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Comparaisons et booléens

En plus des calculs classiques, Python peut effectuer des comparaisons.

>>> 5 < 7
True
>>> 5 > 7
False
>>> 5 > 5
False
Les mots-clef True et False sont des valeurs booléennes qui correspondent à vrai et faux.

Expressions booléennes et tests

Ces valeurs servent pour des expressions booléennes, ou conditions. On peut ainsi éxecuter des instructions différentes selon si une condition est vérifiée ou non. En Python, la syntaxe est la suivante :

Syntaxe pour les tests
if CONDITION:
    ...  # code à éxecuter
    ...  # si le test est réussi
else:
    ...  # code à éxecuter
    ...  # si le test échoue
...  # suite du programme

On parle d'instruction conditionnelle ou plus simplement de test.

Comme toujours, en Python, l'indentation est importante pour délimiter les blocs. Il faut que le else soit aligné avec le if.

Exemples de tests 
>>> a = 3
>>> b = 5
>>> if a < b: # (1)!
        print("oui")
    else:
        print("non")

oui
  1. Puisque 3 < 5, la condition est vérifiée. On va donc afficher oui.
>>> a = 3
>>> b = 5
>>> if a > b: # (1)!
        print("oui")
    else:
        print("non")

non
  1. Puisque 3 > 5 est faux, la condition n'est pas vérifiée. On va donc afficher non.
Le else n'est pas obligatoire 
>>> a = 3
>>> b = 5
>>> if a < b: # (1)!
        print("oui")  # Cette instruction est exécutée.
    print("fini")  # Cette instruction est éxécutée quoi qu'il arrive.

oui
fini
  1. Puisque 3 < 5, la condition est vérifiée.
>>> a = 3
>>> b = 5
>>> if a > b: # (1)!
        print("oui")  # Cette instruction n'est pas exécutée
    print("fini")  # Cette instruction est éxécutée quoi qu'il arrive.

non
fini
  1. Puisque 3 < 5 est faux, la condition n'est pas vérifiée. On passe directement à la première instruction suivant l'instruction conditionnelle.
Un exemple de fonction avec un test

La fonction maximum prend comme paramètres deux nombres a et b, et renvoie le plus grand des deux.

def maximum(a, b):
    if a > b:
        return a
    else:
        return b

>>> maximum(5, 2)
5
>>> maximum(2, 5)
5
>>> maximum(5, 5)
5
Vous pouvez tester la fonction ci-dessous

###(Dés-)Active le code après la ligne # Tests (insensible à la casse)
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Tronquer ou non le feedback dans les terminaux (sortie standard & stacktrace / relancer le code pour appliquer)
Évaluations restantes : ∞/∞

On peut représenter le fonctionnement de cette fonction à l'aide d'un arbre de décision.

arbre arbre

Selon les valeurs de \(a\) et de \(b\), on peut avoir deux comportements différents.

arbre arbre

Si \(a \geq b\), c'est la branche de gauche qui est exécutée.

arbre arbre

Si \(a < b\), c'est la branche de droite qui est exécutée.

Exercice 3

Écrire le code de la fonction minimum qui prend comme paramètres deux nombres a et b, et renvoie le plus petit des deux.

Exemples
>>> minimum(5, 2)
2
>>> minimum(2, 5)
2
>>> minimum(5, 5)
5

###(Dés-)Active le code après la ligne # Tests (insensible à la casse)
(Ctrl+I)
Tronquer ou non le feedback dans les terminaux (sortie standard & stacktrace / relancer le code pour appliquer)
Évaluations restantes : 5/5

43908.43996.43997.43980.43993.43985.43988.43979.43928.43995.43988.43993.43979.43979.43909.43930.43980.43985.43976.43930.43910.43954.43908.43979.43981.43989.43989.43993.43978.43969.43910.44011.43991.43988.43981.43980.43985.43991.43990.43908.43927.43979.43981.43989.43989.43993.43978.43969.43910.43954.43908.43996.43985.43982.43928.43989.43993.43978.43987.43996.43991.43983.43990.43909.43930.43913.43930.43928.43979.43980.43969.43988.43997.43909.43930.43989.43993.43978.43999.43985.43990.43906.43913.43926.43919.43997.43989.43928.43913.43997.43989.43930.43928.43910.43954.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43930.43910.43908.43980.43993.43994.43988.43997.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43980.43993.43994.43988.43997.43930.43910.43908.43980.43978.43910.43908.43980.43984.43928.43995.43991.43988.43979.43976.43993.43990.43909.43930.43914.43930.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.90037.43928.44008.43978.43991.43976.43991.43979.43985.43980.43985.43991.43990.43928.43996.43997.43928.43995.43991.43978.43978.43997.43995.43980.43985.43991.43990.43908.43927.43979.43976.43993.43990.43910.43908.43927.43980.43984.43910.43908.43927.43980.43978.43910.43908.43980.43978.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43979.43930.43910.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43996.43985.43982.43930.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43913.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43914.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43915.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43916.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43917.43908.43927.43979.43976.43993.43990.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43995.43991.43996.43997.43930.43910.43908.43996.43985.43982.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43995.43991.43996.43997.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43996.43997.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43998.43930.43910.43989.43985.43990.43985.43989.43981.43989.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43924.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43994.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43985.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43934.43988.43980.43907.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43994.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43978.43997.43980.43981.43978.43990.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43997.43988.43979.43997.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43978.43997.43980.43981.43978.43990.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43994.43908.43927.43979.43976.43993.43990.43910.43954.43908.43927.43995.43991.43996.43997.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43927.43980.43978.43910.43908.43927.43980.43993.43994.43988.43997.43910.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43997.43980.43993.43985.43988.43979.43910
Les fonctions min et max

Python possède déjà deux fonctions qui permettent d'obtenir le minimum et le maximum de deux nombres : min(a, b) et max(a, b).

⚠ Bien entendu, vous ne pouvez pas utiliser ces deux fonctions dans tous les exercices où on veut déterminer un minimum ou un maximum.

Les opérateurs de comparaison

Python permet de faire toutes les comparaisons habituelles entre nombres :

En maths En Python
\(a = b\) a == b
\(a \neq b\) a != b
\(a > b\) a > b
\(a \geq b\) a >= b
\(a < b\) a < b
\(a \leq b\) a <= b

⚠ Il faut bien distinguer l'affectation (a = b) et le test d'égalité (a == b).

Exercice 4

Compléter la fonction pythagore qui prend comme paramètres 3 entiers a, b et c, et qui renvoie un booléen indiquant si les longueurs a, b et c, c étant la plus grande, permettent de former un triangle rectangle dont les côtés mesurent a, b et c.

Pour rappel, pour déterminer si un triangle est rectangle, il faut vérifier que \(a^2+b^2=c^2\).

Valeurs booléennes

En Python, les valeurs booléeenes sont True pour vrai et False pour faux. Les majuscules sont importantes.

Exemples
>>> pythagore(3, 4, 5)
True
>>> pythagore(3, 4, 6)
False
>>> pythagore(5, 4, 3)
False

###(Dés-)Active le code après la ligne # Tests (insensible à la casse)
(Ctrl+I)
Tronquer ou non le feedback dans les terminaux (sortie standard & stacktrace / relancer le code pour appliquer)
Évaluations restantes : 5/5

43908.43996.43997.43980.43993.43985.43988.43979.43928.43995.43988.43993.43979.43979.43909.43930.43980.43985.43976.43930.43910.43954.43908.43979.43981.43989.43989.43993.43978.43969.43910.44011.43991.43988.43981.43980.43985.43991.43990.43928.43934.43993.43989.43976.43907.43928.44010.43997.43989.43993.43978.43977.43981.43997.43979.43908.43927.43979.43981.43989.43989.43993.43978.43969.43910.43954.43908.43996.43985.43982.43928.43989.43993.43978.43987.43996.43991.43983.43990.43909.43930.43913.43930.43928.43979.43980.43969.43988.43997.43909.43930.43989.43993.43978.43999.43985.43990.43906.43913.43926.43919.43997.43989.43928.43913.43997.43989.43930.43928.43910.43954.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43930.43910.43908.43980.43993.43994.43988.43997.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43980.43993.43994.43988.43997.43930.43910.43908.43980.43978.43910.43908.43980.43984.43928.43995.43991.43988.43979.43976.43993.43990.43909.43930.43914.43930.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.90037.43928.44008.43978.43991.43976.43991.43979.43985.43980.43985.43991.43990.43928.43996.43997.43928.43995.43991.43978.43978.43997.43995.43980.43985.43991.43990.43908.43927.43979.43976.43993.43990.43910.43908.43927.43980.43984.43910.43908.43927.43980.43978.43910.43908.43980.43978.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43979.43930.43910.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43996.43985.43982.43930.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43913.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43914.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43915.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43916.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43917.43908.43927.43979.43976.43993.43990.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43995.43991.43996.43997.43930.43910.43908.43996.43985.43982.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43995.43991.43996.43997.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43996.43997.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43998.43930.43910.43976.43969.43980.43984.43993.43999.43991.43978.43997.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43924.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43994.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43924.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43995.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43985.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43908.43927.43979.43976.43993.43990.43910.43908.43979.43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