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Oleksandr Kulkovadamant-pwn
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‎.github/workflows/deploy-prod.yml‎

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python-version: '3.8'
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- name: Install mkdocs-material
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run: |
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pip install mkdocs-material
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pip install mkdocs-material mkdocs-macros-plugin
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- name: Build pages
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mkdocs build --strict

‎.github/workflows/test.yml‎

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python-version: '3.8'
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- name: Install mkdocs-material
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pip install mkdocs-material
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pip install mkdocs-material mkdocs-macros-plugin
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- name: Set up C++
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sudo apt install -y --no-install-recommends build-essential

‎README.md‎

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‎README.md‎

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src/index_body

‎mkdocs.yml‎

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- pymdownx.emoji:
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emoji_index: !!python/name:materialx.emoji.twemoji
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emoji_generator: !!python/name:materialx.emoji.to_svg
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- meta
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plugins:
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- search
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- macros
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#- git-authors
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extra:
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analytics:
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provider: google
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property: UA-85220282-1
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nav:
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- 'Home':
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- 'index.md'
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- 'navigation.md'
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- 'contrib.md'
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- 'preview.md'
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- 'Algebra':

‎src/algebra/module-inverse.md‎

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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 $O(\log m)$.
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## 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"}
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## 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"}
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The problem is the following:
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we want to compute the modular inverse for every number in the range $[1, m-1]$.

‎src/algebra/phi-function.md‎

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```
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## Divisor sum property {#divsum}
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## Divisor sum property { #divsum}
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This interesting property was established by Gauss:
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‎src/combinatorics/binomial-coefficients.md‎

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}
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```
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### Binomial coefficient modulo prime power {#mod-prime-pow}
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### Binomial coefficient modulo prime power { #mod-prime-pow}
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Here we want to compute the binomial coefficient modulo some prime power, i.e. $m = p^b$ for some prime $p$.
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If $p > \max(k, n-k)$, then we can use the same method as described in the previous section.

‎src/data_structures/disjoint_set_union.md‎

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```
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### Offline RMQ (range minimum query) in $O(\alpha(n))$ on average / Arpa's trick {#arpa data-toc-label="Offline RMQ / Arpa's trick"}
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### Offline RMQ (range minimum query) in $O(\alpha(n))$ on average / Arpa's trick { #arpa data-toc-label="Offline RMQ / Arpa's trick"}
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We are given an array `a[]` and we have to compute some minima in given segments of the array.
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‎src/data_structures/segment_tree.md‎

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!["Sum Segment Tree Update"](sum-segment-tree-update.png)
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### Implementation ### {#implementation}
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### Implementation ### { #implementation}
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The main consideration is how to store the Segment Tree.
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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.
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it is enough to store the GCD / LCM of the corresponding vertex in each vertex of the tree.
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Combining two vertices can be done by computing the GCD / LCM of both vertices.
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#### 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"}
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#### 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"}
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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.
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