Répéter tant que⚓︎

Boucles while

Les boucles for sont utiles quand on connait le nombre d'itérations dont on aura besoin. Mais parfois, on ne sait pas à l'avance combien de tours de boucle seront nécessaires. Pour cela, on utilise une boucle tant que dont la syntaxe en Python est la suivante :

while CONDITION: # (1)!
    instruction_1
    instruction_2
    ...
    instruction_k

Les instructions seront répétées tant que CONDITION est vérifiée.

Lorsqu'on sort de la boucle, c'est que CONDITION n'est plus vérifiée.

Un premier exemple

Voici une fonction qui détermine la plus petite puissance de 2 supérieure ou égale à la valeur donnée en paramètre. On dit que c'est un algorithme de seuil.

def seuil(valeur):
    puissance = 1 # (1)! 
    while puissance < valeur: # (2)!
        puissance = puissance * 2 # (3)!
    return puissance # (4)!

On commence par la première puissance de 2, qui est \(2^0=1\).
Tant que la puissance actuelle est strictement inférieure à valeur, on continue.
On calcule la puissance suivante.
Si on sort de la boucle, c'est que \(\text{puissance} \geq \text{valeur}\), ce qui est ce que l'on cherche.

>>> seuil(7)
8
>>> seuil(8)
8
>>> seuil(35127)
65536

Vous pouvez tester la fonction ici

Évaluations restantes : ∞/∞

Vous pouvez remarquer que même avec des grandes valeurs, cette fonction va très très vite. Nous y reviendrons plus tard dans l'année.

Exercice 1

Écrire une fonction seuil2 qui prend en paramètre un entier valeur et renvoie l'exposant de la plus petite puissance de 2 supérieure ou égale à valeur.

Exemples

>>> seuil2(1) # (1)!
0
>>> seuil2(3) # (2)!
2
>>> seuil2(7) # (3)!
3
>>> seuil2(35) # (4)!
6

\(2^0 = 1\)
\(2^1 < 3 \leq 2^2\)
\(2^2 < 7 \leq 2^3\)
\(2^5 < 35 \leq 2^6\)

Indices

Indice 1

Reprendre le code de seuil n'est pas une si mauvaise idée.

Indice 2

Il faudrait une variable supplémentaire pour mémoriser l'exposant actuel.

Indice 3

puissance	exposant	commentaire
1	0	\(2^0 = 1\)
2	1	\(2^1 = 2\)
4	2	\(2^2 = 4\)
8	3	\(2^3 = 8\)
16	4	\(2^4 = 16\)
32	5	\(2^5 = 32\)
...	...	...

Indice 4

On peut remarquer que la valeur de l'exposant augmente de 1 lorsque la puissance est multipliée par 2.

Évaluations restantes : 5/5

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908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43997.43968.43976.43991.43979.43993.43990.43980.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43989.43985.43930.43910.43912.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43983.43984.43985.43988.43997.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43976.43981.43985.43979.43979.43993.43990.43995.43997.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43934.43988.43980.43907.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43982.43993.43988.43997.43981.43978.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43976.43981.43985.43979.43979.43993.43990.43995.43997.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43976.43981.43985.43979.43979.43993.43990.43995.43997.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43922.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43989.43985.43930.43910.43914.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43997.43968.43976.43991.43979.43993.43990.43980.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43997.43968.43976.43991.43979.43993.43990.43980.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43923.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43989.43985.43930.43910.43913.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43978.43997.43980.43981.43978.43990.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43997.43968.43976.43991.43979.43993.43990.43980.43908.43927.43979.43976.43993.43990.43910.43954.43908.43927.43995.43991.43996.43997.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43927.43980.43978.43910.43908.43927.43980.43993.43994.43988.43997.43910.43908.43927.43996.43985.43982.43910.43954.43908.43976.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43978.43997.43989.44007.43998.43993.43987.43997.44007.43984.43915.43930.43910.44010.43997.43989.43993.43978.43977.43981.43997.43979.43928.43906.43908.43927.43979.43976.43993.43990.43910.43908.43927.43976.43910.43954.43908.43976.43910.44020.43985.43999.43990.43997.43928.43982.43985.43996.43997.43908.43927.43976.43910.43954.43908.43976.43910.44017.43988.43928.43979.43981.43998.43998.43985.43980.43928.43996.43997.43928.43978.43993.43986.43991.43981.43980.43997.43978.43928.43981.43990.43928.43995.43991.43989.43976.43980.43997.43981.43978.43928.43976.43991.43981.43978.43928.43996.43857.43980.43997.43978.43989.43985.43990.43997.43978.43928.43988.43935.43997.43968.43976.43991.43979.43993.43990.43980.43926.43908.43927.43976.43910.43954.43908.43976.43910.44020.43985.43999.43990.43997.43928.43982.43985.43996.43997.43908.43927.43976.43910.43954.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43997.43980.43993.43985.43988.43979.43910

Attention aux boucles infinies

Contrairement à une boucle for, il n'est pas garanti qu'une boucle while se termine. Il faut donc bien faire attention à la condition utilisée. Nous verrons plus tard qu'il est possible de démontrer qu'une boucle se termine. Ce n'est pas toujours le cas, mais il est conseillé de bien vérifier que sa boucle peut se terminer. Si une boucle met trop de temps ou ne se termine pas :

Dans Thonny, il faut appuyer sur le bouton Stop pour interrompre l'exécution.
Sur le site, il faudra probablement fermer l'onglet pour arrêter le programme. Vous pouvez le réouvrir dans Firefox avec les touches Ctrl＋Shift＋T.

Vous pouvez tester le programme suivant sur Thonny :

À ne pas utiliser sur le site

n = 0
while n == 0:
    n = 0

Boucles for et boucles while

Les boucles for peuvent être vues comme un cas particulier des boucles while.

Ainsi, les codes suivants sont équivalents (à condition que les instructions ne modifient pas i) :

# Version avec une boucle bornée
for i in range(n):
    INSTRUCTION_1
    INSTRUCTION_2
    ...
    INSTRUCTION_n

# Version avec une boucle non bornée
i = 0
while i < n:
    INSTRUCTION_1
    INSTRUCTION_2
    ...
    INSTRUCTION_n
    i = i + 1

Les boucles non bornées sont donc plus générales et peuvent être utilisées à la place de n'importe quelle boucle bornée. Par contre, les boucles bornées sont plus simples à écrire.