Exercices - série 2
Exercice 1 : recherche dichotomique
Recherche dichotomique
Bob a voulu écrire une version récursive de la recherche par dichotomie.
Malheureusement son code ne fonctionne pas. Corrigez-le.
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Exercice 2 : parité
Parité
Compléter la fonction suivante qui doit être une fonction récursive.
⚠️ Il est interdit d'utiliser %
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Indice pour la parité
n et n - 2 ont la même parité (tous les deux pairs, ou tous les deux impairs)
Exercice 3 : longueur d'une liste
Longueur de liste
Compléter la fonction suivante qui doit être une fonction récursive.
⚠️ Il est interdit d'utiliser len
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Indice pour la longueur d'une liste
Vous pouvez utiliser .pop()
Exercice 4 : bégaiement
bégaiement
Ecrire une fonction récursive repeat qui prendra en argument un entier n et une chaine de caractère txt, et qui renvoie une chaine de caractères qui contient n fois la chaine de caractères txt juxtaposées.
Exemple: repeat(5, "bla") renvoie blablablablabla
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Exercice 5 : La tête à Toto
La tête à Toto
Compléter la fonction récursive toto telle que :
toto(0) renvoie '0'
toto(1) renvoie '(0 + 0)'
toto(2) renvoie '((0 + 0) + (0 + 0))'
- etc sur le même principe
On garantit que n est un entier positif ou nul.
Compléter ci-dessous
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Exercice 6 : Test de palindrome
Palindrome
Un mot est un palindrome s'il se lit de la même façon de droite à gauche comme de gauche à droite.
Exercice
Écrire une fonction récursive est_palindrome qui prend en paramètre une chaine de caractères mot et renvoie le booléen True si mot est un palindrome ou False sinon.
Premiers indices
- Le premier caractère de la chaine
mot est mot[0]
- Le dernier caractère de la chaine
mot est mot[-1]
- Pour une copie d'une tranche ("slice" en anglais) du second jusqu'à l'avant-dernier caractère d'une chaine
mot, on peut écrire mot[1:-1]
Derniers indices
- Si la chaine fait zéro ou un caractère, c'est un palindrome.
- Sinon on peut comparer le premier et le dernier caractère.
- Enfin, un appel récursif permet de répondre sur le reste de la chaine.
Palindrome
Compléter ci-dessous
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Exercice 7 : triangles
A faire
Écrire deux fonctions (procédures) récursives triangle_bas, puis triangle_haut prenant un entier n non nul en paramètre et qui affichent un triangle. Ces fonctions ne renvoient rien.
Python Console Session>>> triangle_bas(4) # affiche un triangle tête en bas
####
###
##
#
Python Console Session>>> triangle_haut(4) # affiche un triangle tête en haut
#
##
###
####
Triangles
Compléter ci-dessous
Solution
Attention
L'ordre des instructions est bien sûr important !
Pythondef triangle_bas(n):
"""Affiche un triangle tête en bas"""
if n > 0:
print("#" * n)
triangle_bas(n - 1)
def triangle_haut(n):
"""Affiche un triangle tête en haut"""
if n > 0:
triangle_haut(n - 1)
print("#" * n)
Exercice 8 : Si vous avez du temps ... problème de la grenouille
🐸
Une grenouille doit monter un escalier. Quand elle saute pour monter, elle monte de 1 ou 2 marches.
Combien de chemins différents existent-ils pour un escalier de n marches ?
Vous êtes en complète autonomie pour cet exercice facultatif.
👉 Montrer au professeur votre solution, ou vos tentatives.
La fonction nbre_chemins prend en paramètre un entier n que l'on garantit strictement supérieur à zéro.
Compléter ci-dessous
.128013vt4=wf2pmuP(è751:,cSsrézk63;0 dg)/N+nqiyelRhb_CoaA.-050F0P0c0X0N0Q0v0E0t0Q0X0v0v0e010c0N0i010406050v0k0j0j0X0w0O040u0W0Q0k0^0W0L0E020X0j0i0C0E0R0P120w0M0k0P0v050I0 1113150}0i04051A1t1D0I1A0}0F0N0b0-0/0;0?0/0L0G0k0X0G0P0!0i0O0c0S1c0E0S0N0G0S0Q1)0S0c0{050(0T0Q0P1M0:0=011(1*1,1*0c1=1@1:0c0w1B1!0-180v0i0X0L0?0h011_1O010g0*0P0L1g0P1:2b2d2i1{2l1@2o0j2q040a0E0l0w0W0i0W0v0N1b1d0$290w0w0P0t2L1t2s0L1B0I1!2X2527261;0F2u1P0N0L2n2I1:1J1L0.1`2+2-0L0W2;1:0i2Q1B2V2X310~2c1d2?2j2`0w120Q1:0X1%2Q0g0?030U0U0t2{0P1,2_0W0!0q0D3s0{0q1t0X32350|342t371{393b3d3f0P3h013j3l3n3p2.3s3u2g040h3y3A2d3C2V2*013H0X3c1B3e0S3g3i3k3m0$3R2`3T0!0B0{0B3Y2U3B0}3$3F0?3)3+053-3/3N3;3Q2,3S3t0!0d0{0d3~1u403D361N3G0W3a3*3J3.3L3:3P3?4d3^4f0p0{0p4k3141353%454u493O3=3o4A3r4f0A0{0A4G4m424p444r3I3,3K3M4O4c3q3_0o0{0o4X3!1E2 1t2;2!0F272)43014P2:1K1B2~0P303B3 4?4P572t0N0F0?3k2V3_0q3J5e5g4y4Q4-4f5k0E2y0P5n4P3@4S3u5k2X3z4n3%0z0{0$0g592W5E4 0f0{0E5K5c4o2@3(0g0{0L0T2Q3l0S1m2,1s4l4?4Z5U0`040m5R5M4!3(5X5;5,2j5.0H0r5R0}5*5L3$5m015h353_3V470E644b4z5q3U2h5u5w4,4e6g5C040E6p5Q5`1{5G040N5J616o5=5U0L5^6y6r4J4 0W0{0e0e5R6F3E5?0j0N3w5_6G5?5.5~6y6033635f650U5i4f3{4(6c5o5y3_3{5t2p6j6e6l3`1:0I3z6q6~6N5T2j6u2Q0c0k0w0L6M6A2j6Q6S6Y6T5d6$662d3_4h6,7h6.4R7k6h6?6%5x7p4f7l3Y6~7a6t0{4Q6x31704K6D7F7A0?6I046K796s0?7c3W7f711{6W5 7U6b7n6)3u4D7m6@5p6_4D6=2z7*6/4C6{6}6 6p7K01730%76786E7`7S3X7e6y5E6-7$0!4U7)7t6k4B3u4U7.5v8c6^8e897?6o6q7`6u3o0v0P7Z4 7X846!4J87674f4/8b6d7+8l4/8h7:7v3u8E7y7^7G4 7|75777P6U6B5X5Z0P5#5%0L5)8z6O5-0{5:857Q5@047 7J8:7M0!8W8+7b6R043x8/8X5{0{0H8{7V7L0{0K967H8=8!8$6Q8(8v6V8-9i8Y8=9b6H0{8`808:829l9304958y580I5b4@564_531t0c4|9H2%2Y0X1?9E0I4`1z5S3%2Q0j0U0g0X0z8#0S6+1l1n1p1r0E6X331G3C2;3%0X0F0j1c2K0N1$0F2d1V0w0{1z9=9@9_2L0!0^0c23040Y212n2T9/9S0V0%0c1^0v181a9{1d0w0x0t762J0b1^2~2{0k2K0E0k1d250n0,0G0w2d2)2`0j8!0E0F000X0i0i8s0E1p0N5t001r0c0E2c0,0F0k0E0c0W1a0E3L2l0t0X0t0P0s0-13aP9+a?0Qat0+7!ae0N9*0,am0La$ar3*0N0v0x0,arat0wav1maea%192J0Pau0E0g0Wbd0Z0E0uaY0ba.0,ak0vak0y0-ajalan2La%a.0waC1daIaK5t0WaN2Qa}0E1n0t5$0va`a^0/a%2Q0L0FaJ0E0T0P0X0k3m0k0ibXak1hb$0Ea.bs0Pb.010i1Qaka02D1Z1#0L0Z1E3C1A0JbB0E0x751Jc11c0,c40kbC132)b)0~251c0G04aybR1wbL0F0O2yb51q2Ucw1R04ccag9F0b3C9Q0%0)0+04.
Autres exercices :
Exercices CodEx sur la récursivité
Crédits
Franck Chambon
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