From e8f7b22267f72ff8d0c66a441dd130cece53fbe9 Mon Sep 17 00:00:00 2001 From: arthur Date: Thu, 13 Nov 2025 21:07:05 -0300 Subject: [PATCH] feat: added tutorial file --- knight-moves/knight-moves-tutorial.pdf | Bin 0 -> 95316 bytes knight-moves/knight-moves-tutorial.tex | 38 ++++++++++++++++++ knight-moves/knight-moves.pdf | Bin 221050 -> 149509 bytes knight-moves/knight-moves.tex | 2 +- knight-moves/statement/input.tex | 2 +- knight-moves/statement/tutorial.tex | 25 ++++++++++++ sliding-puzzle/sliding-puzzle-tutorial.pdf | Bin 0 -> 94503 bytes sliding-puzzle/sliding-puzzle-tutorial.tex | 43 +++++++++++++++++++++ sliding-puzzle/sliding-puzzle.pdf | Bin 145520 -> 69787 bytes sliding-puzzle/statement/tutorial.tex | 30 ++++++++++++++ 10 files changed, 138 insertions(+), 2 deletions(-) create mode 100644 knight-moves/knight-moves-tutorial.pdf create mode 100644 knight-moves/knight-moves-tutorial.tex create mode 100644 sliding-puzzle/sliding-puzzle-tutorial.pdf create mode 100644 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Nosso objetivo é determinar o número mínimo de movimentos para organizar um tabuleiro $2 \times 3$ a partir de um estado inicial qualquer. + +\subsection*{Representação do estado} + +\begin{itemize} + \item Cada configuração do tabuleiro pode ser representada como uma sequência linear de números, por exemplo, $[1, 2, 3, 4, 5, 0]$ para o estado final. + \item A posição do $0$ indica onde a casa vazia está localizada e determina quais movimentos são válidos. +\end{itemize} + +\subsection*{Estratégia de solução usando BFS} + +Podemos modelar o problema como um grafo, onde cada nó é uma configuração do tabuleiro e cada aresta corresponde a um movimento válido do $0$. Uma abordagem eficiente é iniciar a BFS a partir do \textbf{estado final}: + +\begin{enumerate} + \item Inicialize a fila com o estado final $[1,2,3,4,5,0]$ e marque-o como visitado com distância $0$. + \item Para cada estado na fila: + \begin{itemize} + \item Identifique a posição do $0$ e calcule todas as posições adjacentes (horizontal e vertical) para trocas. + \item Gere os estados resultantes dessas trocas. + \item Se algum novo estado corresponder ao estado inicial fornecido, retorne a distância armazenada, que representa o número mínimo de movimentos. + \item Caso contrário, adicione o novo estado à fila e marque-o como visitado. + \end{itemize} + \item Se a fila se esvaziar sem encontrar o estado inicial, retorne $-1$. +\end{enumerate} + +\subsection*{Complexidade} + +\begin{itemize} + \item \textbf{Espacial:} $O(6!)$, pois existem $6! = 720$ possíveis permutações do tabuleiro $2 \times 3$. +\end{itemize}\end{document} diff --git a/sliding-puzzle/sliding-puzzle.pdf 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