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jeremy.meissner
cours
Commits
979a3941
Verified
Commit
979a3941
authored
1 year ago
by
orestis.malaspin
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corrected a lot of typos
parent
f0244f2b
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slides/cours_24.md
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View file @
979a3941
...
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@@ -32,7 +32,7 @@ initialiser(graphe) // tous sommets sont non-visités
file = visiter(sommet, vide) // sommet est un sommet
// du graphe
tant que !est_vide(file)
v = d
é
filer(file)
v = d
e
filer(file)
file = visiter(v, file)
file visiter(sommet, file)
...
...
@@ -463,7 +463,7 @@ tab dijkstra(graph, s, t)
. . .
*
Pour chaque nouveau noeud à visiter, il suffit d'enregistrer d'où on est venu!
*
On a besoin d'un tableau
`pr
écé
dent`
.
*
On a besoin d'un tableau
`pr
ece
dent`
.
## Modifier le pseudo-code ci-dessus pour ce faire (3min matrix)
...
...
@@ -475,7 +475,7 @@ tab dijkstra(graph, s, t)
tab, tab dijkstra(graph, s, t)
pour chaque v dans graphe
distance[v] = infini
pr
écé
dent[v] = indéfini
pr
ece
dent[v] = indéfini
q = ajouter(q, v)
distance[s] = 0
tant que non_vide(q)
...
...
@@ -489,8 +489,8 @@ tab, tab dijkstra(graph, s, t)
n_distance = distance[u] + w(u, v)
si n_distance < distance[v]
distance[v] = n_distance
pr
écé
dent[v] = u
retourne distance, pr
écé
dent
pr
ece
dent[v] = u
retourne distance, pr
ece
dent
```
# Algorithme de Dijkstra
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@@ -500,14 +500,14 @@ tab, tab dijkstra(graph, s, t)
. . .
```
C
pile parcours(pr
écé
dent, s, t)
pile parcours(pr
ece
dent, s, t)
sommets = vide
u = t
// on a atteint t ou on ne connait pas de chemin
si u != s && pr
écé
dent[u] != indéfini
si u != s && pr
ece
dent[u] != indéfini
tant que vrai
sommets = empiler(sommets, u)
u = pr
écé
dent[u]
u = pr
ece
dent[u]
si u == s // la source est atteinte
retourne sommets
retourne sommets
...
...
@@ -538,11 +538,11 @@ pile parcours(précédent, s, t)
## Trois fonction principales
```
C
booléen est_vide(
élé
ment) // triviale
élé
ment enfiler(
élé
ment, data, priorit
é
)
data d
é
filer(
élé
ment)
rien
modifi
er_priorit
é(élé
ment, data, prio
tié
)
nombre priorit
é(data
) // utilitaire
booléen est_vide(
ele
ment) // triviale
ele
ment enfiler(
ele
ment, data, priorit
e
)
data d
e
filer(
ele
ment)
rien
chang
er_priorit
e(ele
ment, data, prio
rite
)
nombre priorit
e(element
) // utilitaire
```
## Pseudo-implémentation: structure (1min)
...
...
@@ -550,10 +550,10 @@ nombre priorité(data) // utilitaire
. . .
```
C
struct
élé
ment
struct
ele
ment
data
priorit
é
élé
ment suivant
priorit
e
ele
ment suivant
```
# Les files de priorité
...
...
@@ -563,61 +563,61 @@ struct élément
. . .
```
C
élé
ment enfiler(
élé
ment, data, priorit
é
)
n_
élé
ment = cr
é
er_
élé
ment(data, priorit
é
)
si est_vide(
élé
ment)
retourne n_
élé
ment
si priorit
é(d
) > priorit
é
(e
.d
)
n_
élé
ment.suivant =
élé
ment
retourne n_
élé
ment
ele
ment enfiler(
ele
ment, data, priorit
e
)
n_
ele
ment = cr
e
er_
ele
ment(data, priorit
e
)
si est_vide(
ele
ment)
retourne n_
ele
ment
si priorit
e(n_element
) > priorit
e
(e
lement
)
n_
ele
ment.suivant =
ele
ment
retourne n_
ele
ment
sinon
tmp =
élé
ment
pr
é
c =
élé
ment
tant que !est_vide(tmp) && priorit
é
<
tmp.
priorit
é
pr
é
c = tmp
tmp =
ele
ment
pr
e
c =
ele
ment
tant que !est_vide(tmp) && priorit
e
< priorit
e(tmp)
pr
e
c = tmp
tmp = tmp.suivant
prev.suivant = n_
élé
ment
n_
élé
ment.suivant = tmp
retourne
élé
ment
prev.suivant = n_
ele
ment
n_
ele
ment.suivant = tmp
retourne
ele
ment
```
# Les files de priorité
## Pseudo-implémentation: d
é
filer (2min)
## Pseudo-implémentation: d
e
filer (2min)
. . .
```
C
data,
élé
ment d
é
filer(
élé
ment)
si est_vide(
élé
ment)
data,
ele
ment d
e
filer(
ele
ment)
si est_vide(
ele
ment)
retourne AARGL!
sinon
tmp =
élé
ment.data
n_
élé
ment =
élé
ment.suivant
lib
é
rer(
élé
ment)
retourne tmp, n_
élé
ment
tmp =
ele
ment.data
n_
ele
ment =
ele
ment.suivant
lib
e
rer(
ele
ment)
retourne tmp, n_
ele
ment
```
# Algorithme de Dijkstra avec file de priorité min
```
C
distance, pr
écé
dent dijkstra(graphe, s, t):
distance, pr
ece
dent dijkstra(graphe, s, t):
distance[source] = 0
fp = file_p_vide()
pour v dans sommets(graphe)
si v != s
distance[v] = infini
pr
écé
dent[v] = indéfini
pr
ece
dent[v] = indéfini
fp = enfiler(fp, v, distance[v])
tant que !est_vide(fp)
u, fp = d
é
filer(fp)
u, fp = d
e
filer(fp)
pour v dans voisinage de u
n_distance = distance[u] + w(u, v)
si n_distance < distance[v]
distance[v] = n_distance
pr
écé
dent[v] = u
fp = changer_priorit
é
(fp, v, n_distance)
retourne distance, pr
écé
dent
pr
ece
dent[v] = u
fp = changer_priorit
e
(fp, v, n_distance)
retourne distance, pr
ece
dent
```
# Algorithme de Dijkstra avec file
...
...
@@ -633,13 +633,13 @@ O(V) si v != s
O(V) fp = enfiler(fp, v, distance[v]) // notre impl est nulle
------------------O(V * V)-------------------------------
tant que !est_vide(fp)
O(1) u, fp = d
é
filer(fp)
O(1) u, fp = d
e
filer(fp)
---------------------------------------------------------
O(E) pour v dans voisinage de u
n_distance = distance[u] + w(u, v)
si n_distance < distance[v]
distance[v] = n_distance
O(V) fp = changer_priorit
é
(fp, v, n_distance)
O(V) fp = changer_priorit
e
(fp, v, n_distance)
---------------------------------------------------------
retourne distance
```
...
...
@@ -667,7 +667,7 @@ O(V) fp = changer_priorité(fp, v, n_distance)
## A chaque étape donner:
*
Le tableau des distances à
`a`
;
*
Le tableau des prédécess
u
eurs;
*
Le tableau des prédécesseurs;
*
L'état de la file de priorité.
# Algorithme de Dijkstra (corrigé)
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