Tableaux Ă 2 dimensions
Dimension des tableaux Ă 2 dimensions
On dit qu'un tableau à 2 dimensions est de taille \(m\times n\) s'il a \(m\) sous-tableaux de \(n\) éléments.
Dans tous les exercices, on supposera que les tableaux Ă deux dimensions ne sont pas vides.
Exercice 14 : initialise(m, n)
Ăcrire le code de la fonction initialise
qui prend en paramĂštres deux entiers m
et n
et qui renvoie un tableau Ă 2 dimensions de taille m
Ăn
ne contenant que des 0.
Il y a également un paramÚtre optionnel, avec la valeur 0 par défaut, qui permet de choisir la valeur contenue dans toutes les cases du tableau.
Exemples >>> initialise ( 2 , 3 )
[[0, 0, 0], [0, 0, 0]]
>>> initialise ( 2 , 3 , 9 )
[[9, 9, 9], [9, 9, 9]]
Exercice 15 : plus_grand_de(tableau)
Ăcrire le code de la fonction plus_grand_de
qui prend en paramĂštre un tableau Ă deux dimensions et qui renvoie un triplet composĂ© de la plus grande valeur contenue dans le tableau, l'indice de la ligne et l'indice de la colonne oĂč cette valeur se trouve.
On supposera que cette valeur n'apparaĂźt qu'une fois dans le tableau.
Exemples >>> maximum ([[ 1 , 2 , 4 ], [ 2 , 1 , 3 ]])
(4, 0, 2)
>>> maximum ([[ - 21 , - 89 , - 121 ], [ - 17 , - 99 , - 151 ], [ - 25 , - 36 , - 94 ]])
(-17, 1, 0)
Indication
Si on mémorise les coordonnées de la plus grande valeur du tableau, il n'est pas nécessaire de mémoriser sa valeur. Il suffit d'aller la rechercher en utilisant les indices quand on en a besoin.
Exercice 16 : affichage_simple(tableau)
Ăcrire le code de la fonction affichage_simple
qui prend en paramĂštre un tableau Ă deux dimensions et qui affiche les sous-tableaux, un par ligne.
Exemple >>> affichage_simple ([[ - 21 , - 89 , - 121 ], [ - 17 , - 99 , - 151 ], [ - 25 , - 36 , - 94 ]])
[-21, -89, -121]
[-17, -99, -151]
[-25, -36, -94]
Vous pourrez utiliser cette fonction dans tous les exercices suivants.
Exercice 17 : diagonale1(n)
Ăcrire le code de la fonction diagonale1
qui prend en paramĂštre un entier n
et qui renvoie un tableau Ă deux dimensions de taille n
Ăn
composée uniquement de 0, sauf sur la diagonale allant du coint en haut à gauche au coin en bas à droite, composée de 1.
Exemple >>> affichage_simple ( diagonale1 ( 5 ))
[1, 0, 0, 0, 0]
[0, 1, 0, 0, 0]
[0, 0, 1, 0, 0]
[0, 0, 0, 1, 0]
[0, 0, 0, 0, 1]
Exercice 18 : diagonale2(n)
Ăcrire le code de la fonction diagonale2
qui prend en paramĂštre un entier n
et qui renvoie un tableau Ă deux dimensions de taille n
Ăn
composée uniquement de 0, sauf sur la diagonale allant du coint en haut à droite au coin en bas à gauche, composée de 1.
Exemple >>> affichage_simple ( diagonale2 ( 5 ))
[0, 0, 0, 0, 1]
[0, 0, 0, 1, 0]
[0, 0, 1, 0, 0]
[0, 1, 0, 0, 0]
[1, 0, 0, 0, 0]
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Exercice 19 : diagonales(n)
Ăcrire le code de la fonction diagonales
qui prend en paramĂštre un entier n
et qui renvoie un tableau Ă deux dimensions de taille n
Ăn
composée uniquement de 0, sauf sur les deux diagonales, composées de 1.
Exemple >>> affichage_simple ( diagonales ( 5 ))
[1, 0, 0, 0, 1]
[0, 1, 0, 1, 0]
[0, 0, 1, 0, 0]
[0, 1, 0, 1, 0]
[1, 0, 0, 0, 1]
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1.43996.43997.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43927.43980.43978.43910.43908.43927.43980.43993.43994.43988.43997.43910.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43997.43980.43993.43985.43988.43979.43910
Exercice 20 : que_col(n, k)
Ăcrire le code de la fonction que_col
qui prend en paramĂštres deux entiers n
et k
, et qui renvoie un tableau Ă deux dimensions de taille n
Ăn
composée uniquement de 0, sauf sur la colonne d'indice k
composée de 1. On suppose que k
< n
.
Exemple >>> affichage_simple ( que_col ( 5 , 3 ))
[0, 0, 0, 1, 0]
[0, 0, 0, 1, 0]
[0, 0, 0, 1, 0]
[0, 0, 0, 1, 0]
[0, 0, 0, 1, 0]
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Exercice 21 : que_col_paires(n)
Ăcrire le code de la fonction que_col_paires
qui prend en paramĂštre un entier n
et qui renvoie un tableau Ă deux dimensions de taille n
Ăn
composée uniquement de 0, sauf sur les colonnes d'indice pair, composée de 1.
Exemple >>> affichage_simple ( que_col_paires ( 5 ))
[1, 0, 1, 0, 1]
[1, 0, 1, 0, 1]
[1, 0, 1, 0, 1]
[1, 0, 1, 0, 1]
[1, 0, 1, 0, 1]
Exercice 22 : addition(n)
Ăcrire le code de la fonction addition
qui prend en paramĂštre un entier n
et qui renvoie un tableau Ă deux dimensions de taille n
Ăn
dont chaque case contient la somme de l'indice de la ligne et celui de la colonne.
Exemple >>> affichage_simple ( addition ( 5 ))
[0, 1, 2, 3, 4]
[1, 2, 3, 4, 5]
[2, 3, 4, 5, 6]
[3, 4, 5, 6, 7]
[4, 5, 6, 7, 8]
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Exercice 23 : damier(n)
Ăcrire le code de la fonction damier
qui prend en paramĂštre un entier n
et qui renvoie un tableau Ă deux dimensions de taille n
Ăn
dont une case sur deux vaut 1 et les autres valent 0. La case en haut Ă gauche vaut 1.
Exemple >>> affichage_simple ( damier ( 5 ))
[0, 1, 0, 1, 0]
[1, 0, 1, 0, 1]
[0, 1, 0, 1, 0]
[1, 0, 1, 0, 1]
[0, 1, 0, 1, 0]
Indications
Vous pouvez comparer les cases contenant des 1 avec damier
avec la parité des valeurs du tableau généré par addition
.
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Exercice 24 : transpose(tableau)
Ăcrire le code de la fonction transpose
qui prend en paramĂštre un tableau Ă deux dimensions tableau
de taille m
Ăn
et qui renvoie un tableau Ă deux dimensions de taille n
Ăm
, que l'on nommera tab
, et qui est tel que tableau[i][j]
=tab[j][i]
pour tous les indices valides i
et j
.
Exemple >>> transposer ([[ 10 , 11 , 12 ], [ 20 , 21 , 22 ]])
[[10, 20], [11, 21], [12, 22]]
Pour un affichage plus agréable
On considĂšre la fonction ci-dessous qui permet de faire lâaffichage dâun tableau Ă 2 dimensions, en indiquant les indices :
Explications
On cherche la plus grande valeur contenue dans le tableau (on ne mémorise pas ses coordonnées).
On détermine le maximum entre cette plus grande valeur, le nombre de lignes et le nombre de colonnes.
On en déduit le nombre de symboles qu'il faut pour représenter ce maximum, plus 1.
On fait de mĂȘme pour dĂ©terminer la taille nĂ©cessaire pour la colonne de gauche.
On affiche la premiÚre ligne puis la ligne de séparation.
On affiche ensuite chaque ligne.
La méthode texte . rjust ( k )
correspond Ă un texte se terminant par texte
à droite et complétant avec des espaces à gauche si nécessaire jusqu'à avoir au minimum k
symboles.
L'expression '' . join ( iterable )
correspond Ă un texte oĂč tout le contenu de iterable
, qui doit ĂȘtre composĂ© de textes, est concatĂ©nĂ© sans espaces ou retour Ă la ligne.
Exemple >>> affichage_avance ([[ 21 , 89 , 121 ], [ 17 , 99 , 151 ], [ 25 , 36 , 94 ]], "Tableau" )
Tableau| 0 1 2
-------+------------
0| 21 89 121
1| 17 99 151
2| 25 36 94
Exercice 25 : table_addition(n)
Ăcrire le code de la fonction table_addition
qui prend en paramĂštre un entier n
et qui affiche la table d'addition de a
et b
avec a
et b
entre 0 et n
-1.
Vous pouvez utiliser des fonctions réalisées dans les exercices précédents.
Exemple >>> table_addition ( 4 )
+| 0 1 2 3
--+--------
0| 0 1 2 3
1| 1 2 3 4
2| 2 3 4 5
3| 3 4 5 6
43908.43996.43997.43980.43993.43985.43988.43979.43928.43995.43988.43993.43979.43979.43909.43930.43980.43985.43976.43930.43910.43954.43908.43979.43981.43989.43989.43993.43978.43969.43910.44011.43991.43988.43981.43980.43985.43991.43990.43908.43927.43979.43981.43989.43989.43993.43978.43969.43910.43954.43908.43996.43985.43982.43928.43989.43993.43978.43987.43996.43991.43983.43990.43909.43930.43913.43930.43928.43979.43980.43969.43988.43997.43909.43930.43989.43993.43978.43999.43985.43990.43906.43913.43926.43919.43997.43989.43928.43913.43997.43989.43930.43928.43910.43954.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43930.43910.43908.43980.43993.43994.43988.43997.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43980.43993.43994.43988.43997.43930.43910.43908.43980.43978.43910.43908.43980.43984.43928.43995.43991.43988.43979.43976.43993.43990.43909.43930.43914.43930.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.90037.43928.44008.43978.43991.43976.43991.43979.43985.43980.43985.43991.43990.43928.43996.43997.43928.43995.43991.43978.43978.43997.43995.43980.43985.43991.43990.43908.43927.43979.43976.43993.43990.43910.43908.43927.43980.43984.43910.43908.43927.43980.43978.43910.43908.43980.43978.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43979.43930.43910.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43996.43985.43982.43930.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43913.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43914.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43915.43908.43927.43979.43976.43993.43990.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43995.43991.43996.43997.43930.43910.43908.43996.43985.43982.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43995.43991.43996.43997.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43996.43997.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43998.43930.43910.43980.43993.43994.43988.43997.44007.43993.43996.43996.43985.43980.43985.43991.43990.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43990.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43980.43993.43994.43988.43997.43993.43981.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43996.43996.43985.43980.43985.43991.43990.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43990.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43993.43998.43998.43985.43995.43984.43993.43999.43997.44007.43993.43982.43993.43990.43995.43997.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43980.43993.43994.43988.43997.43993.43981.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43924.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43979.43914.43930.43910.43934.43977.43981.43991.43980.43907.43923.43934.43977.43981.43991.43980.43907.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43908.43927.43979.43976.43993.43990.43910.43954.43908.43927.43995.43991.43996.43997.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43927.43980.43978.43910.43908.43927.43980.43993.43994.43988.43997.43910.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43997.43980.43993.43985.43988.43979.43910
# Tests
(insensible Ă la casse)(Ctrl+I)