I competed individually in Japan’s Ministry of Internal Affairs and Communications (MIC) nationwide CTF. The confirmed event rules permitted AI use. The official CTFd profile records 26th place and...

This repository separates validation from publication. A feature-branch build proves the site is valid; only a production workflow publishes generated files to gh-pages. What triggers each workflo...

BOJ 10803 — Making Squares Model and claim A valid cutting plan is a guillotine dissection: every cut splits one rectangle into two rectangles, and every final piece is a square with a positive i...

What the transform computes For a coefficient vector $a_0,\dots,a_{n-1}$, define the discrete Fourier transform (DFT) by evaluating its polynomial at the $n$th roots of unity: [X_k = \sum_{j=0}^{...

BOJ 1199 — Euler Circuit Model the input as a multigraph The adjacency matrix gives the number of undirected edges between each pair of vertices. Parallel edges are distinct and must each appear ...

Theorem Let $(a_n)$ be a sequence of real numbers. If $(a_n)$ is nondecreasing and bounded above, then it converges to $\sup{a_n:n\in\mathbb{N}}$. If $(a_n)$ is nonincreasing and bounded bel...

Theorem for sequences Let $(x_n)$ be a bounded sequence in the finite-dimensional Euclidean space $\mathbb{R}^d$, where $d\geq 1$. Then $(x_n)$ has a convergent subsequence. The limit lies in $\ma...

The nested interval theorem Let $(I_n)_{n\in\mathbb{N}}$ be a sequence of nonempty closed intervals $I_n=[a_n,b_n]$ in $\mathbb{R}$. Write $\lvert I_n\rvert=b_n-a_n$ for the length of $I_n$. If ...

BOJ 7579 — App Minimize the deactivation cost App $i$ releases $m_i$ units of memory when deactivated and costs $c_i$. Choose a set of apps whose released memory is at least $M$, minimizing the s...

Definitions 1. Rings, fields, and distributive laws A ring is a set $R$ equipped with two binary operations, addition $+$ and multiplication $\cdot$, such that: $(R,+)$ is an abelian group. ...