dsu.md)
-    - [Second best Minimum Spanning Tree - Using Kruskal and Lowest Common Ancestor](graph/second_best_mst.md)
-    - [Kirchhoff Theorem](graph/kirchhoff-theorem.md)
-    - [Prüfer code](graph/pruefer_code.md)
-- **Cycles**
-    - [Checking a graph for acyclicity and finding a cycle in O(M)](graph/finding-cycle.md)
-    - [Finding a Negative Cycle in the Graph](graph/finding-negative-cycle-in-graph.md)
-    - [Eulerian Path](graph/euler_path.md)
-- **Lowest common ancestor**
-    - [Lowest Common Ancestor](graph/lca.md)
-    - [Lowest Common Ancestor - Binary Lifting](graph/lca_binary_lifting.md)
-    - [Lowest Common Ancestor - Farach-Colton and Bender algorithm](graph/lca_farachcoltonbender.md)
-    - [Solve RMQ by finding LCA](graph/rmq_linear.md)
-    - [Lowest Common Ancestor - Tarjan's off-line algorithm](graph/lca_tarjan.md)
-- **Flows and related problems**
-    - [Maximum flow - Ford-Fulkerson and Edmonds-Karp](graph/edmonds_karp.md)
-    - [Maximum flow - Push-relabel algorithm](graph/push-relabel.md)
-    - [Maximum flow - Push-relabel algorithm improved](graph/push-relabel-faster.md)
-    - [Maximum flow - Dinic's algorithm](graph/dinic.md)
-    - [Maximum flow - MPM algorithm](graph/mpm.md)
-    - [Flows with demands](graph/flow_with_demands.md)
-    - [Minimum-cost flow](graph/min_cost_flow.md)
-    - [Assignment problem. Solution using min-cost-flow in O (N^5)](graph/Assignment-problem-min-flow.md)
-- **Matchings and related problems**
-    - [Bipartite Graph Check](graph/bipartite-check.md)
-    - [Kuhn's Algorithm - Maximum Bipartite Matching](graph/kuhn_maximum_bipartite_matching.md)
-- **Miscellaneous**
-    - [Topological Sorting](graph/topological-sort.md)
-    - [Edge connectivity / Vertex connectivity](graph/edge_vertex_connectivity.md)
-    - [Tree painting](graph/tree_painting.md)
-    - [2-SAT](graph/2SAT.md)
-    - [Heavy-light decomposition](graph/hld.md)
-
-### Miscellaneous
-
-- **Sequences**
-    - [RMQ task (Range Minimum Query - the smallest element in an interval)](sequences/rmq.md)
-    - [Longest increasing subsequence](sequences/longest_increasing_subsequence.md)
-    - [Search the subsegment with the maximum/minimum sum](others/maximum_average_segment.md)
-    - [K-th order statistic in O(N)](sequences/k-th.md)
-- **Game Theory**
-    - [Games on arbitrary graphs](game_theory/games_on_graphs.md)
-    - [Sprague-Grundy theorem. Nim](game_theory/sprague-grundy-nim.md)
-- **Schedules**
-    - [Scheduling jobs on one machine](schedules/schedule_one_machine.md)
-    - [Scheduling jobs on two machines](schedules/schedule_two_machines.md)
-    - [Optimal schedule of jobs given their deadlines and durations](schedules/schedule-with-completion-duration.md)
-- **Miscellaneous**
-    - [Josephus problem](others/josephus_problem.md)
-    - [15 Puzzle Game: Existence Of The Solution](others/15-puzzle.md)
-    - [The Stern-Brocot Tree and Farey Sequences](others/stern_brocot_tree_farey_sequences.md)
+{% include 'index_body' %}
diff --git a/src/index_body b/src/index_body
diff --git a/src/navigation.md b/src/navigation.md

Original file line number	Diff line number	Diff line change
`@@ -159,7 +159,7 @@ long long binomial_coefficient(int n, int k) {`
`159`	`159`	`}`
`160`	`160`	```
`161`	`161`
`162`		`-### Binomial coefficient modulo prime power {#mod-prime-pow}`
	`162`	`+### Binomial coefficient modulo prime power { #mod-prime-pow}`
`163`	`163`
`164`	`164`	`Here we want to compute the binomial coefficient modulo some prime power, i.e. $m = p^b$ for some prime $p$.`
`165`	`165`	`If $p > \max(k, n-k)$, then we can use the same method as described in the previous section.`
Original file line number	Diff line number	Diff line change
`@@ -422,7 +422,7 @@ bool is_bipartite(int v) {`
`422`	`422`	`}`
`423`	`423`	```
`424`	`424`
`425`		`-### Offline RMQ (range minimum query) in $O(\alpha(n))$ on average / Arpa's trick {#arpa data-toc-label="Offline RMQ / Arpa's trick"}`
	`425`	`+### Offline RMQ (range minimum query) in $O(\alpha(n))$ on average / Arpa's trick { #arpa data-toc-label="Offline RMQ / Arpa's trick"}`
`426`	`426`
`427`	`427`	We are given an array `a[]` and we have to compute some minima in given segments of the array.
`428`	`428`