Jeu du plus ou moins

Deviner le nombre

Règles du jeu

Dans cette partie, nous allons programmer le jeu où un joueur fait deviner un nombre à l’autre. Celui qui devine propose des valeurs et l'autre lui indique si le nombre à trouver est plus grand ou plus petit, jusqu'à ce que la bonne valeur ait été trouvée.

Vous pouvez tester ce jeu ci-dessous. Attention, l'ordinateur se débrouillera pour vous faire faire le nombre maximum d'essais. Nous verrons plus tard comment. Le premier paramètre correspond à la valeur minimale possible et le second à la valeur maximale.

###(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)

Exécuter le code
(Ctrl+S)TéléchargerTéléverserRéinitialiser l'éditeurSauvegarder dans le navigateurÉvaluations restantes : ∞/∞

Exercice 6

Compléter la fonction devine_nombre qui a deux paramètres optionnels qui sont des nombres entiers mini et maxi, et qui permet de jouer contre l'ordinateur. Ce dernier tire un entier au hasard entre mini et maxi inclus. Le joueur propose alors des nombres et l'ordinateur lui dit si le secret est plus grand ou plus petit, jusqu'à ce qu'il trouve. À la fin, on lui indique le nombre d'essais qu'il a fait.

Exemple d'utilisation (attention, le déroulement est aléatoire

>>> devine_nombre(1, 63)
Donne un nombre entre 1 et 63 : 32
C'est moins
Donne un nombre entre 1 et 63 : 16
Bravo
Tu as trouvé en 2 coups

###(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)

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

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Exercice 7

Écrire une fonction devine_nombre_aide qui prend comme paramètres 3 entiers optionnels, mini, maxi et secret. Cette fonction se comporte comme devine_nombre, sauf qu'au moment de demander la prochaine valeur, on indique le meilleur nombre à proposer. De plus, on indique clairement les valeurs minmale et maximuale possibles.

Si secret n'est pas entre mini et maxi, on choisit un nombre au hasard. Sinon, c'est la valeur de secret qui est utilisée. Cela permet de tester plus facilement la fonction.

On suppose que l'utilisateur ne proposera que des nombres entre les valeurs minimales et maximales. Mais on pourra améliorer la fonction pour que les réponses restent valides même s'il donne des valeurs trop grandes ou trop petites.

Exemples d'utilisation

>>> devine_nombre_aide(1, 20)
Donne un nombre entre 1 et 20 (10 serait une bonne idée) : 10
C'est plus
Donne un nombre entre 11 et 20 (15 serait une bonne idée) : 15
C'est moins
Donne un nombre entre 11 et 14 (12 serait une bonne idée) : 12
C'est moins
Donne un nombre entre 11 et 11 (11 serait une bonne idée) : 11
Bravo
Tu as trouvé en 4 coups
>>> devine_nombre_aide(1, 1000, 397)
Donne un nombre entre 1 et 1000 (500 serait une bonne idée) : 397
Bravo
Tu as trouvé en 1 coups

Indice

Il faut penser à mettre mini et maxi à jour en fonction des réponses.

###(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)

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

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Faire deviner le nombre

Exercice 8

Compléter le code de la fonction ordinateur qui prend en paramètres optionnels deux entiers mini et maxi, et qui consiste à faire deviner à l'ordinateur un nombre entre mini et maxi. L'ordinateur propose des valeurs et vous devez lui indiquer si le nombre à chercher est plus grand (+), plus petit (-) ou s'il a trouvé (=).

Exemples d'utilisation

>>> ordinateur(1, 5)
Pense à un nombre entre 1 et 5
C'est 3 ? (+/-/=) -
C'est 1 ? (+/-/=) +
C'est 2 ? (+/-/=) =
J'ai trouvé en 3 coups
>>> ordinateur(1, 5)
Pensez à un nombre entre 1 et 5
C'est 3 ? (+/-/=) -
C'est 1 ? (+/-/=) -
Dis donc, tu triches, non ?

Indication

Le plus dur, c'est de trouver la condition pour continuer de jouer. Il est parfois préférable de prendre le contraire de la condition indiquant qu'il faut s'arrêter.

Dans notre cas, il y a 2 conditions qui font qu'on doit s'arrêter :

• On a trouvé le bon nombre.
• Il n'y a plus de valeurs possibles.

###(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)

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

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Exercice 9

Compléter le code de la fonction ordinateur2 qui prend en paramètres un entier secret et deux entiers optionnels mini et maxi, et qui renvoie le nombre de coups qu'il faut pour trouver secret entre mini et maxi avec la méthode par dichotomie. Si secret n'est pas entre mini et maxi, la réponse est 0.

Exemples d'utilisation

>>> ordinateur2(190, 1, 3000)
11
>>> ordinateur2(0, 1, 3000)
0
>>> {i: ordinateur2(i, 1, 7) for i in range(1, 8)}
{1: 3, 2: 2, 3: 3, 4: 1, 5: 3, 6: 2, 7: 3}

La dernière expression permet de créer un dictionnaire qui associe à chaque nombre de tentatives qu’il faut pour le trouver. Ainsi, il faut 3 tentatives pour trouver 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)

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

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Exercice 10

Compléter le code de la fonction nb_moyen qui prends en paramètres optionnels deux entiers mini et maxi et qui renvoie le nombre moyens d'essais qu'il faut pour deviner chacun des entiers entre mini et maxi.

Vous pouvez, et devriez, utiliser ordinateur2.

Exemples d'utilisation

>>> nb_moyen()
5.095238095238095
>>> nb_moyen(1, 1000000)
18.951445

###(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)

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

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Pour aller plus loin

Exercice 11

Écrire le code de la fonction ordi_malin (que vous avez pu tester au début de cette page), qui prend en paramètres optionnels deux entiers mini et maxi, et qui fait deviner un nombre entre mini et maxi Le nombre n'est pas choisi à l'avance et l'ordinateur s'adapte aux réponses afin de maximiser le nombre d'essais nécessaires.

L'idée, c'est de bien mémoriser la plus petite et la plus grande valeur possible. Lorsque l'utilisateur propose un nombre, il faut regarder s'il y a plus de valeurs possibles strictement inférieures à ce nombre ou strictement supérieures à ce nombre. On indiquera toujours à l'utilisateur le résultat correspondant à l'ensemble le plus grand.

S'il y a autant de nombres des deux côtés, on proposera d'aller chercher du côté des nombres inférieurs à la proposition de l'utilisateur.

Exemple d'utilisation

>>> ordi_malin(1, 10)
Donne un nombre entre 1 et 10 : 5
C'est plus
Donne un nombre entre 1 et 10 : 7
C'est plus
Donne un nombre entre 1 et 10 : 9
C'est moins
Donne un nombre entre 1 et 10 : 8
Tu as trouvé en 4 coups
>>> ordi_malin(1, 10)
Donne un nombre entre 1 et 10 : 6
C'est moins
Donne un nombre entre 1 et 10 : 3
C'est moins
Donne un nombre entre 1 et 10 : 2
C'est moins
Donne un nombre entre 1 et 10 : 1
Tu as trouvé en 4 coups

###(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)

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

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Une autre utilisation de la dichotomie

La dichotomie est aussi utilisée pour chercher des valeurs approchées de solutions d'équations que l'on ne sait pas ou ne peut pas calculer en un temps raisonnable. Dans ce cas, on va s'arrêter lorsque la taille de l'intervalle est inférieur à un seuil déterminé à l'avance.

Par exemple, la fonction suivante permet de déterminer une valeur approchée de la racine carrée de n, avec une erreur de moins de seuil :

###(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)

Exécuter le code
(Ctrl+S)TéléchargerTéléverserRéinitialiser l'éditeurSauvegarder dans le navigateurÉvaluations restantes : ∞/∞

Il est possible de donner des valeurs de g ou de d, mais si elles ne sont pas valides, on prend des valeurs qui permettent de trouver la réponse. C'est surtout utile lorsqu'il peut y avoir plusieurs solutions à une équations.

Exemples d'utilisation

>>> recherche_racine(7, 0.0001)
La racine de 7 est entre 2.645721435546875 et 2.6457748413085938
>>> recherche_racine(7, 0.0001, 0, 1)
La racine de 7 est entre 2.645721435546875 et 2.6457748413085938
>>> recherche_racine(7, 0.0001, 2, 3)
La racine de 7 est entre 2.64569091796875 et 2.645751953125
>>> recherche_racine(7, 0.0000000001)
La racine de 7 est entre 2.6457513110144646 et 2.6457513110653963
>>> recherche_racine(100001023, 0.000000001)
La racine de 100001023 est entre 10000.051149868865 et 10000.05114986956
>>> recherche_racine(4, 0.0000000001)
La racine de 4 est 2.0
>>> recherche_racine(25, 0.0000000001)
La racine de 25 est entre 4.99999999992724 et 5.00000000001819

On peut remarquer que la solution exacte, même lorsqu'elle est entière, n'est pas forcément trouvée.