[OPT] TP 5
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@ -6,7 +6,7 @@ lastDocument=Questions.tex
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@ -31,5 +31,4 @@
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S'il y a reconstruction, dans le pire des cas, cette reconstruction s'effectue sur l'arbre entier en $O(n)$ puis puisque la reconstruction crée un arbre dont tous les noeuds sont équilibrés, il n'y aura donc pas d'autre reconstruction. Ainsi en notant $C_h$ la complexité d'un appel entrainant une reconstruction, on a : $$C_h = O(n) + c_h = O(n) + O(lg(n)) = O(n)$$
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CQFD (ça va, c'est pas si pénible que ça les maths (de ce niveau là en tout cas))
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\end{enumerate}
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\end{document}
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\relax
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\@writefile{toc}{\contentsline {section}{\numberline {I}Graphes définis par listes d'adjacences}{1}\protected@file@percent }
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**Questions.tex
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\documentclass[a4paper,10pt]{article}
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%\documentclass[a4paper,10pt]{scrartcl}
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\usepackage{mathtools}
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\usepackage[utf8]{inputenc}
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\renewcommand{\thesection}{\Roman{section}}
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\newcommand{\sectioni}[2]{\setcounter{section}{#1}\addtocounter{section}{-1}\section{#2}}
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\newcommand{\subsectioni}[2]{\setcounter{subsection}{#1}\addtocounter{subsection}{-1}\subsection{#2}}
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\title{Questions du TP 5}
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\author{}
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\date{}
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\pdfinfo{%
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/Title ()
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/Author ()
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/Creator ()
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/Producer ()
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/Subject ()
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/Keywords ()
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}
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\begin{document}
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\maketitle
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\section{Graphes définis par listes d'adjacences}
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\begin{enumerate}
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\item Si le graphe n'est est orienté, au lieu d'ajouter \textbf{j} à \textbf{g.(i)} et \textbf{i} à \textbf{g.(j)}, on se contente d'ajouter j à g.(i).
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\item De même, au lieu de retirer \textbf{j} de \textbf{g.(i)} et \textbf{i} de \textbf{g.(j)}, on se contente de retirer \textbf{j} de \textbf{g.(i)}.
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\item Ici on a \textbf{ajoute\_sommet : int $\rightarrow$ int $\rightarrow$ graphe1 $\rightarrow$ graphe1}, or l'appel d'exemple est \textbf{ajoute\_sommet g}. On supposera que \textbf{ajoute\_sommet} est du type : \textbf{graphe1 $\rightarrow$ graphe1}.
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\end{enumerate}
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\end{document}
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SPE/OPT/TP 5/main.ml
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type graphel = int list array;;
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let ajoute_arete i j (g:graphel) =
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let rec ajoute k l = match l with
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| [] -> [k]
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| h::t when h=k -> h::(ajoute k t)
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| h::t -> l in
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g.(i) <- ajoute j g.(i);
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g.(j) <- ajoute i g.(j);;
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let supprime_arete i j (g:graphel) =
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let rec retire k l = match l with
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| h::t when h=k -> t
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| h::t -> h::(retire k t)
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| _ -> l in
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g.(i) <- retire j g.(i);
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g.(j) <- retire i g.(j);;
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let ajoute_sommet (g:graphel) =
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let n = Array.length g in
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let g2 = Array.make (n+1) [] in
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for i = 0 to n-1 do
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g2.(i) <- g.(i)
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done;
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g2;;
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let supprime_sommet i (g:graphel) =
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let n = Array.length g in
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let g2 = Array.make (n-1) [] in
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let rec parcours l = match l with
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| [] -> []
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| h::t when h=i -> parcours t
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| h::t when h<i -> h::(parcours t)
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| h::t when h>i -> (h-1)::(parcours t) in
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for j = 0 to n-2 do
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if j < i then
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g2.(j) <- parcours g.(j)
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else
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g2.(j) <- parcours g.(j+1)
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done;
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g2;;
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type graphem = int array array;;
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|
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let ajoute_aretem i j (g:graphem) =
|
||||
g.(i).(j) <- 1;
|
||||
g.(j).(i) <- 1;;
|
||||
|
||||
let supprime_aretem i j (g:graphem) =
|
||||
g.(i).(j) <- 0;
|
||||
g.(j).(i) <- 0;;
|
||||
|
||||
let ajoute_sommetm (g:graphem) =
|
||||
let n = Array.length g in
|
||||
let g2 = Array.make_matrix n n 0 in
|
||||
for i = 0 to n-1 do
|
||||
for j = 0 to n-1 do
|
||||
g2.(i).(j) <- g.(i).(j)
|
||||
done
|
||||
done;
|
||||
g2;;
|
||||
|
||||
let supprime_sommetm k (g:graphem) =
|
||||
let n = Array.length g in
|
||||
let g2 = Array.make_matrix (n-1) (n-1) 0 in
|
||||
for i = 0 to n-2 do
|
||||
for j = 0 to n-2 do
|
||||
let a = if i < k then i else i+1 in
|
||||
let b = if j < k then j else j+1 in
|
||||
g2.(i).(j) <- g.(a).(b)
|
||||
done
|
||||
done;
|
||||
g2;;
|
||||
|
||||
let conversion_lm (g:graphel) =
|
||||
let n = Array.length g in
|
||||
let g2 = Array.make_matrix n n 0 in
|
||||
for i = 0 to n-1 do
|
||||
let ajoute j = ajoute_aretem i j g2 in
|
||||
List.map ajoute g.(i)
|
||||
done;
|
||||
g2;;
|
||||
|
||||
let conversion_ml (g:graphem) =
|
||||
let n = Array.length g in
|
||||
let g2 = Array.make n [] in
|
||||
for i = 0 to n-1 do
|
||||
for j = 0 to n-1 do
|
||||
if g.(i).(j) = 1 then
|
||||
ajoute_arete i j g2
|
||||
else ()
|
||||
done
|
||||
done;
|
||||
g2;;
|
||||
|
||||
31
SPE/OPT/TP 5/questions.kilepr
Normal file
31
SPE/OPT/TP 5/questions.kilepr
Normal file
@ -0,0 +1,31 @@
|
||||
[General]
|
||||
bib_extensions=.bib
|
||||
bibliographyBackendAutoDetected=
|
||||
bibliographyBackendUserOverride=
|
||||
def_graphic_ext=eps
|
||||
img_extIsRegExp=false
|
||||
img_extensions=.eps .jpg .jpeg .png .pdf .ps .fig .gif
|
||||
kileprversion=3
|
||||
kileversion=2.9.93
|
||||
masterDocument=
|
||||
name=Questions
|
||||
pkg_extIsRegExp=false
|
||||
pkg_extensions=.cls .sty .bbx .cbx .lbx
|
||||
src_extIsRegExp=false
|
||||
src_extensions=.tex .ltx .latex .dtx .ins
|
||||
|
||||
[Tools]
|
||||
MakeIndex=
|
||||
QuickBuild=
|
||||
|
||||
[item:Questions.tex]
|
||||
archive=true
|
||||
encoding=UTF-8
|
||||
highlight=LaTeX
|
||||
mode=LaTeX
|
||||
|
||||
[item:questions.kilepr]
|
||||
archive=true
|
||||
encoding=
|
||||
highlight=
|
||||
mode=
|
||||
Loading…
Reference in New Issue
Block a user