From 013c654b61cc8d04dd378cb9adebba5dfaedd292 Mon Sep 17 00:00:00 2001
From: Igor Montagner <igordsm@gmail.com>
Date: Mon, 9 Sep 2024 19:48:29 -0300
Subject: [PATCH] Deployed 5760b52 with MkDocs version: 1.6.0

---
 0-linguagem-C/malloc/index.html             |  16 +-
 1-arvores-intro/balance/index.html          |  14 +-
 1-arvores-intro/insert/index.html           |  14 +-
 1-arvores-intro/intro/index.html            |  12 +-
 1-arvores-intro/remove/index.html           |   8 +-
 2-grafos-componentes/componentes/index.html |  10 +-
 2-grafos-componentes/intro/index.html       |  14 +-
 2-grafos-componentes/slides-intro.html      | 211 +++++++++-----------
 3-grafos-caminhos/bfs/index.html            |   4 +-
 3-grafos-caminhos/dijkstra/index.html       |   6 +-
 10 files changed, 143 insertions(+), 166 deletions(-)

diff --git a/0-linguagem-C/malloc/index.html b/0-linguagem-C/malloc/index.html
index 50e278a..f65f3b2 100644
--- a/0-linguagem-C/malloc/index.html
+++ b/0-linguagem-C/malloc/index.html
@@ -347,7 +347,7 @@ <h2 id="exercicios-basicos">Exercícios básicos</h2>
 <a id="__codelineno-0-28" name="__codelineno-0-28"></a><span class="p">}</span>
 </code></pre></div></td></tr></table></div>
 <p>Vamos começar analisando o código do programa <strong>antes de rodá-lo</strong>. </p>
-<div class="admonition exercise text short tag-text-exercise tag-short-text editable" data-slug="0-linguagem-C/malloc/short_1" id="short_1_0">
+<div class="admonition exercise text short tag-short-text tag-text-exercise editable" data-slug="0-linguagem-C/malloc/short_1" id="short_1_0">
 <p class="admonition-title">Exercise 1<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Analisando seu código-fonte, o que este programa faz?</p>
@@ -362,7 +362,7 @@ <h2 id="exercicios-basicos">Exercícios básicos</h2>
 <p>Aloca um vetor, preenche com $0,1,...,n$ e imprime!</p>
 </div>
 </div>
-<div class="admonition exercise text short tag-text-exercise tag-short-text editable" data-slug="0-linguagem-C/malloc/short_2" id="short_2_0">
+<div class="admonition exercise text short tag-short-text tag-text-exercise editable" data-slug="0-linguagem-C/malloc/short_2" id="short_2_0">
 <p class="admonition-title">Exercise 2<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Na execução deste programa, o que acontece se <code>malloc</code> falhar? </p>
@@ -378,7 +378,7 @@ <h2 id="exercicios-basicos">Exercícios básicos</h2>
 <p>A função de alocação irá retornar <code>NULL</code>, mas nenhuma verificação está sendo feita.</p>
 </div>
 </div>
-<div class="admonition exercise text short tag-text-exercise tag-short-text editable" data-slug="0-linguagem-C/malloc/short_3" id="short_3_0">
+<div class="admonition exercise text short tag-short-text tag-text-exercise editable" data-slug="0-linguagem-C/malloc/short_3" id="short_3_0">
 <p class="admonition-title">Exercise 3<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>O seu programa libera toda memória que aloca? Se não, aponte onde ele deveria fazer isto.</p>
@@ -403,7 +403,7 @@ <h2 id="exercicios-basicos">Exercícios básicos</h2>
 <p class="admonition-title">Tip 2</p>
 <p>O terminal do VSCode é muito bom e podemos usá-lo para rodar todos os comandos dessa atividade. </p>
 </div>
-<div class="admonition exercise text short tag-text-exercise tag-short-text editable" data-slug="0-linguagem-C/malloc/short_4" id="short_4_0">
+<div class="admonition exercise text short tag-short-text tag-text-exercise editable" data-slug="0-linguagem-C/malloc/short_4" id="short_4_0">
 <p class="admonition-title">Exercise 4<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Execute o programa. Ocorreu algum problema durante a execução?</p>
@@ -418,7 +418,7 @@ <h2 id="exercicios-basicos">Exercícios básicos</h2>
 <p>A resposta aqui é provavelmente não. Porém, isso não significa que o programa está correto, apenas que se ocorreu um erro ele não foi suficientemente grave para finalizar o programa.</p>
 </div>
 </div>
-<div class="admonition exercise text short tag-text-exercise tag-short-text editable" data-slug="0-linguagem-C/malloc/short_5" id="short_5_0">
+<div class="admonition exercise text short tag-short-text tag-text-exercise editable" data-slug="0-linguagem-C/malloc/short_5" id="short_5_0">
 <p class="admonition-title">Exercise 5<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>O comportamento de seu programa muda conforme N muda? Começe com <code>N=10</code> e vá incrementando de um em um. Você consegue explicar por que? Discuta com seu grupo e valide sua resposta com o professor.</p>
@@ -499,7 +499,7 @@ <h2 id="ferramentas-de-verificacao-de-memoria">Ferramentas de verificação de m
 <a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>    #3 0x7f1f461bd284 in __libc_start_main_impl ../csu/libc-start.c:360
 <a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a>    #4 0x5645bfb730e0 in _start (/home/coder/project/ex1+0x10e0)
 </code></pre></div>
-<div class="admonition exercise text short tag-text-exercise tag-short-text editable" data-slug="0-linguagem-C/malloc/short_8" id="short_8_0">
+<div class="admonition exercise text short tag-short-text tag-text-exercise editable" data-slug="0-linguagem-C/malloc/short_8" id="short_8_0">
 <p class="admonition-title">Exercise 9<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Em qual linha o erro ocorre? O que a mensagem acima significa?</p>
@@ -533,7 +533,7 @@ <h2 id="ferramentas-de-verificacao-de-memoria">Ferramentas de verificação de m
 <a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a>    #2 0x7f4a8df13284 in __libc_start_main_impl ../csu/libc-start.c:360
 <a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>    #3 0x559e63a320e0 in _start (/home/coder/project/ex1+0x10e0)
 </code></pre></div>
-<div class="admonition exercise text short tag-text-exercise tag-short-text editable" data-slug="0-linguagem-C/malloc/short_9" id="short_9_0">
+<div class="admonition exercise text short tag-short-text tag-text-exercise editable" data-slug="0-linguagem-C/malloc/short_9" id="short_9_0">
 <p class="admonition-title">Exercise 11<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Em qual linha o erro ocorre? O que a mensagem acima significa?</p>
@@ -568,7 +568,7 @@ <h2 id="ferramentas-de-verificacao-de-memoria">Ferramentas de verificação de m
 <a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
 <a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a>SUMMARY: AddressSanitizer: 56 byte(s) leaked in 1 allocation(s). 
 </code></pre></div>
-<div class="admonition exercise text short tag-text-exercise tag-short-text editable" data-slug="0-linguagem-C/malloc/short_10" id="short_10_0">
+<div class="admonition exercise text short tag-short-text tag-text-exercise editable" data-slug="0-linguagem-C/malloc/short_10" id="short_10_0">
 <p class="admonition-title">Exercise 13<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Ela mostra algum problema? Se sim, qual linha de código é apontada? Qual é o problema diagnosticado por este aviso?</p>
diff --git a/1-arvores-intro/balance/index.html b/1-arvores-intro/balance/index.html
index 343ce95..9fdfe51 100644
--- a/1-arvores-intro/balance/index.html
+++ b/1-arvores-intro/balance/index.html
@@ -487,7 +487,7 @@ <h1 id="balanceamento-de-arvores">Balanceamento de árvores</h1>
 n4 [shape=point]
 n5 [shape=point]
 }' /&gt;</p>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="1-arvores-intro/balance/short_1" id="short_1_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="1-arvores-intro/balance/short_1" id="short_1_0">
 <p class="admonition-title">Exercise 5<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Passe pelos nós da árvore em-ordem e coloque-os abaixo.</p>
@@ -555,7 +555,7 @@ <h1 id="balanceamento-de-arvores">Balanceamento de árvores</h1>
 </div>
 </div>
 <p>Vamos agora inserir todos valores menores que a raiz. Aqui temos um problema: com 4 valores no array, não tem um que esteja exatamente no meio. </p>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="1-arvores-intro/balance/short_2" id="short_2_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="1-arvores-intro/balance/short_2" id="short_2_0">
 <p class="admonition-title">Exercise 7<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Vamos tentar então pegando o elemento à esquerda do meio: 10. Aplique a ideia recursivamente e liste abaixo a ordem ideal de inserção.</p>
@@ -570,7 +570,7 @@ <h1 id="balanceamento-de-arvores">Balanceamento de árvores</h1>
 <p><code>10 1 20 30</code> </p>
 </div>
 </div>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="1-arvores-intro/balance/short_3" id="short_3_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="1-arvores-intro/balance/short_3" id="short_3_0">
 <p class="admonition-title">Exercise 8<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Vamos tentar então pegando o elemento à direita do meio: 20. Aplique a ideia recursivamente e liste abaixo a ordem ideal de inserção.</p>
@@ -585,7 +585,7 @@ <h1 id="balanceamento-de-arvores">Balanceamento de árvores</h1>
 <p><code>20 10 1 30</code></p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/balance/long_4" id="long_4_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/balance/long_4" id="long_4_0">
 <p class="admonition-title">Exercise 9<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Agora desenhe as duas árvores dox exercícios anteriores e responda: faz diferença qual das opções escolhemos, em termos de balanceamento da árvore?</p>
@@ -621,7 +621,7 @@ <h1 id="balanceamento-de-arvores">Balanceamento de árvores</h1>
 </div>
 </div>
 <p>O processo pode ser repetido para os elementos maiores que a raiz para obter a ordem de inserção completa. Escreva ela abaixo.</p>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="1-arvores-intro/balance/short_5" id="short_5_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="1-arvores-intro/balance/short_5" id="short_5_0">
 <p class="admonition-title">Exercise 10<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>A ordem de inserção completa para a árvore balanceada é:</p>
@@ -654,7 +654,7 @@ <h1 id="balanceamento-de-arvores">Balanceamento de árvores</h1>
 </div>
 <hr />
 <p>Finalmente, escreva o algoritmo completo abaixo.</p>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/balance/long_6" id="long_6_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/balance/long_6" id="long_6_0">
 <p class="admonition-title">Exercise 11<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Escreva em pseudo-código um algoritmo <code>TREE-TO-ARRAY(R)</code> querecebe uma árvore <code>R</code> e devolve um array ordenado com os valores em <code>R</code></p>
@@ -669,7 +669,7 @@ <h1 id="balanceamento-de-arvores">Balanceamento de árvores</h1>
 <p>Lousa</p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/balance/long_7" id="long_7_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/balance/long_7" id="long_7_0">
 <p class="admonition-title">Exercise 12<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Escreva em pseudo-código um algoritmo <code>REBALANCEIA(R)</code> que recebe uma árovore enraizada em <code>R</code> e devolve uma nova árvore balanceada que tenha os mesmos valores que <code>R</code></p>
diff --git a/1-arvores-intro/insert/index.html b/1-arvores-intro/insert/index.html
index 2cc9430..fc3b4e1 100644
--- a/1-arvores-intro/insert/index.html
+++ b/1-arvores-intro/insert/index.html
@@ -368,7 +368,7 @@ <h1 id="insercao">Inserção</h1>
 <p><strong>Árvores com altura $h &gt; 2$</strong>: Usar o argumento acima nos permite inserir em árvores de qualquer tamanho! Ou a inserção ocorreria em um espaço vazio (ou seja, um dos lados tem uma subárvore de altura 0) ou inserimos na subárvore correspondente (que tem altura $h-1$).</p>
 <h2 id="exercitando-e-formalizando-esse-algoritmo">Exercitando e formalizando esse algoritmo</h2>
 <p>Vejamos alguns exemplos abaixo. </p>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="1-arvores-intro/insert/short_1" id="short_1_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="1-arvores-intro/insert/short_1" id="short_1_0">
 <p class="admonition-title">Exercise 1<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Em qual lugar o valor $27$ seria inserido na árvore abaixo?</p>
@@ -393,7 +393,7 @@ <h2 id="exercitando-e-formalizando-esse-algoritmo">Exercitando e formalizando es
 <p>Na subárvore esquerda de $30$</p>
 </div>
 </div>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="1-arvores-intro/insert/short_2" id="short_2_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="1-arvores-intro/insert/short_2" id="short_2_0">
 <p class="admonition-title">Exercise 2<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Em qual lugar o valor $15$ seria inserido na árvore abaixo?</p>
@@ -420,7 +420,7 @@ <h2 id="exercitando-e-formalizando-esse-algoritmo">Exercitando e formalizando es
 <p>Na subárvore direita de $13$</p>
 </div>
 </div>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="1-arvores-intro/insert/short_3" id="short_3_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="1-arvores-intro/insert/short_3" id="short_3_0">
 <p class="admonition-title">Exercise 3<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Em qual lugar o valor $7$ seria inserido na árvore abaixo?</p>
@@ -449,7 +449,7 @@ <h2 id="exercitando-e-formalizando-esse-algoritmo">Exercitando e formalizando es
 <p>Na subárvore direita de $5$</p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/insert/long_4" id="long_4_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/insert/long_4" id="long_4_0">
 <p class="admonition-title">Exercise 4<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Agora formalize o algoritmo <code>insere(r, K)</code> que aplicamos nos exemplos acima. Escreva um algoritmo iterativo nesta questão.</p>
@@ -464,7 +464,7 @@ <h2 id="exercitando-e-formalizando-esse-algoritmo">Exercitando e formalizando es
 <p>Discutido no fim da aula</p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/insert/long_5" id="long_5_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/insert/long_5" id="long_5_0">
 <p class="admonition-title">Exercise 5<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Agora formalize o algoritmo <code>insere(r, K)</code> que aplicamos nos exemplos acima. Escreva um algoritmo recursivo nesta questão.</p>
@@ -495,7 +495,7 @@ <h2 id="exercitando-e-formalizando-esse-algoritmo">Exercitando e formalizando es
 </div>
 </form>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/insert/long_6" id="long_6_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/insert/long_6" id="long_6_0">
 <p class="admonition-title">Exercise 7<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Qual ordem de inserção nos permitiria reconstruir a árvore abaixo?</p>
@@ -524,7 +524,7 @@ <h2 id="exercitando-e-formalizando-esse-algoritmo">Exercitando e formalizando es
 <p>Discutido em sala.</p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/insert/long_7" id="long_7_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/insert/long_7" id="long_7_0">
 <p class="admonition-title">Exercise 8<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Para a árvore acima, tente encontrar uma ordem de inserção que diminui a altura da árvore. </p>
diff --git a/1-arvores-intro/intro/index.html b/1-arvores-intro/intro/index.html
index 598b9dd..c5e137d 100644
--- a/1-arvores-intro/intro/index.html
+++ b/1-arvores-intro/intro/index.html
@@ -328,7 +328,7 @@ <h2 id="buscando-por-elementos">Buscando por elementos</h2>
   null3 [shape=point]
 }
 '&gt;</graphviz-graph></p>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/intro/long_1" id="long_1_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/intro/long_1" id="long_1_0">
 <p class="admonition-title">Exercise 1<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Busque na árvore acima pelo valor $7$. Escreva abaixo a decisão tomada em cada nó.</p>
@@ -346,7 +346,7 @@ <h2 id="buscando-por-elementos">Buscando por elementos</h2>
 Nó 7 -&gt; encontrou!</p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/intro/long_2" id="long_2_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/intro/long_2" id="long_2_0">
 <p class="admonition-title">Exercise 2<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Busque na árvore acima pelo valor $3$. Escreva abaixo a decisão tomada em cada nó.</p>
@@ -364,7 +364,7 @@ <h2 id="buscando-por-elementos">Buscando por elementos</h2>
 Fim da árvore! -&gt; não encontrou</p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/intro/long_3" id="long_3_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/intro/long_3" id="long_3_0">
 <p class="admonition-title">Exercise 3<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Busque na árvore acima pelo valor $23$. Escreva abaixo a decisão tomada em cada nó.</p>
@@ -382,7 +382,7 @@ <h2 id="buscando-por-elementos">Buscando por elementos</h2>
 Fim da árvore! -&gt; não encontrou</p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/intro/long_4" id="long_4_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/intro/long_4" id="long_4_0">
 <p class="admonition-title">Exercise 4<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Escreva abaixo um algoritmo iterativo <code>query(r, k)</code> que busca pela chave $k$ na ABB enraizada em $r$. Se encontrar devolve <code>VERDADEIRO</code>.</p>
@@ -398,7 +398,7 @@ <h2 id="buscando-por-elementos">Buscando por elementos</h2>
 </div>
 </div>
 <p>Antes de prosseguir, volte nos exercícios acima e simule o seu algoritmo. </p>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/intro/long_5" id="long_5_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/intro/long_5" id="long_5_0">
 <p class="admonition-title">Exercise 5<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Faça agora uma versão recursiva. Veja que ela é muito mais sucinta que a anterior.</p>
@@ -592,7 +592,7 @@ <h2 id="validar-uma-abb">Validar uma <em>ABB</em></h2>
 <li>para checar a propriedade precisamos percorrer toda a subárvore esquerda e toda a subárvore direita.</li>
 </ol>
 <p>Esses dois passos tem algo em comum: eles envolvem visitar todos os nós da árvore. </p>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/intro/long_6" id="long_6_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/intro/long_6" id="long_6_0">
 <p class="admonition-title">Exercise 9<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Escreva abaixo um rascunho de um algoritmo para visitar todos os nós de uma árvore.</p>
diff --git a/1-arvores-intro/remove/index.html b/1-arvores-intro/remove/index.html
index 58d8a56..cea0025 100644
--- a/1-arvores-intro/remove/index.html
+++ b/1-arvores-intro/remove/index.html
@@ -440,7 +440,7 @@ <h2 id="o-caso-complicado-no-tem-dois-filhos">O caso complicado: nó tem dois fi
 </div>
 </div>
 <p>Note que nos 3 casos o nó <code>10</code> <em>desceu de nível na árvore.</em> Ele inicia na raiz (nível 0) e desce para o nível 1 (nos casos 1 e 2) e nível 2 (no caso 3). </p>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="1-arvores-intro/remove/short_1" id="short_1_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="1-arvores-intro/remove/short_1" id="short_1_0">
 <p class="admonition-title">Exercise 2<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Em uma árvore com altura $h = 10$, qual é o número máximo de rotações necessárias para fazer um nó qualquer da árvore se tornar uma folha?</p>
@@ -462,7 +462,7 @@ <h2 id="o-caso-complicado-no-tem-dois-filhos">O caso complicado: nó tem dois fi
 <li>Na <strong>rotação à esquerda</strong> desceremos de nível a raiz $A$. Chamamos o elemento $B$ à direita de $A$ de <strong>pivô</strong>, já que ele será a nova raiz. A subárvore $\beta$ muda da direita de $B$ para a esquerda de $A$.</li>
 <li>Na <strong>rotação à direita</strong> desceremos de nível a raiz $B$. Chamamos o elemento $A$ à esquerda de $B$ de <strong>pivô</strong>, já que ele será a nova raiz. A subárvore $\beta$ muda da esquerda de $A$ para a direita de $B$.</li>
 </ul>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/remove/long_2" id="long_2_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/remove/long_2" id="long_2_0">
 <p class="admonition-title">Exercise 3<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Escreva um algoritmo <code>ROTACAO-DIREITA(R)</code> que recebe um nó de uma <em>ABB</em> e devolve a nova raiz dessa subárvore depois de fazer uma rotação à direita. Simule seu algoritmo com o grafo abaixo e tentando rotacionar os elementos a seguir.</p>
@@ -675,7 +675,7 @@ <h2 id="algoritmo-para-remocao">Algoritmo para remoção</h2>
 </details>
 <h2 id="o-algoritmo-remove">O algoritmo <code>REMOVE</code></h2>
 <p>Agora que já simulou o algoritmo algumas vezes está na hora de formalizá-lo. </p>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/remove/long_3" id="long_3_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/remove/long_3" id="long_3_0">
 <p class="admonition-title">Exercise 7<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Escreva um algoritmo <code>REMOVE(R, K)</code> que remove o nó <code>K</code> da árvore <code>R</code>, devolvendo uma nova raiz da árvore se necessário. Você pode supor que as seguintes funções existem:</p>
@@ -704,7 +704,7 @@ <h2 id="o-algoritmo-remove">O algoritmo <code>REMOVE</code></h2>
 </code></pre></div>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="1-arvores-intro/remove/long_4" id="long_4_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="1-arvores-intro/remove/long_4" id="long_4_0">
 <p class="admonition-title">Exercise 8<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Escreva um algoritmo recursivo <code>REMOVE-RAIZ(R)</code> que remove a raiz <code>R</code> da árvore e devolve a nova raiz. Use rotações para a direita como foi feito no exercício anterior.</p>
diff --git a/2-grafos-componentes/componentes/index.html b/2-grafos-componentes/componentes/index.html
index ae0035f..ae7931c 100644
--- a/2-grafos-componentes/componentes/index.html
+++ b/2-grafos-componentes/componentes/index.html
@@ -445,7 +445,7 @@ <h1 id="componentes-conexos-em-grafos">Componentes Conexos em Grafos</h1>
 </form>
 </div>
 <p>Vamos exercitar nossa compreensão dessa definição com algumas questões teóricas.</p>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="2-grafos-componentes/componentes/long_1" id="long_1_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="2-grafos-componentes/componentes/long_1" id="long_1_0">
 <p class="admonition-title">Exercise 4<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Dado um grafo $G = (V, A), |V| &gt; 0$, quais são os números mínimo e máximode componentes conexos?</p>
@@ -456,7 +456,7 @@ <h1 id="componentes-conexos-em-grafos">Componentes Conexos em Grafos</h1>
 </div>
 </form>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="2-grafos-componentes/componentes/long_2" id="long_2_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="2-grafos-componentes/componentes/long_2" id="long_2_0">
 <p class="admonition-title">Exercise 5<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>O item 1 da definição só diz que o início e o fim do caminho tem que estar em $C$. É possível existir um caminho entre dois vértices em $C$ que contenha ao menos um vértice que não está em $C$?</p>
@@ -470,7 +470,7 @@ <h1 id="componentes-conexos-em-grafos">Componentes Conexos em Grafos</h1>
 <hr />
 <h2 id="um-algoritmo-simples-para-componentes-conexas">Um algoritmo simples para componentes conexas</h2>
 <p>Em IA e TecProg já vimos um algoritmo que lembra muito a definição de Componente Conexo: Busca em Profundidade (DFS)! Como sempre, vamos começar simulando essa ideia para entender como o algoritmo pode ajudar.</p>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="2-grafos-componentes/componentes/long_3" id="long_3_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="2-grafos-componentes/componentes/long_3" id="long_3_0">
 <p class="admonition-title">Exercise 6<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Dado o grafo abaixo, comece uma DFS a partir do vértice <code>D</code> e numere os vértices de acordo com quando eles forem visitados. </p>
@@ -510,7 +510,7 @@ <h2 id="um-algoritmo-simples-para-componentes-conexas">Um algoritmo simples para
 </ah-diagram></p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="2-grafos-componentes/componentes/long_4" id="long_4_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="2-grafos-componentes/componentes/long_4" id="long_4_0">
 <p class="admonition-title">Exercise 7<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Dado o grafo abaixo, comece uma DFS a partir do vértice <code>D</code> e numere os vértices de acordo com quando eles forem visitados. </p>
@@ -579,7 +579,7 @@ <h2 id="um-algoritmo-simples-para-componentes-conexas">Um algoritmo simples para
 <li>todos algoritmos da ADT <a href="https://insper.github.io/tecnicas-de-programacao/modulos/01-ADT/array/">Array</a> que já usamos em TecProg. </li>
 </ol>
 <p>Com isso já temos o necessário para criar nosso algoritmo. Vamos tentar?</p>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="2-grafos-componentes/componentes/long_5" id="long_5_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="2-grafos-componentes/componentes/long_5" id="long_5_0">
 <p class="admonition-title">Exercise 8<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Escreva o algoritmo <code>IDENTIFICA-COMPONENTES(G)</code> abaixo. Você pode criar uma subrotina separada para a parte recursiva se achar conveniente. </p>
diff --git a/2-grafos-componentes/intro/index.html b/2-grafos-componentes/intro/index.html
index d8dc4ff..2dc3201 100644
--- a/2-grafos-componentes/intro/index.html
+++ b/2-grafos-componentes/intro/index.html
@@ -527,7 +527,7 @@ <h2 id="problema-1-redes-sociais">Problema 1 - redes sociais</h2>
 <li>toda vez que um usuário curte um post</li>
 </ul>
 <p>Vamos usar grafos para resolver este problema.</p>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="2-grafos-componentes/intro/short_1" id="short_1_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="2-grafos-componentes/intro/short_1" id="short_1_0">
 <p class="admonition-title">Exercise 5<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Em nosso grafo, o que seriam os vértices?</p>
@@ -538,7 +538,7 @@ <h2 id="problema-1-redes-sociais">Problema 1 - redes sociais</h2>
 </div>
 </form>
 </div>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="2-grafos-componentes/intro/short_2" id="short_2_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="2-grafos-componentes/intro/short_2" id="short_2_0">
 <p class="admonition-title">Exercise 6<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Em nosso grafo, qual relação arestas entre dois vértices representa?</p>
@@ -549,7 +549,7 @@ <h2 id="problema-1-redes-sociais">Problema 1 - redes sociais</h2>
 </div>
 </form>
 </div>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="2-grafos-componentes/intro/short_3" id="short_3_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="2-grafos-componentes/intro/short_3" id="short_3_0">
 <p class="admonition-title">Exercise 7<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>O grafo é direcionado? As arestas tem peso?</p>
@@ -597,7 +597,7 @@ <h2 id="representacao-computacional">Representação computacional</h2>
 <a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>Usuário 9 gostou do post #6
 <a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>Usuário 8 gostou do post #6
 </code></pre></div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="2-grafos-componentes/intro/long_4" id="long_4_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="2-grafos-componentes/intro/long_4" id="long_4_0">
 <p class="admonition-title">Exercise 8<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Com base nas perguntas da seção anterior, escreva abaixo a matriz de adjacências que representa a situação acima</p>
@@ -623,7 +623,7 @@ <h2 id="representacao-computacional">Representação computacional</h2>
 </div>
 </div>
 <p>Conseguimos tirar diversas informações interessantes diretamente da matriz de adjacências. Responda às questões abaixo:</p>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="2-grafos-componentes/intro/short_5" id="short_5_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="2-grafos-componentes/intro/short_5" id="short_5_0">
 <p class="admonition-title">Exercise 9<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Como saber quais usuários postaram algo que foi curtido?</p>
@@ -638,7 +638,7 @@ <h2 id="representacao-computacional">Representação computacional</h2>
 <p>É só procurar na sua coluna correspondente. Como arestas saem da linha <code>i</code> e chegam na coluna <code>j</code>, se tiver algum elemento na coluna <code>j</code> diferente de 0 então aquele usuário postou algo que foi curtido. </p>
 </div>
 </div>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="2-grafos-componentes/intro/short_6" id="short_6_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="2-grafos-componentes/intro/short_6" id="short_6_0">
 <p class="admonition-title">Exercise 10<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Como encontrar o usuário com maior número de posts curtidos?</p>
@@ -653,7 +653,7 @@ <h2 id="representacao-computacional">Representação computacional</h2>
 <p>Será o usuário com a coluna de maior soma = vértice de maior grau de entrada</p>
 </div>
 </div>
-<div class="admonition exercise short tag-text-exercise tag-short-text editable" data-slug="2-grafos-componentes/intro/short_7" id="short_7_0">
+<div class="admonition exercise short tag-short-text tag-text-exercise editable" data-slug="2-grafos-componentes/intro/short_7" id="short_7_0">
 <p class="admonition-title">Exercise 11<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Como encontrar o usuário que mais curtiu posts?</p>
diff --git a/2-grafos-componentes/slides-intro.html b/2-grafos-componentes/slides-intro.html
index b7df7ee..44a1d5e 100644
--- a/2-grafos-componentes/slides-intro.html
+++ b/2-grafos-componentes/slides-intro.html
@@ -1,4 +1,4 @@
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 /*!
  * Marp default theme.
  *
@@ -9,124 +9,101 @@
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  * @size 4:3 960px 720px
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:where(.hljs-emphasis){color:var(--color-prettylights-syntax-markup-italic);font-style:italic}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-strong){color:var(--color-prettylights-syntax-markup-bold);font-weight:700}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-addition){background-color:var(--color-prettylights-syntax-markup-inserted-bg);color:var(--color-prettylights-syntax-markup-inserted-text)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-deletion){background-color:var(--color-prettylights-syntax-markup-deleted-bg);color:var(--color-prettylights-syntax-markup-deleted-text)}div#\:\$p>svg>foreignObject>section footer,div#\:\$p>svg>foreignObject>section header{color:var(--header-footer-color);font-size:18px;left:30px;margin:0;position:absolute}div#\:\$p>svg>foreignObject>section header{top:21px}div#\:\$p>svg>foreignObject>section footer{bottom:21px}div#\:\$p>svg>foreignObject>section{--h1-color:#246;--header-footer-color:hsla(0,0%,40%,.75);--heading-strong-color:#48c;--paginate-color:#777;align-items:stretch;display:flex;flex-flow:column nowrap;font-size:29px;height:720px;justify-content:center;padding:78.5px;width:1280px}div#\:\$p>svg>foreignObject>section{--marpit-root-font-size:29px}div#\:\$p>svg>foreignObject>section:where(.invert){--h1-color:#cee7ff;--header-footer-color:hsla(0,0%,60%,.75);--heading-strong-color:#7bf;--paginate-color:#999}div#\:\$p>svg>foreignObject>section>:last-child,div#\:\$p>svg>foreignObject>section[data-footer]>:nth-last-child(2){margin-bottom:0}div#\:\$p>svg>foreignObject>section>:first-child,div#\:\$p>svg>foreignObject>section>header:first-child+*{margin-top:0}div#\:\$p>svg>foreignObject>section:after{bottom:21px;color:var(--paginate-color);font-size:24px;padding:0;position:absolute;right:30px}div#\:\$p>svg>foreignObject>section:after{--marpit-root-font-size:24px}div#\:\$p>svg>foreignObject>section[data-color] :is(h1,marp-h1),div#\:\$p>svg>foreignObject>section[data-color] :is(h2,marp-h2),div#\:\$p>svg>foreignObject>section[data-color] :is(h3,marp-h3),div#\:\$p>svg>foreignObject>section[data-color] :is(h4,marp-h4),div#\:\$p>svg>foreignObject>section[data-color] :is(h5,marp-h5),div#\:\$p>svg>foreignObject>section[data-color] :is(h6,marp-h6){color:currentcolor}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]{columns:initial!important;display:block!important;padding:0!important}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]:after,div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]:before,div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=content]:after,div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=content]:before{display:none!important}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]>div[data-marpit-advanced-background-container]{all:initial;display:flex;flex-direction:row;height:100%;overflow:hidden;width:100%}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]>div[data-marpit-advanced-background-container][data-marpit-advanced-background-direction=vertical]{flex-direction:column}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background][data-marpit-advanced-background-split]>div[data-marpit-advanced-background-container]{width:var(--marpit-advanced-background-split,50%)}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background][data-marpit-advanced-background-split=right]>div[data-marpit-advanced-background-container]{margin-left:calc(100% - var(--marpit-advanced-background-split, 50%))}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]>div[data-marpit-advanced-background-container]>figure{all:initial;background-position:center;background-repeat:no-repeat;background-size:cover;flex:auto;margin:0}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]>div[data-marpit-advanced-background-container]>figure>figcaption{position:absolute;border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;white-space:nowrap;width:1px}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=content],div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=pseudo]{background:transparent!important}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=pseudo],div#\:\$p>svg[data-marpit-svg]>foreignObject[data-marpit-advanced-background=pseudo]{pointer-events:none!important}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background-split]{width:100%;height:100%}</style></head><body><div class="bespoke-marp-osc"><button data-bespoke-marp-osc="prev" tabindex="-1" title="Previous slide">Previous slide</button><span data-bespoke-marp-osc="page"></span><button data-bespoke-marp-osc="next" tabindex="-1" title="Next slide">Next slide</button><button data-bespoke-marp-osc="fullscreen" tabindex="-1" title="Toggle fullscreen (f)">Toggle fullscreen</button><button data-bespoke-marp-osc="presenter" tabindex="-1" title="Open presenter view (p)">Open presenter view</button></div><div id=":$p"><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="1" data-marpit-fragments="8" lang="en-US">
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.bespoke-marp-presenter-note-container button:hover:not(:disabled){transition:none}body[data-bespoke-view=""] .bespoke-marp-parent&gt;.bespoke-marp-osc&gt;button[data-bespoke-marp-osc=prev],body[data-bespoke-view=next] .bespoke-marp-parent&gt;.bespoke-marp-osc&gt;button[data-bespoke-marp-osc=prev],body[data-bespoke-view=presenter] .bespoke-marp-presenter-container .bespoke-marp-presenter-info-container button.bespoke-marp-presenter-info-page-prev{background:#0000 url("data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9IjAgMCAxMDAgMTAwIj48cGF0aCBmaWxsPSJub25lIiBzdHJva2U9IiNmZmYiIHN0cm9rZS1saW5lY2FwPSJyb3VuZCIgc3Ryb2tlLWxpbmVqb2luPSJyb3VuZCIgc3Ryb2tlLXdpZHRoPSI1IiBkPSJNNjggOTAgMjggNTBsNDAtNDAiLz48L3N2Zz4=") no-repeat 50%;background-size:contain;overflow:hidden;text-indent:100%;white-space:nowrap}body[data-bespoke-view=""] .bespoke-marp-parent&gt;.bespoke-marp-osc&gt;button[data-bespoke-marp-osc=next],body[data-bespoke-view=next] 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url("data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9IjAgMCAxMDAgMTAwIj48ZGVmcz48c3R5bGU+LmF7ZmlsbDpub25lO3N0cm9rZTojZmZmO3N0cm9rZS1saW5lY2FwOnJvdW5kO3N0cm9rZS1saW5lam9pbjpyb3VuZDtzdHJva2Utd2lkdGg6NXB4fTwvc3R5bGU+PC9kZWZzPjxyZWN0IGNsYXNzPSJhIiB4PSIxMCIgeT0iMjAiIHdpZHRoPSI4MCIgaGVpZ2h0PSI2MCIgcng9IjUuNjciLz48cGF0aCBjbGFzcz0iYSIgZD0iTTQwIDcwSDIwVjUwbTIwIDBMMjAgNzBtNDAtNDBoMjB2MjBtLTIwIDAgMjAtMjAiLz48L3N2Zz4=") no-repeat 50%;background-size:contain;overflow:hidden;text-indent:100%;white-space:nowrap}body[data-bespoke-view=""] .bespoke-marp-parent&gt;.bespoke-marp-osc&gt;button.exit[data-bespoke-marp-osc=fullscreen],body[data-bespoke-view=next] 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-<p>/*!</p>
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:is(pre,marp-pre) :where(.hljs-type),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-variable.language_){color:var(--color-prettylights-syntax-keyword)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-title),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-title.class_),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-title.class_.inherited__),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-title.function_){color:var(--color-prettylights-syntax-entity)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-attr),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-attribute),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-literal),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-meta),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-number),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-operator),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-selector-attr),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-selector-class),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-selector-id),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-variable){color:var(--color-prettylights-syntax-constant)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-meta .hljs-string),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-regexp),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-string){color:var(--color-prettylights-syntax-string)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-built_in),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-symbol){color:var(--color-prettylights-syntax-variable)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-code),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-comment),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-formula){color:var(--color-prettylights-syntax-comment)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-name),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-quote),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-selector-pseudo),div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-selector-tag){color:var(--color-prettylights-syntax-entity-tag)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-subst){color:var(--color-prettylights-syntax-storage-modifier-import)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-section){color:var(--color-prettylights-syntax-markup-heading);font-weight:700}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-bullet){color:var(--color-prettylights-syntax-markup-list)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-emphasis){color:var(--color-prettylights-syntax-markup-italic);font-style:italic}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-strong){color:var(--color-prettylights-syntax-markup-bold);font-weight:700}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-addition){background-color:var(--color-prettylights-syntax-markup-inserted-bg);color:var(--color-prettylights-syntax-markup-inserted-text)}div#\:\$p>svg>foreignObject>section :is(pre,marp-pre) :where(.hljs-deletion){background-color:var(--color-prettylights-syntax-markup-deleted-bg);color:var(--color-prettylights-syntax-markup-deleted-text)}div#\:\$p>svg>foreignObject>section footer,div#\:\$p>svg>foreignObject>section header{color:var(--header-footer-color);font-size:18px;left:30px;margin:0;position:absolute}div#\:\$p>svg>foreignObject>section header{top:21px}div#\:\$p>svg>foreignObject>section footer{bottom:21px}div#\:\$p>svg>foreignObject>section{--h1-color:#246;--header-footer-color:hsla(0,0%,40%,.75);--heading-strong-color:#48c;--paginate-color:#777;align-items:stretch;display:flex;flex-flow:column nowrap;font-size:29px;height:720px;justify-content:center;padding:78.5px;width:1280px}div#\:\$p>svg>foreignObject>section{--marpit-root-font-size:29px}div#\:\$p>svg>foreignObject>section:where(.invert){--h1-color:#cee7ff;--header-footer-color:hsla(0,0%,60%,.75);--heading-strong-color:#7bf;--paginate-color:#999}div#\:\$p>svg>foreignObject>section>:last-child,div#\:\$p>svg>foreignObject>section[data-footer]>:nth-last-child(2){margin-bottom:0}div#\:\$p>svg>foreignObject>section>:first-child,div#\:\$p>svg>foreignObject>section>header:first-child+*{margin-top:0}div#\:\$p>svg>foreignObject>section:after{bottom:21px;color:var(--paginate-color);font-size:24px;padding:0;position:absolute;right:30px}div#\:\$p>svg>foreignObject>section:after{--marpit-root-font-size:24px}div#\:\$p>svg>foreignObject>section[data-color] :is(h1,marp-h1),div#\:\$p>svg>foreignObject>section[data-color] :is(h2,marp-h2),div#\:\$p>svg>foreignObject>section[data-color] :is(h3,marp-h3),div#\:\$p>svg>foreignObject>section[data-color] :is(h4,marp-h4),div#\:\$p>svg>foreignObject>section[data-color] :is(h5,marp-h5),div#\:\$p>svg>foreignObject>section[data-color] :is(h6,marp-h6){color:currentcolor}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]{columns:initial!important;display:block!important;padding:0!important}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]:after,div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]:before,div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=content]:after,div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=content]:before{display:none!important}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]>div[data-marpit-advanced-background-container]{all:initial;display:flex;flex-direction:row;height:100%;overflow:hidden;width:100%}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]>div[data-marpit-advanced-background-container][data-marpit-advanced-background-direction=vertical]{flex-direction:column}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background][data-marpit-advanced-background-split]>div[data-marpit-advanced-background-container]{width:var(--marpit-advanced-background-split,50%)}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background][data-marpit-advanced-background-split=right]>div[data-marpit-advanced-background-container]{margin-left:calc(100% - var(--marpit-advanced-background-split, 50%))}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]>div[data-marpit-advanced-background-container]>figure{all:initial;background-position:center;background-repeat:no-repeat;background-size:cover;flex:auto;margin:0}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=background]>div[data-marpit-advanced-background-container]>figure>figcaption{position:absolute;border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;white-space:nowrap;width:1px}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=content],div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=pseudo]{background:transparent!important}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background=pseudo],div#\:\$p>svg[data-marpit-svg]>foreignObject[data-marpit-advanced-background=pseudo]{pointer-events:none!important}div#\:\$p>svg>foreignObject>section[data-marpit-advanced-background-split]{width:100%;height:100%}</style></head><body><div class="bespoke-marp-osc"><button data-bespoke-marp-osc="prev" tabindex="-1" title="Previous slide">Previous slide</button><span data-bespoke-marp-osc="page"></span><button data-bespoke-marp-osc="next" tabindex="-1" title="Next slide">Next slide</button><button data-bespoke-marp-osc="fullscreen" tabindex="-1" title="Toggle fullscreen (f)">Toggle fullscreen</button><button data-bespoke-marp-osc="presenter" tabindex="-1" title="Open presenter view (p)">Open presenter view</button></div><div id=":$p"><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="1" lang="en-US">
+<h1 id="grafos-e-%C3%A1rvores">Grafos e Árvores</h1>
+<h2 id="introdu%C3%A7%C3%A3o-a-grafos">Introdução a grafos</h2>
+</section>
+</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="2" lang="en-US">
+<p><img src="mapa.png" alt="" /></p>
+</section>
+</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="3" lang="en-US">
+<h1 id="enchentes-em-heli%C3%B3polis">Enchentes em Heliópolis</h1>
 <ul>
-<li data-marpit-fragment="1">Marp default theme.</li>
-<li data-marpit-fragment="2"></li>
-<li data-marpit-fragment="3">@theme default</li>
-<li data-marpit-fragment="4">@author Yuki Hattori</li>
-<li data-marpit-fragment="5"></li>
-<li data-marpit-fragment="6">@auto-scaling true</li>
-<li data-marpit-fragment="7">@size 16:9 1280px 720px</li>
-<li data-marpit-fragment="8">@size 4:3 960px 720px<br />
-<em>/div#p&gt;svg&gt;foreignObject&gt;section{--color-prettylights-syntax-comment:#6e7781;--color-prettylights-syntax-constant:#0550ae;--color-prettylights-syntax-entity:#8250df;--color-prettylights-syntax-storage-modifier-import:#24292f;--color-prettylights-syntax-entity-tag:#116329;--color-prettylights-syntax-keyword:#cf222e;--color-prettylights-syntax-string:#0a3069;--color-prettylights-syntax-variable:#953800;--color-prettylights-syntax-brackethighlighter-unmatched:#82071e;--color-prettylights-syntax-invalid-illegal-text:#f6f8fa;--color-prettylights-syntax-invalid-illegal-bg:#82071e;--color-prettylights-syntax-carriage-return-text:#f6f8fa;--color-prettylights-syntax-carriage-return-bg:#cf222e;--color-prettylights-syntax-string-regexp:#116329;--color-prettylights-syntax-markup-list:#3b2300;--color-prettylights-syntax-markup-heading:#0550ae;--color-prettylights-syntax-markup-italic:#24292f;--color-prettylights-syntax-markup-bold:#24292f;--color-prettylights-syntax-markup-deleted-text:#82071e;--color-prettylights-syntax-markup-deleted-bg:#ffebe9;--color-prettylights-syntax-markup-inserted-text:#116329;--color-prettylights-syntax-markup-inserted-bg:#dafbe1;--color-prettylights-syntax-markup-changed-text:#953800;--color-prettylights-syntax-markup-changed-bg:#ffd8b5;--color-prettylights-syntax-markup-ignored-text:#eaeef2;--color-prettylights-syntax-markup-ignored-bg:#0550ae;--color-prettylights-syntax-meta-diff-range:#8250df;--color-prettylights-syntax-brackethighlighter-angle:#57606a;--color-prettylights-syntax-sublimelinter-gutter-mark:#8c959f;--color-prettylights-syntax-constant-other-reference-link:#0a3069;--color-fg-default:#24292f;--color-fg-muted:#57606a;--color-fg-subtle:#6e7781;--color-canvas-default:#fff;--color-canvas-subtle:#f6f8fa;--color-border-default:#d0d7de;--color-border-muted:#d8dee4;--color-neutral-muted:rgba(175,184,193,.2);--color-accent-fg:#0969da;--color-accent-emphasis:#0969da;--color-attention-subtle:#fff8c5;--color-danger-fg:#cf222e;color-scheme:light}div#p&gt;svg&gt;foreignObject&gt;section:where(.invert){--color-prettylights-syntax-comment:#8b949e;--color-prettylights-syntax-constant:#79c0ff;--color-prettylights-syntax-entity:#d2a8ff;--color-prettylights-syntax-storage-modifier-import:#c9d1d9;--color-prettylights-syntax-entity-tag:#7ee787;--color-prettylights-syntax-keyword:#ff7b72;--color-prettylights-syntax-string:#a5d6ff;--color-prettylights-syntax-variable:#ffa657;--color-prettylights-syntax-brackethighlighter-unmatched:#f85149;--color-prettylights-syntax-invalid-illegal-text:#f0f6fc;--color-prettylights-syntax-invalid-illegal-bg:#8e1519;--color-prettylights-syntax-carriage-return-text:#f0f6fc;--color-prettylights-syntax-carriage-return-bg:#b62324;--color-prettylights-syntax-string-regexp:#7ee787;--color-prettylights-syntax-markup-list:#f2cc60;--color-prettylights-syntax-markup-heading:#1f6feb;--color-prettylights-syntax-markup-italic:#c9d1d9;--color-prettylights-syntax-markup-bold:#c9d1d9;--color-prettylights-syntax-markup-deleted-text:#ffdcd7;--color-prettylights-syntax-markup-deleted-bg:#67060c;--color-prettylights-syntax-markup-inserted-text:#aff5b4;--color-prettylights-syntax-markup-inserted-bg:#033a16;--color-prettylights-syntax-markup-changed-text:#ffdfb6;--color-prettylights-syntax-markup-changed-bg:#5a1e02;--color-prettylights-syntax-markup-ignored-text:#c9d1d9;--color-prettylights-syntax-markup-ignored-bg:#1158c7;--color-prettylights-syntax-meta-diff-range:#d2a8ff;--color-prettylights-syntax-brackethighlighter-angle:#8b949e;--color-prettylights-syntax-sublimelinter-gutter-mark:#484f58;--color-prettylights-syntax-constant-other-reference-link:#a5d6ff;--color-fg-default:#c9d1d9;--color-fg-muted:#8b949e;--color-fg-subtle:#484f58;--color-canvas-default:#0d1117;--color-canvas-subtle:#161b22;--color-border-default:#30363d;--color-border-muted:#21262d;--color-neutral-muted:hsla(215,8%,47%,.4);--color-accent-fg:#58a6ff;--color-accent-emphasis:#1f6feb;--color-attention-subtle:rgba(187,128,9,.15);--color-danger-fg:#f85149;color-scheme:dark}div#p&gt;svg&gt;foreignObject&gt;section{-ms-text-size-adjust:100%;-webkit-text-size-adjust:100%;word-wrap:break-word;background-color:var(--color-canvas-default);color:var(--color-fg-default);font-family:-apple-system,BlinkMacSystemFont,Segoe 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details,div#p&gt;svg&gt;foreignObject&gt;section figcaption,div#p&gt;svg&gt;foreignObject&gt;section figure{display:block}div#p&gt;svg&gt;foreignObject&gt;section summary{display:list-item}div#p&gt;svg&gt;foreignObject&gt;section [hidden]{display:none!important}div#p&gt;svg&gt;foreignObject&gt;section a{background-color:transparent;color:var(--color-accent-fg);text-decoration:none}div#p&gt;svg&gt;foreignObject&gt;section a:active,div#p&gt;svg&gt;foreignObject&gt;section a:hover{outline-width:0}div#p&gt;svg&gt;foreignObject&gt;section abbr[title]{border-bottom:none;-webkit-text-decoration:underline dotted;text-decoration:underline dotted}div#p&gt;svg&gt;foreignObject&gt;section b,div#p&gt;svg&gt;foreignObject&gt;section strong{font-weight:600}div#p&gt;svg&gt;foreignObject&gt;section dfn{font-style:italic}div#p&gt;svg&gt;foreignObject&gt;section :is(h1,marp-h1){border-bottom:1px solid var(--color-border-muted);font-size:2em;font-weight:600;margin:.67em 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data-bespoke-marp-osc="page"&gt;&lt;/span&gt;&lt;button data-bespoke-marp-osc="next" tabindex="-1" title="Next slide"&gt;Next slide&lt;/button&gt;&lt;button data-bespoke-marp-osc="fullscreen" tabindex="-1" title="Toggle fullscreen (f)"&gt;Toggle fullscreen&lt;/button&gt;&lt;button data-bespoke-marp-osc="presenter" tabindex="-1" title="Open presenter view (p)"&gt;Open presenter view&lt;/button&gt;&lt;/div&gt;&lt;div id="p"&gt;&lt;svg data-marpit-svg="" viewBox="0 0 1280 720"&gt;&lt;foreignObject width="1280" height="720"&gt;&lt;section id="1"&gt;</li>
+<li>Alguma área está isolada do resto da comunidade?</li>
+<li>Como sair de sua casa até um destino?</li>
+<li>Qual o mínimo de intervenções necessárias para que todos pontos isolados sejam restaurados?</li>
 </ul>
-&lt;h1&gt;Grafos e Árvores&lt;/h1&gt;
-&lt;h2&gt;Introdução a grafos&lt;/h2&gt;
-&lt;/section&gt;
-&lt;/foreignObject&gt;&lt;/svg&gt;&lt;svg data-marpit-svg="" viewBox="0 0 1280 720"&gt;&lt;foreignObject width="1280" height="720"&gt;&lt;section id="2"&gt;
-&lt;p&gt;&lt;img src="mapa.png" alt="" /&gt;&lt;/p&gt;
-&lt;/section&gt;
-&lt;/foreignObject&gt;&lt;/svg&gt;&lt;svg data-marpit-svg="" viewBox="0 0 1280 720"&gt;&lt;foreignObject width="1280" height="720"&gt;&lt;section id="3"&gt;
-&lt;h1&gt;Enchentes em Heliópolis&lt;/h1&gt;
-&lt;ul&gt;
-&lt;li&gt;Alguma área está isolada do resto da comunidade?&lt;/li&gt;
-&lt;li&gt;Como sair de sua casa até um destino?&lt;/li&gt;
-&lt;li&gt;Qual o mínimo de intervenções necessárias para que todos pontos isolados sejam restaurados?&lt;/li&gt;
-&lt;/ul&gt;
-&lt;/section&gt;
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-&lt;h1&gt;Como representar esse mapa?&lt;/h1&gt;
-&lt;/section&gt;
-&lt;/foreignObject&gt;&lt;/svg&gt;&lt;svg data-marpit-svg="" viewBox="0 0 1280 720"&gt;&lt;foreignObject width="1280" height="720"&gt;&lt;section id="5"&gt;
-&lt;p&gt;&lt;img src="grafo.png" alt="" /&gt;&lt;/p&gt;
-&lt;/section&gt;
-&lt;/foreignObject&gt;&lt;/svg&gt;&lt;svg data-marpit-svg="" viewBox="0 0 1280 720"&gt;&lt;foreignObject width="1280" height="720"&gt;&lt;section id="6"&gt;
-&lt;h1&gt;Grafo&lt;/h1&gt;
-&lt;ul&gt;
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-&lt;ul&gt;
-&lt;li&gt;conjunto de arestas (&lt;em&gt;edges&lt;/em&gt;)&lt;/li&gt;
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-&lt;/li&gt;
-&lt;/ul&gt;
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-&lt;h1&gt;E o mapa?&lt;/h1&gt;
-&lt;h2&gt;Alguma área está isolada do resto da comunidade?&lt;/h2&gt;
-&lt;ol&gt;
-&lt;li&gt;o que cada vértice do grafo representa?&lt;/li&gt;
-&lt;li&gt;qual relação  entre vértices uma aresta representa?&lt;/li&gt;
-&lt;li&gt;essa relação tem direção ou é sempre simétrica?&lt;/li&gt;
-&lt;li&gt;essa relação tem pesos/preferências ou todas arestas são equivalentes?&lt;/li&gt;
-&lt;/ol&gt;
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-&lt;h1&gt;Tipos de grafos&lt;/h1&gt;
-&lt;ol&gt;
-&lt;li&gt;simetria:
-&lt;ul&gt;
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-&lt;li&gt;direcionado: associações podem ou não ser bi-direcionais&lt;/li&gt;
-&lt;/ul&gt;
-&lt;/li&gt;
-&lt;li&gt;pesos:
-&lt;ul&gt;
-&lt;li&gt;arestas são todas equivalente&lt;/li&gt;
-&lt;li&gt;cada aresta tem um número real associado a ela&lt;/li&gt;
-&lt;/ul&gt;
-&lt;/li&gt;
-&lt;/ol&gt;
-&lt;p&gt;Em alguns problema específicos podem ser permitidos loops (&lt;mjx-container class="MathJax" jax="SVG"&gt;&lt;svg style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="7.062ex" height="1.977ex" role="img" focusable="false" viewBox="0 -680 3121.2 874"&gt;&lt;g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"&gt;&lt;g data-mml-node="math"&gt;&lt;g data-mml-node="TeXAtom" data-mjx-texclass="ORD"&gt;&lt;g data-mml-node="mi"&gt;&lt;path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g data-mml-node="mo" transform="translate(345,0)"&gt;&lt;path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g data-mml-node="mi" transform="translate(789.7,0)"&gt;&lt;path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/g&gt;&lt;g data-mml-node="mo" transform="translate(1412.4,0)"&gt;&lt;path data-c="2208" d="M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g data-mml-node="mi" transform="translate(2357.2,0)"&gt;&lt;path data-c="1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/mjx-container&gt;) ou mais de uma aresta por par de vértices. Isso &lt;strong&gt;não deve ocorrer nos problemas desta disciplina&lt;/strong&gt;.&lt;/p&gt;
-&lt;/section&gt;
-&lt;/foreignObject&gt;&lt;/svg&gt;&lt;svg data-marpit-svg="" viewBox="0 0 1280 720"&gt;&lt;foreignObject width="1280" height="720"&gt;&lt;section id="9"&gt;
-&lt;h1&gt;Outros exemplos&lt;/h1&gt;
-&lt;ul&gt;
-&lt;li&gt;dependência entre partes de produção&lt;/li&gt;
-&lt;li&gt;traçar caminhos em um mapa&lt;/li&gt;
-&lt;li&gt;conectar cidades com mínimo de ligações&lt;/li&gt;
-&lt;li&gt;criação de agrupamentos ou equipes&lt;/li&gt;
-&lt;/ul&gt;
-&lt;/section&gt;
-&lt;/foreignObject&gt;&lt;/svg&gt;&lt;svg data-marpit-svg="" viewBox="0 0 1280 720"&gt;&lt;foreignObject width="1280" height="720"&gt;&lt;section id="10"&gt;
-&lt;h1&gt;Representação computacional&lt;/h1&gt;
-&lt;p&gt;&lt;strong&gt;Representação formal&lt;/strong&gt;:&lt;/p&gt;
-&lt;ul&gt;
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-&lt;/ul&gt;
-&lt;p&gt;Como transformar em uma representação &lt;strong&gt;computacional&lt;/strong&gt; eficiente?&lt;/p&gt;
-&lt;/section&gt;
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-&lt;h1&gt;Representação computacional&lt;/h1&gt;
-&lt;ul&gt;
-&lt;li&gt;&lt;mjx-container class="MathJax" jax="SVG"&gt;&lt;svg style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.74ex" height="1.595ex" role="img" focusable="false" viewBox="0 -683 769 705"&gt;&lt;g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"&gt;&lt;g data-mml-node="math"&gt;&lt;g data-mml-node="mi"&gt;&lt;path data-c="1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/mjx-container&gt; pode ser representado só pelos números mesmo. Só preciso guardar &lt;mjx-container class="MathJax" jax="SVG"&gt;&lt;svg style="vertical-align: -0.564ex;" xmlns="http://www.w3.org/2000/svg" width="8.795ex" height="2.26ex" role="img" focusable="false" viewBox="0 -749.5 3887.5 999"&gt;&lt;g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"&gt;&lt;g data-mml-node="math"&gt;&lt;g data-mml-node="mo" transform="translate(0 -0.5)"&gt;&lt;path data-c="7C" d="M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g data-mml-node="mi" transform="translate(278,0)"&gt;&lt;path data-c="1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g data-mml-node="mo" transform="translate(1047,0) translate(0 -0.5)"&gt;&lt;path data-c="7C" d="M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g data-mml-node="mo" transform="translate(1602.8,0)"&gt;&lt;path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g data-mml-node="msub" transform="translate(2658.6,0)"&gt;&lt;g data-mml-node="mi"&gt;&lt;path data-c="1D441" d="M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g data-mml-node="mi" transform="translate(836,-150) scale(0.707)"&gt;&lt;path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/mjx-container&gt;&lt;/li&gt;
-&lt;li&gt;&lt;mjx-container class="MathJax" jax="SVG"&gt;&lt;svg style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="1.729ex" height="1.538ex" role="img" focusable="false" viewBox="0 -680 764 680"&gt;&lt;g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"&gt;&lt;g data-mml-node="math"&gt;&lt;g data-mml-node="mi"&gt;&lt;path data-c="1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/mjx-container&gt; pode ser representado como uma matriz &lt;mjx-container class="MathJax" jax="SVG"&gt;&lt;svg style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="1.697ex" height="1.62ex" role="img" focusable="false" viewBox="0 -716 750 716"&gt;&lt;g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"&gt;&lt;g data-mml-node="math"&gt;&lt;g data-mml-node="mi"&gt;&lt;path data-c="1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/mjx-container&gt; quadrada com &lt;mjx-container class="MathJax" jax="SVG"&gt;&lt;svg style="vertical-align: -0.357ex;" xmlns="http://www.w3.org/2000/svg" width="2.78ex" height="1.902ex" role="img" focusable="false" viewBox="0 -683 1228.9 840.8"&gt;&lt;g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"&gt;&lt;g data-mml-node="math"&gt;&lt;g data-mml-node="msub"&gt;&lt;g data-mml-node="mi"&gt;&lt;path data-c="1D441" d="M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g data-mml-node="mi" transform="translate(836,-150) scale(0.707)"&gt;&lt;path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/mjx-container&gt; linhas e colunas&lt;/li&gt;
-&lt;/ul&gt;
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-&lt;h1&gt;Representação computacional&lt;/h1&gt;
-&lt;ul&gt;
-&lt;li&gt;quantas arestas &lt;strong&gt;chegam&lt;/strong&gt; no vértice &lt;mjx-container class="MathJax" jax="SVG"&gt;&lt;svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.781ex" height="1.52ex" role="img" focusable="false" viewBox="0 -661 345 672"&gt;&lt;g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"&gt;&lt;g data-mml-node="math"&gt;&lt;g data-mml-node="mi"&gt;&lt;path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/mjx-container&gt;?&lt;/li&gt;
-&lt;li&gt;quantas arestas &lt;strong&gt;saem&lt;/strong&gt; no vértice &lt;mjx-container class="MathJax" jax="SVG"&gt;&lt;svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.781ex" height="1.52ex" role="img" focusable="false" viewBox="0 -661 345 672"&gt;&lt;g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"&gt;&lt;g data-mml-node="math"&gt;&lt;g data-mml-node="mi"&gt;&lt;path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/g&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/mjx-container&gt;?&lt;/li&gt;
-&lt;li&gt;como é a matriz se o grafo for &lt;strong&gt;não direcionado&lt;/strong&gt;?&lt;/li&gt;
-&lt;li&gt;e se tiver pesos?&lt;/li&gt;
-&lt;/ul&gt;
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+</section>
+</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="4" lang="en-US">
+<h1 id="como-representar-esse-mapa">Como representar esse mapa?</h1>
+</section>
+</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="5" lang="en-US">
+<p><img src="grafo.png" alt="" /></p>
+</section>
+</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="6" lang="en-US">
+<h1 id="grafo">Grafo</h1>
+<ul>
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+<ul>
+<li>conjunto de arestas (<em>edges</em>)</li>
+<li>sai de <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.294ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 572 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path></g></g></g></svg></mjx-container> e chega em <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.464ex;" xmlns="http://www.w3.org/2000/svg" width="1.109ex" height="1.464ex" role="img" focusable="false" viewBox="0 -442 490 647"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D466" d="M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z"></path></g></g></g></svg></mjx-container></li>
+</ul>
+</li>
+</ul>
+</section>
+</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="7" lang="en-US">
+<h1 id="e-o-mapa">E o mapa?</h1>
+<h2 id="alguma-%C3%A1rea-est%C3%A1-isolada-do-resto-da-comunidade">Alguma área está isolada do resto da comunidade?</h2>
+<ol>
+<li>o que cada vértice do grafo representa?</li>
+<li>qual relação  entre vértices uma aresta representa?</li>
+<li>essa relação tem direção ou é sempre simétrica?</li>
+<li>essa relação tem pesos/preferências ou todas arestas são equivalentes?</li>
+</ol>
+</section>
+</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="8" lang="en-US">
+<h1 id="tipos-de-grafos">Tipos de grafos</h1>
+<ol>
+<li>simetria:
+<ul>
+<li>não direcionado: associações são sempre bi-direcionais (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.462ex;" xmlns="http://www.w3.org/2000/svg" width="17.946ex" height="2ex" role="img" focusable="false" viewBox="0 -680 7932 884"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 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+<li>direcionado: associações podem ou não ser bi-direcionais</li>
+</ul>
+</li>
+<li>pesos:
+<ul>
+<li>arestas são todas equivalente</li>
+<li>cada aresta tem um número real associado a ela</li>
+</ul>
+</li>
+</ol>
+<p>Em alguns problema específicos podem ser permitidos loops (<mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.439ex;" xmlns="http://www.w3.org/2000/svg" width="7.062ex" height="1.977ex" role="img" focusable="false" viewBox="0 -680 3121.2 874"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="TeXAtom" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(345,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g data-mml-node="mi" transform="translate(789.7,0)"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g></g><g data-mml-node="mo" transform="translate(1412.4,0)"><path data-c="2208" d="M84 250Q84 372 166 450T360 539Q361 539 377 539T419 540T469 540H568Q583 532 583 520Q583 511 570 501L466 500Q355 499 329 494Q280 482 242 458T183 409T147 354T129 306T124 272V270H568Q583 262 583 250T568 230H124V228Q124 207 134 177T167 112T231 48T328 7Q355 1 466 0H570Q583 -10 583 -20Q583 -32 568 -40H471Q464 -40 446 -40T417 -41Q262 -41 172 45Q84 127 84 250Z"></path></g><g data-mml-node="mi" transform="translate(2357.2,0)"><path data-c="1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path></g></g></g></svg></mjx-container>) ou mais de uma aresta por par de vértices. Isso <strong>não deve ocorrer nos problemas desta disciplina</strong>.</p>
+</section>
+</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="9" lang="en-US">
+<h1 id="outros-exemplos">Outros exemplos</h1>
+<ul>
+<li>dependência entre partes de produção</li>
+<li>traçar caminhos em um mapa</li>
+<li>conectar cidades com mínimo de ligações</li>
+<li>criação de agrupamentos ou equipes</li>
+</ul>
+</section>
+</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="10" lang="en-US">
+<h1 id="representa%C3%A7%C3%A3o-computacional">Representação computacional</h1>
+<p><strong>Representação formal</strong>:</p>
+<ul>
+<li><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.186ex;" xmlns="http://www.w3.org/2000/svg" width="11.303ex" height="1.731ex" role="img" focusable="false" viewBox="0 -683 4995.9 765"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path></g><g data-mml-node="mo" transform="translate(1046.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(2102.6,0)"><g data-mml-node="mn"><path data-c="31" d="M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z"></path></g><g data-mml-node="mo" transform="translate(666.7,0)"><path data-c="2026" d="M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60ZM525 60Q525 84 542 102T585 120Q609 120 627 104T646 61Q646 36 629 18T586 0T543 17T525 60ZM972 60Q972 84 989 102T1032 120Q1056 120 1074 104T1093 61Q1093 36 1076 18T1033 0T990 17T972 60Z"></path></g><g data-mml-node="mi" transform="translate(2005.3,0)"><path data-c="1D441" d="M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z"></path></g></g></g></g></svg></mjx-container></li>
+<li><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="24.884ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 10998.7 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 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+</ul>
+<p>Como transformar em uma representação <strong>computacional</strong> eficiente?</p>
+</section>
+</foreignObject></svg><svg data-marpit-svg="" viewBox="0 0 1280 720"><foreignObject width="1280" height="720"><section id="11" lang="en-US">
+<h1 id="representa%C3%A7%C3%A3o-computacional-1">Representação computacional</h1>
+<ul>
+<li><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.05ex;" xmlns="http://www.w3.org/2000/svg" width="1.74ex" height="1.595ex" role="img" focusable="false" viewBox="0 -683 769 705"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path></g></g></g></svg></mjx-container> pode ser representado só pelos números mesmo. Só preciso guardar <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.564ex;" xmlns="http://www.w3.org/2000/svg" width="8.795ex" height="2.26ex" role="img" focusable="false" viewBox="0 -749.5 3887.5 999"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo" transform="translate(0 -0.5)"><path data-c="7C" d="M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z"></path></g><g data-mml-node="mi" transform="translate(278,0)"><path data-c="1D449" d="M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z"></path></g><g data-mml-node="mo" transform="translate(1047,0) translate(0 -0.5)"><path data-c="7C" d="M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z"></path></g><g data-mml-node="mo" transform="translate(1602.8,0)"><path data-c="3D" d="M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z"></path></g><g data-mml-node="msub" transform="translate(2658.6,0)"><g data-mml-node="mi"><path data-c="1D441" d="M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z"></path></g><g data-mml-node="mi" transform="translate(836,-150) scale(0.707)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g></g></g></g></svg></mjx-container></li>
+<li><mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="1.729ex" height="1.538ex" role="img" focusable="false" viewBox="0 -680 764 680"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D438" d="M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path></g></g></g></svg></mjx-container> pode ser representado como uma matriz <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: 0;" xmlns="http://www.w3.org/2000/svg" width="1.697ex" height="1.62ex" role="img" focusable="false" viewBox="0 -716 750 716"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path></g></g></g></svg></mjx-container> quadrada com <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.357ex;" xmlns="http://www.w3.org/2000/svg" width="2.78ex" height="1.902ex" role="img" focusable="false" viewBox="0 -683 1228.9 840.8"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D441" d="M234 637Q231 637 226 637Q201 637 196 638T191 649Q191 676 202 682Q204 683 299 683Q376 683 387 683T401 677Q612 181 616 168L670 381Q723 592 723 606Q723 633 659 637Q635 637 635 648Q635 650 637 660Q641 676 643 679T653 683Q656 683 684 682T767 680Q817 680 843 681T873 682Q888 682 888 672Q888 650 880 642Q878 637 858 637Q787 633 769 597L620 7Q618 0 599 0Q585 0 582 2Q579 5 453 305L326 604L261 344Q196 88 196 79Q201 46 268 46H278Q284 41 284 38T282 19Q278 6 272 0H259Q228 2 151 2Q123 2 100 2T63 2T46 1Q31 1 31 10Q31 14 34 26T39 40Q41 46 62 46Q130 49 150 85Q154 91 221 362L289 634Q287 635 234 637Z"></path></g><g data-mml-node="mi" transform="translate(836,-150) scale(0.707)"><path data-c="1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path></g></g></g></g></svg></mjx-container> linhas e colunas</li>
+</ul>
+<p><mjx-container class="MathJax" jax="SVG" display="true" style="margin: 0;"><svg style="vertical-align: -2.148ex; display: block; width: 100%; height: auto; max-height: 5.428ex;" xmlns="http://www.w3.org/2000/svg" width="24.406ex" height="5.428ex" role="img" focusable="false" viewBox="0 -1449.5 10787.4 2399"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><path data-c="1D434" d="M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z"></path></g><g data-mml-node="TeXAtom" transform="translate(783,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g><g data-mml-node="mo" transform="translate(345,0)"><path data-c="2C" d="M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z"></path></g><g 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433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z" transform="translate(644,0)"></path><path data-c="A0" d="" transform="translate(1088,0)"></path></g><g data-mml-node="TeXAtom" data-mjx-texclass="ORD" transform="translate(1838,0)"><g data-mml-node="mi"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 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664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z"></path></g></g></g><g data-mml-node="mtr" transform="translate(0,-600)"><g data-mml-node="mtd"><g data-mml-node="mn"><path data-c="30" d="M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z"></path></g><g data-mml-node="mtext" transform="translate(500,0)"><path data-c="A0" d=""></path><path data-c="63" d="M370 305T349 305T313 320T297 358Q297 381 312 396Q317 401 317 402T307 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+<h1 id="representa%C3%A7%C3%A3o-computacional-2">Representação computacional</h1>
+<ul>
+<li>quantas arestas <strong>chegam</strong> no vértice <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.781ex" height="1.52ex" role="img" focusable="false" viewBox="0 -661 345 672"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g></g></g></svg></mjx-container>?</li>
+<li>quantas arestas <strong>saem</strong> no vértice <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.781ex" height="1.52ex" role="img" focusable="false" viewBox="0 -661 345 672"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g></g></g></svg></mjx-container>?</li>
+<li>como é a matriz se o grafo for <strong>não direcionado</strong>?</li>
+<li>e se tiver pesos?</li>
+</ul>
+</section>
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\ No newline at end of file
diff --git a/3-grafos-caminhos/bfs/index.html b/3-grafos-caminhos/bfs/index.html
index 95afb5d..09e583b 100644
--- a/3-grafos-caminhos/bfs/index.html
+++ b/3-grafos-caminhos/bfs/index.html
@@ -262,7 +262,7 @@ <h2 id="grafo-1">Grafo 1</h2>
     D --- E
     E --- F
 </ah-diagram></p>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="3-grafos-caminhos/bfs/long_1" id="long_1_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="3-grafos-caminhos/bfs/long_1" id="long_1_0">
 <p class="admonition-title">Exercise 1<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Use o campo abaixo para anotações sobre esta simulação.</p>
@@ -288,7 +288,7 @@ <h2 id="grafo-2">Grafo 2</h2>
     E --- F
     F --- G
 </ah-diagram></p>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="3-grafos-caminhos/bfs/long_2" id="long_2_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="3-grafos-caminhos/bfs/long_2" id="long_2_0">
 <p class="admonition-title">Exercise 2<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Use o campo abaixo para anotações sobre esta simulação.</p>
diff --git a/3-grafos-caminhos/dijkstra/index.html b/3-grafos-caminhos/dijkstra/index.html
index 523f4be..c66aa86 100644
--- a/3-grafos-caminhos/dijkstra/index.html
+++ b/3-grafos-caminhos/dijkstra/index.html
@@ -382,7 +382,7 @@ <h2 id="simulacoes-grafos-com-pesos">Simulações: grafos com pesos</h2>
 </form>
 </div>
 <h2 id="min-heap">Min-heap</h2>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="3-grafos-caminhos/dijkstra/long_1" id="long_1_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="3-grafos-caminhos/dijkstra/long_1" id="long_1_0">
 <p class="admonition-title">Exercise 7<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Escreva a representação em array do heap abaixo</p>
@@ -409,7 +409,7 @@ <h2 id="min-heap">Min-heap</h2>
 <p><code>1 5 9 10 44 11 44 13 55 46</code></p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="3-grafos-caminhos/dijkstra/long_2" id="long_2_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="3-grafos-caminhos/dijkstra/long_2" id="long_2_0">
 <p class="admonition-title">Exercise 8<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Execute <code>MENOR</code> no heap abaixo e escreva sua representação em array.</p>
@@ -436,7 +436,7 @@ <h2 id="min-heap">Min-heap</h2>
 <p><code>5 10 9 13 44 11 44 46 55</code></p>
 </div>
 </div>
-<div class="admonition exercise long tag-text-exercise tag-long-text editable" data-slug="3-grafos-caminhos/dijkstra/long_3" id="long_3_0">
+<div class="admonition exercise long tag-long-text tag-text-exercise editable" data-slug="3-grafos-caminhos/dijkstra/long_3" id="long_3_0">
 <p class="admonition-title">Exercise 9<button class="editable-button"></button></p>
 <form class="exercise-form">
 <p>Execute <code>INSERE(3)</code> no heap abaixo e escreva sua representação em array.</p>