Parcours plus complexes
Mélanges et échanges
Exercice 8 : echange(tab, i, j)
Écrire le code la fonction echange
qui prend en paramètres un tableau tab
et deux entiers i
et j
, et qui échange les valeurs de tab
se trouvant aux indices i
et j
. On suppose que i
et j
sont des indices valides de tab
.
Exemples >>> tab = [ 15 , - 7 , 1 , 9 , 11 ]
>>> echange ( tab , 0 , 2 )
>>> tab
[1, -7, 15, 9, 11]
>>> echange ( tab , 2 , 4 )
>>> tab
[1, -7, 11, 9, 15]
Indication
Il faut juste échanger 2 valeurs dont on connaît les indices.
Pas besoin de parcourir tout le tableau.
43908.43996.43997.43980.43993.43985.43988.43979.43928.43995.43988.43993.43979.43979.43909.43930.43980.43985.43976.43930.43910.43954.43908.43979.43981.43989.43989.43993.43978.43969.43910.44011.43991.43988.43981.43980.43985.43991.43990.43908.43927.43979.43981.43989.43989.43993.43978.43969.43910.43954.43908.43996.43985.43982.43928.43989.43993.43978.43987.43996.43991.43983.43990.43909.43930.43913.43930.43928.43979.43980.43969.43988.43997.43909.43930.43989.43993.43978.43999.43985.43990.43906.43913.43926.43919.43997.43989.43928.43913.43997.43989.43930.43928.43910.43954.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43930.43910.43908.43980.43993.43994.43988.43997.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43980.43993.43994.43988.43997.43930.43910.43908.43980.43978.43910.43908.43980.43984.43928.43995.43991.43988.43979.43976.43993.43990.43909.43930.43914.43930.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.90037.43928.44008.43978.43991.43976.43991.43979.43985.43980.43985.43991.43990.43928.43996.43997.43928.43995.43991.43978.43978.43997.43995.43980.43985.43991.43990.43908.43927.43979.43976.43993.43990.43910.43908.43927.43980.43984.43910.43908.43927.43980.43978.43910.43908.43980.43978.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43979.43930.43910.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43996.43985.43982.43930.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43913.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43914.43908.43927.43979.43976.43993.43990.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43995.43991.43996.43997.43930.43910.43908.43996.43985.43982.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43995.43991.43996.43997.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43996.43997.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43998.43930.43910.43997.43995.43984.43993.43990.43999.43997.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43980.43993.43994.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43924.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43985.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43924.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43986.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43980.43993.43994.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44003.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43985.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44005.43924.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43980.43993.43994.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44003.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43986.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44005.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43980.43993.43994.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44003.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43986.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44005.43924.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43980.43993.43994.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44003.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43985.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44005.43908.43927.43979.43976.43993.43990.43910.43954.43908.43927.43995.43991.43996.43997.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43927.43980.43978.43910.43908.43927.43980.43993.43994.43988.43997.43910.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43997.43980.43993.43985.43988.43979.43910
Exercice 9 : melange(tab)
Pour mélanger aléatoirement les valeurs d'un tableau, on peut utiliser l'algorithme suivant :
On parcourt tab
par indice i
.
À chaque tour de boucle on tire au hasard un indice j
entre 0
et i
inclus.
On échange les éléments de tab
d'indice i
et j
.
Ce mélange permet d'obtenir un résultat totalemet aléatore en ne faisant qu'un parcours du tableau.
Écrire le code de la fonction melange
qui prend en paramètre un tableau tab
et qui mélange ce tableau selon l'algorithme précédent.
Exemples (aléatoire, donc vous aurez certainement d'autres résultats) >>> tab = list ( range ( 10 ))
>>> melange ( tab )
>>> tab
[1, 6, 5, 9, 2, 0, 7, 8, 4, 3]
>>> melange ( tab )
>>> tab
[5, 1, 7, 0, 2, 8, 4, 9, 3, 6]
>>> melange ( tab )
>>> tab
[5, 6, 1, 4, 2, 0, 8, 9, 7, 3]
La nature de cet exercice fait qu'il n'est pas possible de totalement vérifier le comportement de la fonction. La validation du code ne garantit pas la correction de la fonction.
Tirages aléatoires
Pour faire des tirages aléatoires en Python, il faut utiliser la bibliothèque random
. Nous allons utiliser la fonction randint
de cette bibliothèque. Elle est telle que ranint(a, b)
renvoie un entier tiré au hasard entre a
et b
tous les deux inclus.
Vous pouvez utiliser la fonction echange
de l'exercice précédent.
Exemples >>> from random import randint # pour importer la fonction
>>> random ( 1 , 7 )
4
>>> random ( 1 , 7 )
1
>>> random ( 1 , 7 )
5
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Exercice 10 : miroir(tab)
Compléter le code de la fonction miroir
qui prend en paramètre un tableau tab
et le modifie en place en inversant l'ordre des éléments. Le premier devient le dernier, le deuxième devient l'avant dernier et ainsi de suite.
Vous pouvez utiliser la fonction echange
de l'exercice 8.
Exemples >>> tab = [ 1 , 5 , 2 , 9 , - 1 , 8 ]
>>> miroir ( tab )
>>> tab
[8, -1, 9, 2, 5, 1]
Indices
Indice 1
L'élément d'indice 0
correspond à len(tab)-1
.
L'élément d'indice 1
correspond à len(tab)-2
.
...
L'élément d'indice len(tab)-1
correspond à 0
.
Indice 2
Attention, si on échange le premier avec le dernier et le dernier avec le premier, on n'a rien changé.
Il faut savoir s'arrêter à temps.
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Comparaisons
Attention à l'arrêt
Pour les fonctions suivantes, il faut parcourir les tableaux en comparant les valeurs deux à deux. Il faut faire attention aux valeurs données en paramètres pour range
:
Exercice 11 : valeurs_consecutives_egales ( nombres )
Compléter le code de la fonction valeurs_consecutives_egales
qui prend en paramètre un tableau d'entiers nombres
et renvoie True
si deux entiers consécutifs sont égaux et False
sinon.
Indices
Indice 1
Il faut comparer nombres[i]
et nombres[i+1
, où i
est la variable de boucle.
Indice 2
Si on utilise range ( len ( nombres ))
, on obtient une jolie erreur parce qu'on essaie de comparer nombres [ len ( nombres ) - 1 ]
et nombres [ len ( nombres )]
. Or ce dernier n'existe pas.
Peut-être qu'il faut s'arrêter un peu plus tôt...
Indice 3
Il faut utiliser range ( len ( nombres ) - 1 )
.
Exemples >>> valeurs_consecutives_egales ([ 5 , 3 , 5 ]) # les deux 5 ne se suivent pas directement
False
>>> valeurs_consecutives_egales ([ 3 , 5 , 5 ])
True
>>> valeurs_consecutives_egales ([ 3 ])
False
Exercice 12 : deux_entiers_consecutifs ( nombres )
Compléter le code de la fonction deux_entiers_consecutifs
qui prend en paramètre un tableau d'entiers nombres
et renvoie la liste des couples d'entiers consécutifs qui se suivent dans le tableau.
Vous pouvez utiliser append
pour construire la liste des résultats.
Exemples >>> deux_entiers_successifs ([ 3 , 4 ]) # 3 et 4 sont des entiers consécutifs
[(3, 4)]
>>> deux_entiers_successifs ([ 1 , 3 , 4 , 2 ])
[(3, 4)]
>>> deux_entiers_successifs ([ 1 , 3 , 7 , 4 , 2 ]) # 3 et 4, et 1 et 2 ne se suivent pas
[]
>>> deux_entiers_successifs ([ 4 , 3 , 2 , 1 ]) # les entiers ne sont pas dans le bon ordre
[]
>>> deux_entiers_successifs ([ 1 , 2 , 3 ])
[(1, 2), (2, 3)]
Exercice 13 : est_trie(tab)
Écrire le code de la fonction est_trie
qui prend en paramètre un tableau d'entiers tab
et renvoie True
si tous ses éléments sont dans l'ordre croissant et False
sinon.
Indices
Indice 1
Pour savoir si un tableau est trié, il suffit de comparer chaque élément avec le suivant.
Indice 2
Puisqu'on a besoin de regarder 2 valeurs en même temps, il faut faire un parcours par indice.
Indice 3
Si l'élément qu'on regarde est tab[i]
, alors le suivant est tab[...]
.
Indice 4
La dernière comparaison se fait entre l'avant-dernier élément et le dernier. Il faut donc que la parcours d'arrête une étape avant la fin du tableau.
Indice 5
Pour la boucle, il faut écrire for i in range ( len ( tab ) - 1 )
.
Exemples >>> est_trie ([ 1 , 2 , 2 , 4 , 9 , 19 ])
True
>>> est_trie ([ 3 , 2 , 1 ])
False
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# Tests
(insensible à la casse)(Ctrl+I)