Table of Contents¶
Texte d'oral de modélisation - Agrégation Option Informatique¶
Préparation à l'agrégation - ENS de Rennes, 2016-17¶
- Date : 7 avril 2017
- Auteur : Lilian Besson
- Texte: Annale 2009, "Contraintes temporelles"
À propos de ce document¶
- Ceci est une proposition de correction, partielle et probablement non-optimale, pour la partie implémentation d'un texte d'annale de l'agrégation de mathématiques, option informatique.
- Ce document est un notebook Jupyter, et est open-source sous Licence MIT sur GitHub, comme les autres solutions de textes de modélisation que j'ai écrite cette année.
- L'implémentation sera faite en OCaml, version 4+ :
In [2]:
Sys.command "ocaml -version";;
The OCaml toplevel, version 4.04.2
Out[2]:
- : int = 0
Question de programmation¶
La question de programmation pour ce texte était donnée en question 1 en page 9 :
"Programmer l'algorithme PC. Faites le tourner sur l'exemple de réseau non distributif."
La consigne était très courte, mais avec aucune indication. Notez qu'il est rare que le texte exige un exemple particulier.
Réponse à l'exercice requis¶
Ça va être assez long, en fait...
- D'abord, il faut définir les types de données avec lesquels on va travailler,
- Ensuite, implémenter les deux opérations $\oplus$ et $\otimes$ sur les ensembles d'intervalles,
- Puis implémenter l'algorithme PC (similaire à Floyd-Warshall),
- Et enfin, l'exécuter sur l'exemple de réseau non distributif donné en page 8.
Si possible, on va essayer de faire des tests pour chaque fonction intermédiaire, et un exemple de plus à la fin.
Un des problèmes que l'on va rencontrer est le fait que l'on doit manipuler $-\infty$ et $+\infty$, pour pouvoir gérer une contrainte qui n'est pas une contrainte, à savoir l'interavalle $(-\infty, +\infty)$.
Structures de données¶
On va travailler avec des valeurs entières ou $\pm\infty$. En écrivant nous même les opérations arithmétiques ($+,max$) sur les entiers "étendus" on obtiendra ce qu'on veut.
In [75]:
type entier_etendu = MInf | PInf | E of int;;
Out[75]:
type entier_etendu = MInf | PInf | E of int
On se restreint aux intervalles à coordonnées entières, et on considère des listes d'intervalles. Tous les intervalles sont fermés à gauche et à droite.
In [76]:
type intervalle = (entier_etendu * entier_etendu);; (* (a, b) représente l'intervalle [a, b] *)
Out[76]:
type intervalle = entier_etendu * entier_etendu
In [77]:
type intervalles = intervalle list;;
Out[77]:
type intervalles = intervalle list
On définit tout de suite deux exemples, $T_a$ et $S_a$ tirés de la Figure 2.a) et $T_b,S_b$ de la Figure 2.b). Cela permettra de vérifier les opérations $\oplus$ et $\otimes$.
- $T_a = \{ [1, 4], [6, 8] \}$ et $S_a = \{ [0, 1], [3, 5], [6, 7] \}$.
In [78]:
let t_a : intervalles = [
(E(1), E(4));
(E(6), E(8))
];;
let s_a : intervalles = [
(E(0), E(1));
(E(3), E(5));
(E(6), E(7))
];;
Out[78]:
val t_a : intervalles = [(E 1, E 4); (E 6, E 8)]
Out[78]:
val s_a : intervalles = [(E 0, E 1); (E 3, E 5); (E 6, E 7)]
- $T_b = \{ [-1, 0], [2, 4] \}$ et $S_b = \{ [0, 1], [4, 4] \}$.
In [80]:
let t_b : intervalles = [
(E(-1), E(0));
(E(2), E(4))
];;
let s_b : intervalles = [
(E(0), E(1));
(E(4), E(4)) (* Intervalle de longueur nulle *)
];;
Out[80]:
val t_b : intervalles = [(E (-1), E 0); (E 2, E 4)]
Out[80]:
val s_b : intervalles = [(E 0, E 1); (E 4, E 4)]
- Et la contrainte vide, $T = \{[-\infty, +\infty\}$ :
In [79]:
let t_vide : intervalles = [
(MInf, PInf)
];;
Out[79]:
val t_vide : intervalles = [(MInf, PInf)]
Arithmétiques sur nos entiers étendus¶
Max/min¶
In [81]:
let max_ee x y =
match x, y with
| MInf, _ -> y
| PInf, _ -> PInf
| _, MInf -> x
| _, PInf -> PInf
| E(vx), E(vy) -> E(max vx vy)
;;
Out[81]:
val max_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>
In [86]:
max_ee MInf (E(10));;
max_ee PInf (E(10));;
max_ee (E(10)) MInf;;
max_ee (E(10)) PInf;;
max_ee (E(-10)) (E(10));;
max_ee (E(10)) (E(-10));;
Out[86]:
- : entier_etendu = E 10
Out[86]:
- : entier_etendu = PInf
Out[86]:
- : entier_etendu = E 10
Out[86]:
- : entier_etendu = PInf
Out[86]:
- : entier_etendu = E 10
Out[86]:
- : entier_etendu = E 10
In [87]:
let min_ee x y =
match x, y with
| PInf, _ -> y
| MInf, _ -> MInf
| _, PInf -> x
| _, MInf -> MInf
| E(vx), E(vy) -> E(min vx vy)
;;
Out[87]:
val min_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>
In [90]:
min_ee MInf (E(10));;
min_ee PInf (E(10));;
min_ee (E(10)) MInf;;
min_ee (E(10)) PInf;;
min_ee (E(-10)) (E(10));;
min_ee (E(10)) (E(-10));;
Out[90]:
- : entier_etendu = MInf
Out[90]:
- : entier_etendu = E 10
Out[90]:
- : entier_etendu = MInf
Out[90]:
- : entier_etendu = E 10
Out[90]:
- : entier_etendu = E (-10)
Out[90]:
- : entier_etendu = E (-10)
On peut utiliser la fonction minimum pour trier deux entiers étendus :
In [115]:
let pluspetiteq_ee x y =
let m = min_ee x y in
m = x || x = y
;;
Out[115]:
val pluspetiteq_ee : entier_etendu -> entier_etendu -> bool = <fun>
In [116]:
let pluspetit_ee x y =
let m = min_ee x y in
m = x && x != y
;;
Out[116]:
val pluspetit_ee : entier_etendu -> entier_etendu -> bool = <fun>
Somme/produit¶
In [88]:
let plus_ee x y =
match x, y with
| MInf, PInf -> failwith "-inf + +inf = ?"
| PInf, MInf -> failwith "-inf + +inf = ?"
| PInf, _ -> PInf
| MInf, _ -> MInf
| _, MInf -> MInf
| _, PInf -> PInf
| E(vx), E(vy) -> E(vx + vy)
;;
Out[88]:
val plus_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>
In [92]:
plus_ee MInf (E(10));;
plus_ee PInf (E(10));;
plus_ee (E(10)) MInf;;
plus_ee (E(10)) PInf;;
plus_ee (E(-10)) (E(10));;
plus_ee (E(10)) (E(-10));;
plus_ee (E(10)) (E(10));;
plus_ee (E(-10)) (E(-10));;
Out[92]:
- : entier_etendu = MInf
Out[92]:
- : entier_etendu = PInf
Out[92]:
- : entier_etendu = MInf
Out[92]:
- : entier_etendu = PInf
Out[92]:
- : entier_etendu = E 0
Out[92]:
- : entier_etendu = E 0
Out[92]:
- : entier_etendu = E 20
Out[92]:
- : entier_etendu = E (-20)
In [93]:
let produit_ee x y =
match x, y with
| MInf, PInf -> MInf
| PInf, MInf -> PInf
| PInf, E(vy) when vy < 0 -> MInf
| PInf, _ -> PInf
| MInf, E(vy) when vy < 0 -> PInf
| MInf, _ -> MInf
| E(vx), PInf when vx < 0 -> MInf
| _, PInf -> PInf
| E(vx), MInf when vx < 0 -> PInf
| _, MInf -> MInf
| E(vx), E(vy) -> E(vx * vy)
;;
Out[93]:
val produit_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>
In [94]:
produit_ee MInf (E(10));;
produit_ee PInf (E(10));;
produit_ee (E(10)) MInf;;
produit_ee (E(10)) PInf;;
produit_ee (E(-10)) (E(10));;
produit_ee (E(10)) (E(-10));;
produit_ee (E(10)) (E(10));;
produit_ee (E(-10)) (E(-10));;
Out[94]:
- : entier_etendu = MInf
Out[94]:
- : entier_etendu = PInf
Out[94]:
- : entier_etendu = MInf
Out[94]:
- : entier_etendu = PInf
Out[94]:
- : entier_etendu = E (-100)
Out[94]:
- : entier_etendu = E (-100)
Out[94]:
- : entier_etendu = E 100
Out[94]:
- : entier_etendu = E 100
Opérations de base, $\oplus$ et $\otimes$¶
On peut écrire des opérations d'intersection et de composition sur deux intervalles, ensuite il suffira de les généraliser à un ensemble d'intervalle.
On suit les définitions de l'énoncé.
Intersection¶
$$ \forall T = (I_1,\dots,I_l), \forall S = (J_1,\dots,J_m),\\ T \oplus S := \{ K_1, \dots, K_n\} \;\;\text{Où}\;\; K_k = I_i \cap J_j. $$Notez que $n \leq l + m$ ici.
Pour l'intersection de deux intervalles, l'intervalle vide $\emptyset$ peut être obtenu, donc la fonction suivante renvoie un type intervalle option : soit None si $I \cap J = \emptyset$, soit Some (x, y) si $I \cap J = [x, y]$.
In [96]:
let intersection (i : intervalle) (j : intervalle) : intervalle option =
let a = fst i and b = snd i in
let c = fst j and d = snd j in
if pluspetit_ee b c || pluspetit_ee d a then
None
else
Some (max_ee a c, min_ee b d)
;;
Out[96]:
val intersection : intervalle -> intervalle -> intervalle option = <fun>
Ensuite, il suffit d'explorer tous les couples $(I, J)$ possible, et de ne garder que ceux qui donnent un intervalle. On supprimera les doublons en vérifiant au fur et à mesure (ça a la même complexité que si on le fait à la fin).
En manipulant une liste d'intervalle option, on doit ruser un peu pour n'ajouter que ceux qui ne sont pas dans acc et qui sont des vrais intervalles.
In [98]:
let ajoute_nouveaux_option (acc : intervalles) (liste_option : intervalle option list) =
List.map
(fun i -> match i with Some i2 -> i2 | None -> (MInf, PInf))
(List.filter (fun i ->
match i with
| None -> false
| Some i2 -> not (List.mem i2 acc)
) liste_option)
;;
Out[98]:
val ajoute_nouveaux_option : intervalles -> intervalle option list -> intervalle list = <fun>
Avec tout ça, on a une belle fonction récursive, avec un accumulateur acc qui contient la liste des intervalles dans $T \oplus S$, construite en considérant les intervalles de $S$ les un après les autres.
On s'assure de n'avoir ni intervalles vide, ni doublon, grâce à ajoute_nouveaux_option.
In [101]:
let intersections (t : intervalles) (s : intervalles) : intervalles =
let rec inter_aux acc tx sx =
match sx with
| [] -> acc (* Plus rien à ajouter *)
| j :: s2 -> (* On traite j, puis récursivement la suite de s *)
let t_inter_j = List.map (intersection j) tx in
inter_aux ((ajoute_nouveaux_option acc t_inter_j) @ acc) tx s2
in
List.sort compare (inter_aux [] t s)
(* On trie pour les avoir en ordre croissant, c'est tout *)
;;
Out[101]:
val intersections : intervalles -> intervalles -> intervalles = <fun>
Pour frimer un peu et simplifier l'écriture de l'algorithme PC, on peut définir une opération infixe en raccourci : $$ T \oplus S = \texttt{t ++ s}.$$
In [102]:
let ( ++ ) = intersections;;
Out[102]:
val ( ++ ) : intervalles -> intervalles -> intervalles = <fun>
Composition¶
Ce sera plus facile. $$ \forall T = (I_1,\dots,I_l), \forall S = (J_1,\dots,J_m),\\ T \otimes S := \{ K_1, \dots, K_n\} \;\;\text{Où}\;\; K_k = [a + c, b + d], \;\text{si}\; I_i = [a, b], J_j = [c, d]. $$ Notez que $n \leq l \times m$ ici.
Pour la composition de deux intervalles, il n'y pas de difficulté particulière :
In [103]:
let composition (i : intervalle) (j : intervalle) : intervalle =
let a = fst i and b = snd i in
let c = fst j and d = snd j in
(* (a + c, b + d) *)
((plus_ee a c), (plus_ee d b))
;;
Out[103]:
val composition : intervalle -> intervalle -> intervalle = <fun>
Et on les combine facilement, en gardant la même architecture que pour intersections.
In [104]:
let ajoute_nouveaux (acc : intervalles) (liste : intervalles) : intervalles =
List.filter (fun i -> not (List.mem i acc)) liste
;;
Out[104]:
val ajoute_nouveaux : intervalles -> intervalles -> intervalles = <fun>
In [105]:
let compositions (t : intervalles) (s : intervalles) : intervalles =
let rec compo_aux acc tx sx =
match sx with
| [] -> acc (* Plus rien à ajouter *)
| j :: s2 -> (* On traite j, puis récursivement la suite de s *)
let t_compo_j = List.map (composition j) tx in
compo_aux ((ajoute_nouveaux acc t_compo_j) @ acc) tx s2
in
List.sort compare (compo_aux [] t s)
(* On trie pour les avoir en ordre croissant, c'est tout *)
;;
Out[105]:
val compositions : intervalles -> intervalles -> intervalles = <fun>
Pour frimer un peu et simplifier l'écriture de l'algorithme PC, on peut définir une opération infixe en raccourci : $$ T \otimes S = \texttt{t ** s}.$$
In [106]:
let ( ** ) = compositions;;
Out[106]:
val ( ** ) : intervalles -> intervalles -> intervalles = <fun>
Union¶
On peut aussi rapidement définier $T \cup S$, pour l'union. C'est très facile.
In [107]:
let union (t : intervalles) (s : intervalles) : intervalles =
List.append t s
;;
Out[107]:
val union : intervalles -> intervalles -> intervalles = <fun>
Exemples¶
On aimerait reproduire les exemples de la Figure 2 du texte.
- Pour les deux intervalles de la Figure 2.a) : $T_a = \{ [1, 4], [6, 8] \}$ et $S_a = \{ [0, 1], [3, 5], [6, 7] \}$.
In [108]:
t_a ++ s_a;;
Out[108]:
- : intervalles = [(E 3, E 4); (E 6, E 7)]
On retrouve bien le résultat de la Figure 2.a).
In [109]:
t_a ** s_a;;
union t_a s_a;;
Out[109]:
- : intervalles = [(E 1, E 5); (E 4, E 9); (E 6, E 9); (E 7, E 11); (E 9, E 13); (E 12, E 15)]
Out[109]:
- : intervalles = [(E 1, E 4); (E 6, E 8); (E 0, E 1); (E 3, E 5); (E 6, E 7)]
- Pour les deux intervalles de la Figure 2.b) : $T_b = \{ [-1, 0], [2, 4] \}$ et $S_b = \{ [0, 1], [4, 4] \}$.
In [110]:
t_b ** s_b;;
Out[110]:
- : intervalles = [(E (-1), E 1); (E 2, E 5); (E 3, E 4); (E 6, E 8)]
On retrouve bien le résultat de la Figure 2.b).
L'intervalle $[3, 4]$ est inclus dans $[2, 5]$, donc on devrait ajouter une étape de nettoyage pour donner une forme canonique aux intervalles produit par composition. On le fait plus bas.
In [113]:
t_b;;
s_b;;
Out[113]:
- : intervalles = [(E (-1), E 0); (E 2, E 4)]
Out[113]:
- : intervalles = [(E 0, E 1); (E 4, E 4)]
In [114]:
t_b ++ s_b;;
union t_b s_b;;
Out[114]:
- : intervalles = []
Out[114]:
- : intervalles = [(E (-1), E 0); (E 2, E 4); (E 0, E 1); (E 4, E 4)]
On remarque que les intervalles sont bien donnés dans l'ordre croissant, puisqu'on a pensé à trier la sortie des deux fonctions, mais ça ne change rien.
Une étape de plus : ne pas inclure des intervalles inclus dans ceux déjà présents¶
On va raffiner les fonctions définis ci-dessus en ajoutant un test, sur leur résultat final.
est_inclus i jteste si $I \subseteq J$.
In [119]:
let est_inclus (i : intervalle) (j : intervalle) : bool =
let a = fst i and b = snd i in
let c = fst j and d = snd j in
(* on peut aussi écrire directement
let a, b = i and c, d = j in
pour extraire les valeurs d'un coupe i=(a,b) et j=(c,d)
*)
(* c <= a && b <= d *)
(pluspetiteq_ee c a) && (pluspetiteq_ee b d)
;;
Out[119]:
val est_inclus : intervalle -> intervalle -> bool = <fun>
In [121]:
est_inclus (E(3), E(4)) (E(2), E(5));; (* true *)
est_inclus (E(2), E(5)) (E(3), E(4));; (* false *)
est_inclus (E(1), E(1)) (E(1), E(1));; (* true *)
Out[121]:
- : bool = true
Out[121]:
- : bool = false
Out[121]:
- : bool = true
est_inclus_dans_un i accteste si $I \subseteq J$ pour un $J \neq I \in \mathrm{Acc}$.
In [122]:
let est_inclus_dans_un (i : intervalle) (acc : intervalles) : bool =
List.exists (fun j -> (i != j) && (est_inclus i j)) acc
;;
Out[122]:
val est_inclus_dans_un : intervalle -> intervalles -> bool = <fun>
- On peut écrire une fonction
filtrequi retire les intervalles inclus dans d'autres, puis retire les doublons.
In [123]:
let retire_les_inclus (liste : intervalles) : intervalles =
List.filter (fun i -> not (est_inclus_dans_un i liste)) liste
;;
let retire_les_doublons (liste : intervalles) : intervalles =
let reponse = ref [] in
List.iter (fun i ->
if not (List.mem i !reponse) then
reponse := i :: !reponse
) liste;
!reponse
;;
let filtre liste =
retire_les_doublons (retire_les_inclus liste)
;;
Out[123]:
val retire_les_inclus : intervalles -> intervalles = <fun>
Out[123]:
val retire_les_doublons : intervalles -> intervalles = <fun>
Out[123]:
val filtre : intervalles -> intervalles = <fun>
- L'intersection ne devrait pas être impactée.
In [124]:
let intersections2 (t : intervalles) (s : intervalles) : intervalles =
List.sort compare (filtre (intersections t s))
(* On trie pour les avoir en ordre croissant, c'est tout *)
;;
Out[124]:
val intersections2 : intervalles -> intervalles -> intervalles = <fun>
In [125]:
let ( ++ ) = intersections2;;
t_a ++ s_a;;
Out[125]:
val ( ++ ) : intervalles -> intervalles -> intervalles = <fun>
Out[125]:
- : intervalles = [(E 3, E 4); (E 6, E 7)]
- Mais la composition va donner la bonne réponse désormais pour l'exemple de la figure 2.b).
In [126]:
let compositions2 (t : intervalles) (s : intervalles) : intervalles =
List.sort compare (filtre (compositions t s))
(* On trie pour les avoir en ordre croissant, c'est tout *)
;;
Out[126]:
val compositions2 : intervalles -> intervalles -> intervalles = <fun>
In [127]:
let ( ** ) = compositions2;;
t_b ** s_b;;
Out[127]:
val ( ** ) : intervalles -> intervalles -> intervalles = <fun>
Out[127]:
- : intervalles = [(E (-1), E 1); (E 2, E 5); (E 6, E 8)]
C'était un peu long, mais c'est propre au moins.
Notez que pour obtenir une vraie forme canonique, il faudrait aussi rassembler les intervalles consécutifs ($\{ [0, 1], [1, 2] \} \rightarrow \{ [0, 1] \}$) et se recoupant ($\{ [0, 3], [2, 4] \} \rightarrow \{ [0, 4] \}$).
Ça prendrait trop de temps. Et ce n'était pas exigé.
L'algorithme PC¶
Structure de données pour les réseaux STP¶
On a besoin désormais de considérer des réseaux STP, qui sont des graphes dont les sommets sont des entiers, et dont les arêtes sont étiquetées par des listes (non vides) d'intervalles.
L'algorithme PC demande de pouvoir accéder rapidement et facilement à l'arête entre deux sommets $x,y$, $T_{x,y}$.
Ainsi, la structure de matrice d'adjacence semble appropriée.
Les arêtes inexistantes dans le réseau auront simplement $T_{x,y} = \emptyset$, c'est-à-dire [] (liste vide).
On supposera que toutes les matrices données aux différentes fonctions définies plus bas sont carrées, on ne le vérifie pas (mais ce serait facile).
In [128]:
type sommet = int;;
type arete = intervalles;; (* c'est l'idée *)
type reseauSTP = intervalles array array;;
Out[128]:
type sommet = int
Out[128]:
type arete = intervalles
Out[128]:
type reseauSTP = intervalles array array
On essaie tout de suite notre structure de données avec l'exemple du réseau STP de la figure 4 :
In [235]:
let t_01 : intervalles = [(E(0), E(1)); (E(10), E(20))];;
let t_12 : intervalles = [(E(0), E(10))];;
let t_13 : intervalles = [(E(25), E(50))];;
let t_23 : intervalles = [(E(0), E(20)); (E(40), E(40))];;
let t_vide = [(MInf, PInf)];;
let stp_4 : reseauSTP = [|
[| t_vide; t_01; t_vide; t_vide |];
[| t_vide; t_vide; t_12; t_13 |];
[| t_vide; t_vide; t_vide; t_23 |];
[| t_vide; t_vide; t_vide; t_vide |];
|];;
Out[235]:
val t_01 : intervalles = [(E 0, E 1); (E 10, E 20)]
Out[235]:
val t_12 : intervalles = [(E 0, E 10)]
Out[235]:
val t_13 : intervalles = [(E 25, E 50)]
Out[235]:
val t_23 : intervalles = [(E 0, E 20); (E 40, E 40)]
Out[235]:
val t_vide : (entier_etendu * entier_etendu) list = [(MInf, PInf)]
Out[235]:
val stp_4 : reseauSTP =
[|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];
[(MInf, PInf)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
[(E 0, E 20); (E 40, E 40)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]
On peut vérifier qu'il n'est pas distributif, en prenant l'exemple du texte (fin page 8) :
In [236]:
let s_13 = t_12 ** t_23;;
t_13 ++ s_13;;
t_01 ** (t_13 ++ s_13);; (* 1er cas *)
t_01 ** t_13;;
t_01 ** s_13;;
(t_01 ** t_13) ++ (t_01 ** s_13);; (* 2nd cas *)
Out[236]:
val s_13 : intervalles = [(E 0, E 30); (E 40, E 50)]
Out[236]:
- : intervalles = [(E 25, E 30); (E 40, E 50)]
Out[236]:
- : intervalles = [(E 25, E 31); (E 35, E 50); (E 40, E 51); (E 50, E 70)]
Out[236]:
- : intervalles = [(E 25, E 51); (E 35, E 70)]
Out[236]:
- : intervalles = [(E 0, E 31); (E 10, E 50); (E 40, E 51); (E 50, E 70)]
Out[236]:
- : intervalles = [(E 25, E 50); (E 50, E 70)]
En simplifiant, on obtient :
- $T_{01} \otimes (T_{13} \oplus S_{13} = \{ [25, 31], [35, 70] \}$,
- $(T_{01} \otimes T_{13}) \oplus (T_{01} \otimes S_{13}) = \{ [25, 70] \}$,
qui sont bien différents.
Enfin, on peut rapidement vérifier si la matrice d'un graphe est bien carrée :
In [237]:
let est_carree matrice =
let n = Array.length matrice in
Array.fold_left (fun b x -> b && (n = (Array.length x))) true matrice
;;
Out[237]:
val est_carree : 'a array array -> bool = <fun>
In [238]:
est_carree stp_4;;
Out[238]:
- : bool = true
.Il n'y a pas de boucle until en Caml, mais avec une boucle while on arrivera presque à la même chose.
In [239]:
exception Fini;; (* Pour faire le [exit]. *)
Out[239]:
exception Fini
On peut l'écrire avant pour la rendre plus claire, mais l'étape clé de l'algorithme PC (et Floyd-Warshall) est une opération dite de relaxation : $$ T_{i,j} \oplus (T_{i,k} \otimes T_{k,j}).$$
In [240]:
let relaxe (reseau : reseauSTP) i j k =
let t_ij = reseau.(i).(j)
and t_ik = reseau.(i).(k)
and t_kj = reseau.(k).(j)
in t_ij ++ (t_ik ** t_kj)
;;
Out[240]:
val relaxe : reseauSTP -> int -> int -> int -> intervalles = <fun>
On a tout ce qu'il faut pour écrire l'algorithme. Mais comme il ne marche pas encore, on va le débogguer.
In [241]:
let string_of_entieretendu = function
| MInf -> "-oo"
| PInf -> "+oo"
| E(x) -> string_of_int x
;;
Out[241]:
val string_of_entieretendu : entier_etendu -> string = <fun>
In [242]:
let print_intervalle (une_contrainte : intervalle) =
let a, b = une_contrainte in
Printf.printf "(%s, %s) " (string_of_entieretendu a) (string_of_entieretendu b)
;;
Out[242]:
val print_intervalle : intervalle -> unit = <fun>
In [243]:
let print_intervalles (contraintes : intervalles) =
List.iter print_intervalle contraintes
;;
Out[243]:
val print_intervalles : intervalles -> unit = <fun>
In [244]:
let flush_force () =
Printf.printf "\n";
flush_all();
Printf.printf "\n";
flush_all();
Printf.printf "\n";
flush_all();
;;
Out[244]:
val flush_force : unit -> unit = <fun>
In [245]:
let print_reseau (reseau : reseauSTP) : unit =
flush_force ();
Printf.printf "\nReseau =\n";
Array.iteri (fun i ligne ->
Array.iteri (fun j case ->
if case != [(MInf, PInf)] then begin
Printf.printf "\n T[i=%i, j=%i] = [" i j;
print_intervalles case;
Printf.printf "]";
end) ligne
) reseau;
flush_all ();
;;
Out[245]:
val print_reseau : reseauSTP -> unit = <fun>
In [246]:
stp_4;;
Out[246]:
- : reseauSTP =
[|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];
[(MInf, PInf)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
[(E 0, E 20); (E 40, E 40)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]
In [247]:
flush_force();;
T[i=3, j=3] = [(-oo, +oo) ]
Out[247]:
- : unit = ()
In [248]:
print_reseau stp_4;;
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
Out[248]:
- : unit = ()
On est prêt à écrire l'algorithme :
In [249]:
let algorithmePC ?(max_etape=10) (reseau : reseauSTP) : (reseauSTP * intervalles list) =
let resT = Array.map Array.copy reseau in (* on ne modifie pas l'entrée *)
let resS = ref [||] in
let n = Array.length resT in
let allseen = ref [] in (* Pour débogguer, je veux la liste des Tij vus *)
let etape = ref 0 in
begin
try begin
while !etape < max_etape && !resS != resT do
incr etape;
resS := Array.map Array.copy resT; (* S := T *)
for k = 0 to n - 1 do
for i = 0 to n - 1 do
for j = 0 to n - 1 do
Printf.printf "\n\nEtape %i, k = %i, i = %i, j = %i.\n" !etape k i j;
print_string "Contraintes :";
print_reseau resT;
resT.(i).(j) <- relaxe resT i j k;
allseen := (resT.(i).(j)) :: !allseen; (* on l'ajoute *)
if resT.(i).(j) = [] then
raise Fini
done
done
done
done;
end
with Fini -> () (* On ignore l'exception, on a juste terminé. *)
end;
resT, !allseen
;;
Out[249]:
val algorithmePC : ?max_etape:int -> reseauSTP -> reseauSTP * intervalles list = <fun>
Exemple de réseau non distributif¶
On va traiter l'exemple de la Figure 4 du texte, comme défini plus haut :
In [250]:
stp_4;;
Out[250]:
- : reseauSTP =
[|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];
[(MInf, PInf)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
[(E 0, E 20); (E 40, E 40)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]
In [251]:
relaxe stp_4 1 2 3;;
Out[251]:
- : intervalles = [(E 0, E 10)]
In [252]:
stp_4.(1).(3)
Out[252]:
- : intervalles = [(E 25, E 50)]
In [ ]:
In [253]:
algorithmePC stp_4;;
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 0, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 0, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 0, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 0, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 1, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 1, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 1, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 1, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 2, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 2, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 2, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 2, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 3, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 3, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 3, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 0, i = 3, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
T[i=3, j=3] = [(-oo, +oo) ]
Etape 1, k = 1, i = 0, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(0, 1) (10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(0, 10) ]
T[i=1, j=3] = [(25, 50) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(0, 20) (40, 40) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(-oo, +oo) ]
Out[253]:
- : reseauSTP * intervalles list =
([|[|[]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)]; [(MInf, PInf)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
[(E 0, E 20); (E 40, E 40)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|],
[[]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
[(E 0, E 20); (E 40, E 40)]; [(MInf, PInf)]; [(MInf, PInf)];
[(MInf, PInf)]; [(E 25, E 50)]; [(E 0, E 10)]; [(MInf, PInf)];
[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)];
[(MInf, PInf)]])
Je ne suis pas sûr de comment interprêter ce résultat...
- soit j'ai fait une erreur dans l'implémentation,
- soit l'algorithme PC devait ne rien modifier à $T$ sur cet exemple...
D'autres exemples¶
On peut étudier le STP de la Figure 1., en enlevant la contrainte $[60, \infty)$, qui ne rentre pas dans notre implémentation.
.
In [254]:
let t_01 : intervalles = [(E(10), E(20))];;
let t_12 : intervalles = [(E(30), E(40))];;
let t_32 : intervalles = [(E(10), E(20))];;
let t_34 : intervalles = [(E(20), E(30)); (E(40), E(50))];;
let t_40 : intervalles = [(E(60), E(70))];;
let stp_1 : reseauSTP = [|
[| t_vide; t_01; t_vide; t_vide; t_vide |];
[| t_vide; t_vide; t_12; t_vide; t_vide |];
[| t_vide; t_vide; t_vide; t_vide; t_vide |];
[| t_vide; t_vide; t_32; t_vide; t_34 |];
[| t_40; t_vide; t_vide; t_vide; t_vide |];
|];;
Out[254]:
val t_01 : intervalles = [(E 10, E 20)]
Out[254]:
val t_12 : intervalles = [(E 30, E 40)]
Out[254]:
val t_32 : intervalles = [(E 10, E 20)]
Out[254]:
val t_34 : intervalles = [(E 20, E 30); (E 40, E 50)]
Out[254]:
val t_40 : intervalles = [(E 60, E 70)]
Out[254]:
val stp_1 : reseauSTP =
[|[|[(MInf, PInf)]; [(E 10, E 20)]; [(MInf, PInf)]; [(MInf, PInf)];
[(MInf, PInf)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)]; [(MInf, PInf)];
[(MInf, PInf)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
[(MInf, PInf)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(E 10, E 20)]; [(MInf, PInf)];
[(E 20, E 30); (E 40, E 50)]|];
[|[(E 60, E 70)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
[(MInf, PInf)]|]|]
In [255]:
print_reseau stp_1;;
Out[255]:
- : unit = ()
T[i=3, j=3] = [(-oo, +oo) ]
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
In [256]:
algorithmePC stp_1;;
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 0, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 0, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 0, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 0, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 0, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 1, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 1, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 1, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 1, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 1, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 2, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 2, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 2, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 2, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 2, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 3, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 3, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 3, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 3, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 3, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 4, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 4, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(-oo, +oo) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 4, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 4, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 0, i = 4, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 0, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 0, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 0, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(-oo, +oo) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 0, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 0, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 1, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 1, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 1, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 1, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 1, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 2, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 2, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 2, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 2, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 2, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 3, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 3, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 3, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 3, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 3, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 4, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 4, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 4, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(-oo, +oo) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 4, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 1, i = 4, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 0, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 0, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 0, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 0, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 0, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 1, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 1, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 1, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 1, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 1, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 2, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 2, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 2, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 2, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 2, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 3, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 3, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 3, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 3, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 3, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 4, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 4, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 4, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 4, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 2, i = 4, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 0, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 0, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 0, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 0, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 0, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 1, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 1, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 1, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 1, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 1, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 2, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 2, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 2, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 2, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 2, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 3, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 3, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 3, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 3, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 3, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 4, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 4, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 4, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 4, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 3, i = 4, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 0, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 0, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 0, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 0, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 0, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 1, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 1, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 1, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 1, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 1, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 2, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 2, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 2, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 2, j = 3.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 2, j = 4.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 3, j = 0.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(-oo, +oo) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 3, j = 1.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(80, 100) (100, 120) ]
T[i=3, j=1] = [(-oo, +oo) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
T[i=4, j=4] = [(-oo, +oo) ]
Etape 1, k = 4, i = 3, j = 2.
Contraintes :
Reseau =
T[i=0, j=0] = [(-oo, +oo) ]
T[i=0, j=1] = [(10, 20) ]
T[i=0, j=2] = [(40, 60) ]
T[i=0, j=3] = [(-oo, +oo) ]
T[i=0, j=4] = [(-oo, +oo) ]
T[i=1, j=0] = [(-oo, +oo) ]
T[i=1, j=1] = [(-oo, +oo) ]
T[i=1, j=2] = [(30, 40) ]
T[i=1, j=3] = [(-oo, +oo) ]
T[i=1, j=4] = [(-oo, +oo) ]
T[i=2, j=0] = [(-oo, +oo) ]
T[i=2, j=1] = [(-oo, +oo) ]
T[i=2, j=2] = [(-oo, +oo) ]
T[i=2, j=3] = [(-oo, +oo) ]
T[i=2, j=4] = [(-oo, +oo) ]
T[i=3, j=0] = [(80, 100) (100, 120) ]
T[i=3, j=1] = [(90, 120) (110, 140) ]
T[i=3, j=2] = [(10, 20) ]
T[i=3, j=3] = [(-oo, +oo) ]
T[i=3, j=4] = [(20, 30) (40, 50) ]
T[i=4, j=0] = [(60, 70) ]
T[i=4, j=1] = [(70, 90) ]
T[i=4, j=2] = [(100, 130) ]
T[i=4, j=3] = [(-oo, +oo) ]
Out[256]:
- : reseauSTP * intervalles list =
([|[|[(MInf, PInf)]; [(E 10, E 20)]; [(E 40, E 60)]; [(MInf, PInf)];
[(MInf, PInf)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)]; [(MInf, PInf)];
[(MInf, PInf)]|];
[|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
[(MInf, PInf)]|];
[|[(E 80, E 100); (E 100, E 120)]; [(E 90, E 120); (E 110, E 140)];
[]; [(MInf, PInf)]; [(E 20, E 30); (E 40, E 50)]|];
[|[(E 60, E 70)]; [(E 70, E 90)]; [(E 100, E 130)]; [(MInf, PInf)];
[(MInf, PInf)]|]|],
[[]; [(E 90, E 120); (E 110, E 140)]; [(E 80, E 100); (E 100, E 120)];
[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)];
[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];
[(E ...); ...]; ...])
Je ne suis pas sûr de comment interprêter ce résultat...
- soit j'ai fait une erreur dans l'implémentation,
- soit l'algorithme PC devait ne rien modifier à $T$ sur cet exemple...
Conclusion¶
Voilà pour la question obligatoire de programmation :
- on a décomposé le problème en sous-fonctions,
- on a essayé d'être fainéant, en réutilisant les sous-fonctions,
- on a fait des exemples et on les garde dans ce qu'on présente au jury,
- on a testé la fonction exigée sur de petits exemples et sur un exemple de taille réelle (venant du texte)
Et on a essayé de faire un peu plus, en implémentant la vérification d'une contrainte de plus.
Bien-sûr, ce petit notebook ne se prétend pas être une solution optimale, ni exhaustive.