3_gradient.jl

@@ -78,7 +78,7 @@ $$\nabla f = (\partial f/\partial x, \partial f/\partial y)$$
 md"""
 ## Calculer le gradient à la main
 
-Comment calculer les valeurs de $\partial f/\partial x$ et $\partial f/\partial x$ ?
+Comment calculer les valeurs de $\partial f/\partial x$ et $\partial f/\partial y$ ?
 Commençant par voir comment faire ça à la main. Nous verrons au cours suivant comment le calculer algorithmiquement.
 L'astuce: pour calculer $\frac{\partial}{\partial x}f(x, y)$, il faut voir $y$ comme constant et donc voir $f$ comme fonction de $x$ uniquement. Par exemple:
 

biblio.bib

@@ -11,6 +11,20 @@
   file = {/home/blegat/Downloads/(9th ed) Robert A. Adams, Christopher Essex - Adams - Calculus A Complete Course 9th ed 2018 solutions-Pearson (2018).pdf;/home/blegat/Downloads/Robert A. Adams, Christopher Essex - Calculus_ A complete course-Pearson Canada Inc. (2018)-1.pdf}
 }
 
+@book{cormen2022Introduction,
+  title = {Introduction to {{Algorithms}}, Fourth Edition},
+  author = {Cormen, Thomas H. and Leiserson, Charles E. and Rivest, Ronald L. and Stein, Clifford},
+  year = {2022},
+  month = apr,
+  publisher = {MIT Press},
+  abstract = {A comprehensive update of the leading algorithms text, with new material on matchings in bipartite graphs, online algorithms, machine learning, and other topics.Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. It covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers, with self-contained chapters and algorithms in pseudocode. Since the publication of the first edition, Introduction to Algorithms has become the leading algorithms text in universities worldwide as well as the standard reference for professionals. This fourth edition has been updated throughout.New for the fourth edition New chapters on matchings in bipartite graphs, online algorithms, and machine learningNew material on topics including solving recurrence equations, hash tables, potential functions, and suffix arrays140 new exercises and 22 new problemsReader feedback–informed improvements to old problemsClearer, more personal, and gender-neutral writing styleColor added to improve visual presentationNotes, bibliography, and index updated to reflect developments in the fieldWebsite with new supplementary materialWarning: Avoid counterfeit copies of Introduction to Algorithms by buying only from reputable retailers. Counterfeit and pirated copies are incomplete and contain errors.},
+  googlebooks = {RSMuEAAAQBAJ},
+  isbn = {978-0-262-36750-9},
+  langid = {english},
+  keywords = {Computers / Computer Science,Computers / Programming / Algorithms,Computers / Reference},
+  file = {/home/blegat/Downloads/Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein - Introduction to Algorithms-MIT Press (2009).pdf}
+}
+
 @book{hoffstein2014Introduction,
   title = {An {{Introduction}} to {{Mathematical Cryptography}}},
   author = {Hoffstein, Jeffrey and Pipher, Jill and Silverman, Joseph H.},
@@ -27,3 +41,11 @@
   keywords = {coding theory,digital signatures,discrete logarithms,elliptic curves,information and communication circuits,information theory,lattices and cryptography,probability theory},
   file = {/home/blegat/Zotero/storage/86SK789Z/Hoffstein et al. - 2014 - An Introduction to Mathematical Cryptography.pdf}
 }
+
+@book{west2022Introduction,
+  title = {Introduction to Graph Theory},
+  author = {West, Douglas Brent},
+  year = {2022},
+  isbn = {81-7808-830-4},
+  file = {/home/blegat/Downloads/West.pdf}
+}

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labs/ConnectedComponents/Project.toml

+[deps]
+Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
+GraphPlot = "a2cc645c-3eea-5389-862e-a155d0052231"
+Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"

labs/ConnectedComponents/main.jl

+using Graphs, GraphPlot, SparseArrays, Colors
+
+function myplot(graph, components)
+    cols = Colors.distinguishable_colors(length(components))
+    node_cols = Vector{eltype(cols)}(undef, nv(graph))
+    for (comp, col) in zip(components, cols)
+        node_cols[comp] .= col
+    end
+    gplot(graph, nodefillc = node_cols)
+end
+
+n = 40
+adjacency = sprand(Bool, n, n, 0.02)
+
+graph = Graph(max.(adjacency, adjacency'))
+
+connected_components(graph)
+
+myplot(graph, connected_components(graph))
+
+function my_connected_component(graph)
+    # TODO
+    # Vous pouvez commencer par utiliser https://juliacollections.github.io/DataStructures.jl/stable/disjoint_sets/
+    # pour vous aider
+    # Ensuite, essayez d'implémenter DisjointSet vous-même !
+    for edge in edges
+        # Arête liant les noeuds `edge.src` et `edge.dst`
+    end
+end