From 9b0d2d9fd257ef5bce61c92bb51f2f9313adb76d Mon Sep 17 00:00:00 2001 From: arthur Date: Thu, 2 Apr 2026 23:26:45 -0300 Subject: [PATCH] feat: new tutorials added. --- bolhas/bolhas-tutorial.pdf | Bin 0 -> 95120 bytes bolhas/bolhas-tutorial.tex | 47 +++++++++++++++++ bolhas/bolhas.pdf | Bin 88946 -> 88946 bytes bolhas/statement/tutorial.tex | 34 ++++++++++++ caching-offline/caching-offline-tutorial.pdf | Bin 0 -> 74514 bytes caching-offline/caching-offline-tutorial.tex | 49 ++++++++++++++++++ caching-offline/caching-offline.pdf | Bin 99709 -> 99694 bytes caching-offline/statement/tutorial.tex | 36 +++++++++++++ .../conversor-fonetico-generico-tutorial.pdf | Bin 0 -> 84915 bytes .../conversor-fonetico-generico-tutorial.tex | 46 ++++++++++++++++ .../conversor-fonetico-generico.pdf | Bin 188557 -> 87173 bytes .../statement/tutorial.tex | 33 ++++++++++++ 12 files changed, 245 insertions(+) create mode 100644 bolhas/bolhas-tutorial.pdf create mode 100644 bolhas/bolhas-tutorial.tex create 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determinar o vencedor de um jogo baseado em trocas de elementos adjacentes de uma permutação, o que se traduz em calcular a paridade do número de inversões da sequência inicial. + +\subsection*{Representação do estado} + +\begin{itemize} + \item Uma \textbf{inversão} ocorre quando um elemento maior aparece antes de um elemento menor na sequência. + \item Cada movimento válido no jogo (trocar um par de elementos adjacentes fora de ordem) reduz o número total de inversões em exatamente $1$. + \item Como o jogo termina quando a sequência está ordenada (zero inversões) e Marcelo faz o primeiro movimento, a vitória depende exclusivamente da paridade das inversões: se for ímpar, Marcelo fará o último movimento e vencerá; se for par, Carlos vencerá. +\end{itemize} + +\subsection*{Estratégia de solução usando Divisão e Conquista (Merge Sort)} + +Para contar o número de inversões de forma eficiente, evitamos a contagem trivial de comparar todos os pares (que custaria $O(N^2)$) e utilizamos uma adaptação do algoritmo \textit{Merge Sort}. + +\begin{enumerate} + \item Leia o tamanho da sequência ($N$) e armazene a permutação inicial em um vetor. + \item Crie uma função recursiva baseada no \textit{Merge Sort} que divide o vetor ao meio até que os subvetores tenham tamanho $1$ (onde o número de inversões é $0$). + \item Na etapa de conquista (\textit{merge}): + \begin{itemize} + \item Mantenha dois ponteiros, um para o subvetor da esquerda e outro para o subvetor da direita. + \item Compare os elementos apontados. Se o elemento da direita for menor que o da esquerda, ele precisará saltar todos os elementos restantes do subvetor da esquerda para ser ordenado. + \item Nesse caso, adicione ao contador de inversões a quantidade exata de elementos restantes no subvetor da esquerda. + \item Copie o menor elemento para a posição correta do vetor principal para mantê-lo ordenado. + \end{itemize} + \item Após a execução de toda a recursão, avalie o número total de inversões contabilizadas. + \item Se o número de inversões for ímpar, imprima "Marcelo". Caso contrário, imprima "Carlos". +\end{enumerate} + +\subsection*{Complexidade} + +\begin{itemize} + \item \textbf{Espacial:} $O(N)$, devido à criação de vetores temporários auxiliares durante as etapas de intercalação do \textit{Merge Sort}, além de $O(\log N)$ referente ao espaço utilizado pela pilha de chamadas recursivas. + \item \textbf{Temporal:} $O(N \log N)$. O algoritmo divide a sequência de tamanho $N$ pela metade $\log N$ vezes. Em cada um desses níveis de recursão, a etapa de intercalação percorre os subvetores de forma linear, custando globalmente $O(N)$ por nível. +\end{itemize}\end{document} diff --git a/bolhas/bolhas.pdf b/bolhas/bolhas.pdf index 29b2519bdf9589d54d5367c37610e2504ee5e1e8..1d1b4e3071489a7aadbd97c0d4330ed01d05df62 100644 GIT binary patch delta 195 zcmeygjrG$u)`l&Nx80Q-V+;%o3P3~=h{yyHIUpj&zyyd542-t_b!YTv(lIeGGBP$Y zHMP(+FjhA(P}k(r_svgnNi0cK&~ULbGB7d&YJe))Ug5>~oHx+X(a^xz*~GxY%*evR z&DG7>%+lPz$iTqa+|kL=!r9zT!G@rcST22^)V%bP3Wn%i$iFwSHG0JrHg A-2eap delta 185 zcmeygjrG$u)`l&Nx80{}yEF0&C&w5V7-WEm7y}a^HZU;T{@0z+pGn8qz|6qF$kM=E z*T7iaz(8G-OW!v?#U-&MRYAkW%E-XT%mA)rdxaO{bKXEFCpTkfLuWHb6K5wg6Bko6 wV^a%9CqpAk6GLN5R|7XY1sj4&V!8BvQuESFG8D{=%qJ@fYHq(7!8nr%0Dkx|@Bjb+ diff --git a/bolhas/statement/tutorial.tex b/bolhas/statement/tutorial.tex index e69de29..3fb43ad 100644 --- a/bolhas/statement/tutorial.tex +++ b/bolhas/statement/tutorial.tex @@ -0,0 +1,34 @@ +O problema consiste em determinar o vencedor de um jogo baseado em trocas de elementos adjacentes de uma permutação, o que se traduz em calcular a paridade do número de inversões da sequência inicial. + +\subsection*{Representação do estado} + +\begin{itemize} + \item Uma \textbf{inversão} ocorre quando um elemento maior aparece antes de um elemento menor na sequência. + \item Cada movimento válido no jogo (trocar um par de elementos adjacentes fora de ordem) reduz o número total de inversões em exatamente $1$. + \item Como o jogo termina quando a sequência está ordenada (zero inversões) e Marcelo faz o primeiro movimento, a vitória depende exclusivamente da paridade das inversões: se for ímpar, Marcelo fará o último movimento e vencerá; se for par, Carlos vencerá. +\end{itemize} + +\subsection*{Estratégia de solução usando Divisão e Conquista (Merge Sort)} + +Para contar o número de inversões de forma eficiente, evitamos a contagem trivial de comparar todos os pares (que custaria $O(N^2)$) e utilizamos uma adaptação do algoritmo \textit{Merge Sort}. + +\begin{enumerate} + \item Leia o tamanho da sequência ($N$) e armazene a permutação inicial em um vetor. + \item Crie uma função recursiva baseada no \textit{Merge Sort} que divide o vetor ao meio até que os subvetores tenham tamanho $1$ (onde o número de inversões é $0$). + \item Na etapa de conquista (\textit{merge}): + \begin{itemize} + \item Mantenha dois ponteiros, um para o subvetor da esquerda e outro para o subvetor da direita. + \item Compare os elementos apontados. Se o elemento da direita for menor que o da esquerda, ele precisará saltar todos os elementos restantes do subvetor da esquerda para ser ordenado. + \item Nesse caso, adicione ao contador de inversões a quantidade exata de elementos restantes no subvetor da esquerda. + \item Copie o menor elemento para a posição correta do vetor principal para mantê-lo ordenado. + \end{itemize} + \item Após a execução de toda a recursão, avalie o número total de inversões contabilizadas. + \item Se o número de inversões for ímpar, imprima "Marcelo". Caso contrário, imprima "Carlos". +\end{enumerate} + +\subsection*{Complexidade} + +\begin{itemize} + \item \textbf{Espacial:} $O(N)$, devido à criação de vetores temporários auxiliares durante as etapas de intercalação do \textit{Merge Sort}, além de $O(\log N)$ referente ao espaço utilizado pela pilha de chamadas recursivas. + \item \textbf{Temporal:} $O(N \log N)$. O algoritmo divide a sequência de tamanho $N$ pela metade $\log N$ vezes. Em cada um desses níveis de recursão, a etapa de intercalação percorre os subvetores de forma linear, custando globalmente $O(N)$ por nível. +\end{itemize} \ No newline at end of file diff --git a/caching-offline/caching-offline-tutorial.pdf b/caching-offline/caching-offline-tutorial.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e5fdb1fb6d1eb2f656ba2c39b24b345dbf10b1f1 GIT binary patch literal 74514 zcma&MQ;aTL)NWa}ZPzZ_*k#+cZQHh8yKLLGZQJ%+RsEe#|4ApOlRoQW<(Zl5W?jr= zWM+^nh=|cK(X+vj&o7Ux!>|!C64@JB!SM3JFvytNnY&mJF*CDr5&ho>hC$5I#>Lc$ zh(XN8(8W~5)Y#s{6o!uv#@WTm)X)~jW3xt6I{ug)p?9wCya?XKlTOp`gdLkKT9Y<` z=pv^TRlvBaDwS@F%?~aJI$@7MsTff16`M3ymL)As%R!&}Y?yL&;MqIqw#W$YnggbldIir#Mh z19&;$uQ&Hm7c>3Cvi(Sef?eY1=03hiDUZ7O4Czrf9^|~|%b6)=%z#)~i+|0ClNBrm z2LBha6`EYaaq%x*uE(K;*OHpr8ovB8z%7&nW1y+P(C$)UzPIQCcS}g#xUS5d+iLS3 z$ewSM8CsdQnaNkYj-vo6$SkRFIJ~_DzEAB5TmJL8I@}YE6@*(su>!4`gnB7O#i11S zkaJ#q>k>+ZM)baR=-Z@Jf!PM)$q~ks0Dw`+3%zY>S$LWCG!e5swA658*nxj-oHJaY 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a/caching-offline/statement/tutorial.tex +++ b/caching-offline/statement/tutorial.tex @@ -0,0 +1,36 @@ +O problema consiste em simular um gerenciador de cache e determinar o número mínimo de falhas de página. Como a sequência completa de requisições é conhecida previamente, podemos utilizar uma estratégia gulosa para resolver o problema. + +\subsection*{Representação do estado} + +\begin{itemize} + \item A memória principal (cache) é representada por um conjunto (\textit{hash set}), que armazena os identificadores das páginas atualmente carregadas, permitindo consultas em tempo constante. + \item O histórico futuro de cada página é mapeado em vetores, registrando todos os índices (momentos no tempo) em que cada página será requisitada. + \item Um vetor de ponteiros auxiliares acompanha qual a próxima ocorrência futura correspondente para cada página. +\end{itemize} + +\subsection*{Estratégia de solução usando Algoritmo Guloso} + +A estratégia ótima dita que, quando a cache estiver cheia e ocorrer uma falha, a página a ser substituída deve ser aquela que demorará mais tempo para ser referenciada novamente no futuro. + +\begin{enumerate} + \item Leia a capacidade da cache ($k$) e o tamanho da sequência de requisições ($v$). + \item Faça um pré-processamento da sequência de páginas: + \begin{itemize} + \item Armazene a sequência original em um vetor. + \item Para cada página lida, adicione o índice atual à sua respectiva lista de referências futuras. + \end{itemize} + \item Inicialize a cache vazia, o controle de progresso das referências futuras e o contador de falhas (\textit{misses}). + \item Percorra a sequência de requisições passo a passo: + \begin{itemize} + \item Se a página atual \textbf{não} estiver na cache, ocorreu uma falha de página. Incremente o contador de \textit{misses}. + \item Se a cache já estiver cheia (tamanho igual a $k$) no momento da falha, é necessário eleger uma página residente para remoção: + \begin{itemize} + \item Inspecione todas as páginas atualmente na cache. + \item Se alguma página não possuir mais requisições futuras, ela é a candidata ideal e deve ser escolhida para remoção imediata. + \item Caso contrário, compare a próxima requisição de todas e encontre aquela que vai demorar mais tempo para aparecer de novo (índice mais distante no futuro), removendo-a. + \end{itemize} + \item Insira a nova página na cache. + \item Ao final de cada iteração, independentemente de ter ocorrido acerto ou falha, avance o ponteiro de ocorrências da página que acabou de ser processada. + \end{itemize} + \item Ao término da simulação, imprima o total de falhas contabilizadas. +\end{enumerate} \ No newline at end of file diff --git a/conversor-fonetico-generico/conversor-fonetico-generico-tutorial.pdf 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restrição de que todas as palavras intermediárias devem pertencer a um dicionário fornecido. + +\subsection*{Representação do estado} + +\begin{itemize} + \item Cada palavra do dicionário (incluindo a palavra inicial) representa um nó em um grafo não direcionado. + \item Uma aresta conecta duas palavras se elas diferem em exatamente uma letra, uma "mutação" válida. + \item A transformação mais eficiente equivale a encontrar o caminho mais curto entre o nó inicial e o nó final neste grafo. +\end{itemize} + +\subsection*{Estratégia de solução usando BFS (Busca em Largura)} + +Como precisamos encontrar o menor número de passos em um grafo com arestas de peso uniforme e não direcionadas, a Busca em Largura (BFS) é a abordagem algorítmica ideal. + +\begin{enumerate} + \item Leia o número de palavras no dicionário ($N$) e o comprimento das palavras ($M$), seguidos das palavras inicial e final. + \item Armazene todas as palavras do dicionário em um conjunto (\textit{hash set}) para buscas eficientes. Insira também a palavra inicial neste conjunto, pois ela é o nosso ponto de partida. + \item Construa o grafo através de uma lista de adjacências: + \begin{itemize} + \item Para cada palavra no conjunto, itere sobre cada um de seus $M$ caracteres. + \item Substitua o caractere atual temporariamente por todas as 26 letras minúsculas do alfabeto ('a' a 'z'). + \item Se a nova palavra gerada após essa substituição também existir no dicionário, adicione-a à lista de adjacências da palavra original. + \end{itemize} + \item Inicialize a simulação da BFS: crie uma fila e insira a palavra inicial. Utilize um conjunto auxiliar para registrar os nós já visitados (\texttt{seen}), evitando ciclos infinitos. Defina a distância (profundidade) inicial da sequência como $1$. + \item Processe a fila operando por camadas (nível por nível): + \begin{itemize} + \item Descubra quantos elementos existem na fila atual. Este é o número de palavras no nível de profundidade atual. + \item Para cada uma dessas palavras, retire-a da fila e verifique: se for a palavra final desejada, a missão foi concluída! Imprima a profundidade atual e encerre. + \item Caso contrário, acesse a lista de adjacência da palavra. Para cada vizinho (mutação válida) que ainda não foi visitado, insira-o na fila e marque-o como visitado. + \end{itemize} + \item Ao terminar de processar todas as palavras da camada atual, incremente a profundidade. + \item Se a fila se esvaziar completamente e a palavra final nunca for atingida, a transformação é impossível sob essas regras. Retorne $0$. +\end{enumerate}\end{document} diff --git a/conversor-fonetico-generico/conversor-fonetico-generico.pdf b/conversor-fonetico-generico/conversor-fonetico-generico.pdf index e1babd5fa54a2f0d58ef0a288e406d1a63e13b18..0b8d1c8ee9c5c5ea8a665339621f26c66c8be9c4 100644 GIT binary patch delta 53781 zcma&ObySsW*F6k-v+3^c?(Poh?vj=eX_1mmmvl%Y-AD@3-Q6K6ji|Kr{_w~-&-R_V(PLuzdHUbeDJ-Z$DRSz1YIUd#Qt_7lyZY_GX~u}qlINNl2G zMRZ=hS*(~DY^Qp6|Eu}KM~9yuMW4&ZB4f(OV#vq+j6R=rZ0~Qz>;o_LN_J0x?@GO_ zFTt!RM7_DLmf$Vz%Y(Q}D0U`uj7P5h>oeCHGd#X(`y{H5okna3L6NG~Yl% zpZQ|)%iEmX`o{Ti;!+F6Krw!?i47=X;8waZYXmnBJy=v-(t7X*IhVSP@)Y>vft}OQ zYqQ)bh-wGtIROjSr^*Ys399&2`ulF_p%n@|jnwmB2w=zDrP*JCv&L3e-bwlGEoQ-I zN)!dbBO@9)^T|2i*M$-+C&$N7Jh+eEC%}8m_qY0b zCgk!0iTMKXKdlnokg)Uu=z3;MV@)J$tMBtD4uec*(hA@=breKo;w4@ai*TFQX*r zG4;;rq66_~*+5S$YPV8y)F_68LFoNuRM>1gEq0imi6V5NCclNjDF*k8@Oc1T;pHNo zQz8o(s7NJ~g(JbawAb8FJdWn!AR)MNAxf*(9HBgOF{?JYVN>YpGlSF>uIwG?>UnnD z^obBbjOLwc^e~FEJJTbWdF78~+Vpe&J$jHB1-HOaDo!#x1AHJl$ 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a/conversor-fonetico-generico/statement/tutorial.tex b/conversor-fonetico-generico/statement/tutorial.tex index e69de29..e1abe2e 100644 --- a/conversor-fonetico-generico/statement/tutorial.tex +++ b/conversor-fonetico-generico/statement/tutorial.tex @@ -0,0 +1,33 @@ +O problema de transformação de palavras exige encontrar o menor caminho entre uma palavra inicial e uma palavra final, alterando apenas uma letra por vez, com a restrição de que todas as palavras intermediárias devem pertencer a um dicionário fornecido. + +\subsection*{Representação do estado} + +\begin{itemize} + \item Cada palavra do dicionário (incluindo a palavra inicial) representa um nó em um grafo não direcionado. + \item Uma aresta conecta duas palavras se elas diferem em exatamente uma letra, uma "mutação" válida. + \item A transformação mais eficiente equivale a encontrar o caminho mais curto entre o nó inicial e o nó final neste grafo. +\end{itemize} + +\subsection*{Estratégia de solução usando BFS (Busca em Largura)} + +Como precisamos encontrar o menor número de passos em um grafo com arestas de peso uniforme e não direcionadas, a Busca em Largura (BFS) é a abordagem algorítmica ideal. + +\begin{enumerate} + \item Leia o número de palavras no dicionário ($N$) e o comprimento das palavras ($M$), seguidos das palavras inicial e final. + \item Armazene todas as palavras do dicionário em um conjunto (\textit{hash set}) para buscas eficientes. Insira também a palavra inicial neste conjunto, pois ela é o nosso ponto de partida. + \item Construa o grafo através de uma lista de adjacências: + \begin{itemize} + \item Para cada palavra no conjunto, itere sobre cada um de seus $M$ caracteres. + \item Substitua o caractere atual temporariamente por todas as 26 letras minúsculas do alfabeto ('a' a 'z'). + \item Se a nova palavra gerada após essa substituição também existir no dicionário, adicione-a à lista de adjacências da palavra original. + \end{itemize} + \item Inicialize a simulação da BFS: crie uma fila e insira a palavra inicial. Utilize um conjunto auxiliar para registrar os nós já visitados (\texttt{seen}), evitando ciclos infinitos. Defina a distância (profundidade) inicial da sequência como $1$. + \item Processe a fila operando por camadas (nível por nível): + \begin{itemize} + \item Descubra quantos elementos existem na fila atual. Este é o número de palavras no nível de profundidade atual. + \item Para cada uma dessas palavras, retire-a da fila e verifique: se for a palavra final desejada, a missão foi concluída! Imprima a profundidade atual e encerre. + \item Caso contrário, acesse a lista de adjacência da palavra. Para cada vizinho (mutação válida) que ainda não foi visitado, insira-o na fila e marque-o como visitado. + \end{itemize} + \item Ao terminar de processar todas as palavras da camada atual, incremente a profundidade. + \item Se a fila se esvaziar completamente e a palavra final nunca for atingida, a transformação é impossível sob essas regras. Retorne $0$. +\end{enumerate} \ No newline at end of file