Tests imbriqués et étude de cas

Étude de cas

Parfois, lorsqu'il y a plusieurs cas possibles, il faut plusieurs tests pour déterminer dans lequel on se trouve.

On dit qu'on fait une étude de cas.

La fonction ci-dessous est sensé afficher la mention obtenue à partir de la note (sur 20) :

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Essayer différentes notes et comparer ce qui est affiché avec ce qui est attendu.

Explications

On peut remarquer qu'il peut y avoir plusieurs affichages pour une même note :

>>> mention(15)
Mention B
Mention AB
Pas de mention
>>> mention(17)
Mention TB
Mention B
Mention AB

En fait, cela vient du fait que les tests sont indépendants les uns des autres. Voici ce qui se passe si on remplace note par 15 :

if 15 >= 12: # (1)!
    print("Mention AB")
if 15 >= 14: # (2)!
    print("Mention B")
if 15 >= 16: # (3)!
    print("Mention TB")
else:
    print("Pas de mention")

1. La condition est vérifiée, donc on va afficher Mention AB.
2. La condition est vérifiée, donc on va afficher Mention B.
3. La condition n'est pas vérifiée, donc on va afficher Pas de mention.

Ce n'est pas du tout le comportement attendu. On peut remarquer par exemple que si la note est strictement inférieur à 16, on aura toujours le message Pas de mention, ce qui n'est pas normal.

Globalement, le problème, c'est que même si un test est réussi, les suivants sont quand même évalués, ce qui peut provoquer d'autres affichages.

Tests imbriqués

Pour éviter les problèmes de l'exemple précédent, il faut imbriquer les tests. C'est-à-dire qu'il faut faire des tests dans des tests.

Vous pouvez tester cette nouvelle fonction et vous assurer qu'elle marche comme prévu.

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if ... elif ... else ...

À cause du système d'indentation, la lecture de cette fonction n'est pas si simple.

C'est pourquoi il existe une syntaxe permettant de simplifier la rédaction des études de cas :

Version avec des tests imbriqués

if test1:
    bloc1
else:
    if test2:
        bloc2
    else:
        bloc3

est équivalent à :

Version avec elif

if test1:
    bloc1
elif test2:
    bloc2
else:
    bloc3

Le mot-clef elif est une contraction de else if. On peut en mettre autant que nécessaire.

Et là aussi, le else n'est pas obligatoire.

C'est le bloc d'instructions associé au premier test vérifié qui ext exécuté, même si d'autres tests auraient pu être vérifiés.

Nouvelle version de mention

On peut donc écrire la fonction suivante, qui est équivalente à la précédente version :

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Ordre des tests

Il faut vraiment faire attention à l'ordre des testes.

Il faut que lorsque le premier test est vérifié, la note correspond au message que l'on veut afficher. Il faut donc commencer par note >= 16 ou note < 12.

Si on commence par note >= 14, il y a deux mentions possibles. Cela ne peut donc pas être le premier test de la liste.

Voici une explication de ce qui se passe dans la fonction :

def mention(note):
    if note >= 16: # (1)!
        print("Mention TB") # (2)!
    elif note >= 14: # (3)!
        print("Mention B") # (4)!
    elif note >= 12: # (5)!
        print("Mention AB") # (6)!
    else: # (7)!
        print("Pas de mention") # (7)!

1. 16 est la note correspondant à la mention la plus élevée.
2. Si on arrive là, c'est que la note est supérieure à 16.
3. Si on arrive là, c'est que la note est strictement inférieure à 16.
4. Si on arrive là, c'est que 14 <= note < 16.
5. Si on arrive là, c'est que la note est strictement inférieure à 14.
6. Si on arrive là, c'est que 12 <= note < 14.
7. Si on arrive là, c'est que la note est strictement inférieure à 12.
8. On n'a donc pas de mention.

Un autre exemple

La fonction suivante permet de déterminer le maximum de 3 nombres.

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On peut résumer les différents cas à l'aide de l'arbre de décision suivant :

Exercice 5 (sur papier)

Déterminer des valeurs pour \(a\), \(b\) et \(c\) qui correspondent à chacun des cas d'exécution possibles :

Cas 1Cas 2Cas 3Cas 4

Solutions

• Cas 1 : Il faut avoir \(a \geq b\) et \(a \geq c\). On peut prendre, par exemple, \(a=4\), \(b=3\) et \(c=2\) ou \(a=4\), \(b=2\) et \(c=3\).
• Cas 2 : Il faut avoir \(a \geq b\) et \(a < c\). On a donc \(c > a \geq b\). On peut prendre, par exemple, \(a=4\), \(b=3\) et \(c=5\).
• Cas 3 : Il faut avoir \(a < b\) et \(b \geq c\). On peut prendre, par exemple, \(a=4\), \(b=6\) et \(c=5\). ou \(a=5\), \(b=6\) et \(c=4\).
• Cas 4 : Il faut avoir \(a < b\) et \(b < c\). On a donc \(c > b > a\). On peut prendre, par exemple, \(a=2\), \(b=3\) et \(c=5\).

Savoir tester ses fonctions

L'exercice précédent est fondamental. Lorsqu'une fonction contient des instructions conditionnelles, il est très important de savoir déterminer des valeurs pour les paramètres qui permettent de couvrir tous les cas possibles afin de pouvoir tester la fonction pour rechercher des bugs.

Utiliser les fonctions précédentes

Parfois, il est possible d'utiliser des fonctions écrites précédemment pour simplifier le travail.

Par exemple, on peut remplacer maximum3(a, b, c) par maximum(maximum(a, b), c). On commence par déterminer le maximum entre a et b, puis on compare avec c.

Exercice 6

Pour éviter les tests imbriqués, on peut utiliser l'opérateur booléen and. L'expression booléenne TEST1 and TEST2 est vraie si et seulement si TEST1 et TEST2 sont tous les deux vrais.

On peut remarquer que dans maximum3, pour que la valeur renvoyée soit a, il faut que a >= b et a >= c soient tous les deux vrais.

Compléter le code de la fonction max3 qui se comporte exactement comme maximum3.

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987.43930.43910.43985.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43934.43999.43980.43907.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43994.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43983.43930.43910.43993.43990.43996.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43934.43999.43980.43907.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43995.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43978.43997.43980.43981.43978.43990.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43997.43988.43985.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43994.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43934.43999.43980.43907.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43983.43930.43910.43993.43990.43996.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43994.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43934.43999.43980.43907.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43995.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43978.43997.43980.43981.43978.43990.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43994.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43997.43988.43979.43997.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43978.43997.43980.43981.43978.43990.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43995.43908.43927.43979.43976.43993.43990.43910.43954.43908.43927.43995.43991.43996.43997.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43927.43980.43978.43910.43908.43927.43980.43993.43994.43988.43997.43910.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43997.43980.43993.43985.43988.43979.43910

Le retour de min et max

Ces deux fonctions peuvent également déterminer le minimum de 3, 4 ou plus, paramètres.

>>> min(7, 8, 1)
1
>>> max(7, 8, 1, 3, 4, 7, 5)
8

Exercice 7 (difficile)

Voici une autre version de max3.

def max3(a, b, c):
    if a > b and a > c:
        return a
    elif b > a and b > c:
        return b
    else:
        return c

Cette version comporte des bugs et ne donne pas toujours la bonne réponse.

La fonction est cachée dans l'IDE ci-dessous. Vous pouvez l'utiliser dans le terminal lorsque vous exécutez le programme, mais vous ne pouvez pas la modifier.

À vous de trouver au moins un cas où le résultat n'est pas celui attendu.

Indice

On n'a jamais dit que a, b et c devaient être tous différents...

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Solution

On peut remarquer que si \(a = b\), alors les deux premiers cas ne sont pas vérifiés. On arrive directement au else. On renvoie donc c sans avoir regardé sa valeur. Si on prend a=4, b=4 et c=1, la valeur renvoyée sera 1, alors qu'on attendait 4.

Exercice 8

Écrire le code de la fonction pythagore2 qui prend en paramètres 3 nombres a, b et c, et qui renvoie un booléen indiquant si on peut faire un triangle rectangle dont les côtés mesurent a, b et c dans n'importe quel ordre.

Contrairement à l'exercice 4, c n'est pas forcément la plus grande valeur des trois.

Exemples

>>> pythagore2(3, 4, 5)
True
>>> pythagore2(5, 3, 4)
True
>>> pythagore2(4, 5, 3)
True
>>> pythagore2(6, 3, 4)
False

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(Ctrl+S)Valider
(Ctrl+Enter)TéléchargerTéléverserRéinitialiser l'éditeurSauvegarder dans le navigateurÉvaluations restantes : 5/5

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