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.

Évaluations restantes : 5/5

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Exercice 2 : parité⚓︎

Parité

Compléter la fonction suivante qui doit être une fonction récursive.

⚠️ Il est interdit d'utiliser %

Évaluations restantes : 5/5

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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

Évaluations restantes : 5/5

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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

Évaluations restantes : 5/5

.128013l(9î _4:;=vm26-uS8w.s3èC/+fr7gebhpPicNé05qa,onkyd1x)t050X0F0#0R0K0b0v0f0L0b0R0v0v0k010#0K0I010406050v0q0m0m0R0C0W040r0T0b0q0_0T0U050z101214160~0I04051m1f1p0z1m0~0X0K0l0.0:0=0@0:0U0E0q0R0E0F0p0I0W0#0H1d0f0H0K0E0H0b1R0H0#0|050)0G0b0F1y0;0?011Q1S1U1S0#1!1$1Y0#0C1n1M0.190v0I0R0U0@0n011(1A010B0+0F0U0R0m0F1Y1}1 241*271$2a2c0|0a0f0J0C0T0I0T0v0K1c0U0f0%1{0C0C0F0L2x1f2f0U1n0z1M2K1@1_1^1Z0X2h1B0K0U292u1Y1v1x0/1)2U2W0U0T2!1Y0I2D1n2I2K2;0 1~2y2$252*0C130b1Y0R1P2D0B0@030g0g0L2+0F1U2)0T0p0w0p0Y0|0Y1f0R2=2^0}2@2g2`1*2|2~30320F340136383a3c2X3f0p22040n3l3n1 3p2I2T013u0R2 1n310H333537390%3E2*3G0w0|0w3L2H3o0~3P3s0@3S3U053W3Y3A3!3D2V3F3g0h0|0h3-1g3/3q2_1z3t0T2}3T3w3X3y3Z3C3$3 3(3g0P0|0P452;3:2^3Q3@4f3{3B3#3b4l3e3g0o0|0o4r473;4a3?4c3v3V3x3z4z3~3d3G0D0|0D4I3N4t3r4L3R4N4e4P4g4R3}4k4U3g0s0|0s4Z2J4#492%4(4d3^3`4h3|4j4B4:0p0d0|0d4^2K2.0F2K2!2N0X1_2S3=014A2Z1w1n5c2:3o3.3N054A5r2g0K0X0@372I3G3i4P5z5B533%4D3h232l0F5I4A5K5E1Y0z3m483Q0V0|0%0B5t2J5X5k0t0|0f5%5x4{2{0B0|2D0I0F0R0#5.5)4%0{040c5|4K4|0U0|1e465u63255 0i5.5-6a3t0G0|2V5{685(6g0@5 0S6e5}640|0#0Z6l2?6o016c6s6A0U6i040v1@624u5k5 0!6D6L4%0T0|0p020E0#0j6P4$646G6I0C6Z5:1*6C6m3p6-5X5H015C2^3G3I3_0f6;4.54403H5N2b5P6=5J4C6^5U5W6A5+040f7d5-6/6A0v0X0|020Q0q0T6X7l7n7p7m7o6Y6-0~7g4u6|0g5D3g3*5G5A745R767D712c5Q4T6 7E3-7h7j7c7e0i1~0C2b0f0U0i2z1%0#0W5^0f290_0F0C0u0f0M0T0m0G2D7%0f0B0T0K0-7m1%0b02030w0d0j1O2D390I0K82310L0H0R0e2W7{0L140R2F0x2D0v0u5.7x6z7z7G6?1 3G427F7N4/6 427!728E6~4m0p8C7R6Q4|7i5,7V7X7Z6w0#7$2A7)7+6%7;0y8h3 8l8n8p8r0f810f8385871O0X7~0#0f0C0N0I0N0#7/8t7w6K5y8y7B6@4n3w7A7I554o8I7M7H7O8M4o2K798Q258S7U7d7q7u9u7s7r7v4s962y7A7C0p4F8D9j8F8M4F9h736}5S4E789s6f9p1*5Z040K5$6-9T6!2{666)3Q6S040k0k9)5k0m0K0|0O9/5~0|6d957y975I9E4W9H9O7J0p4W9M8K9Pa59R7eac9#6*0@9W2D0#0q0C672;ae3Q0v5F84860jas878u9B6{989E4=a275554=a79I8L5LaC3Lac6t259W3b0v0F9^4|6,9A9}9CaA9a569c989e6 57aHa355579n9SaN6Aah0(akam3oao5k65048XaU259+0Ab13t5?0F5^5`ay6M0|61aY4v9(9!aO1*9+0pb50@9;3jbb9_046rbi6E6v6xbraV0|6O9|2?0z5w1q2/1f5f1f0#5hbL2Q2L0R1#5dbJ5o7x0%0)0+0v04.

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

Évaluations restantes : 5/5

.128013l(9 _4:;=vm26-uS8ws3/+fr7geUbhpPic05qa`onkêyd1)t050T0B0W0M0H0b0t0e0I0b0M0t0t0j010W0H0F010406050t0p0l0l0M0y0S040q0O0b0p0;0O0P050v0{0}0 110_0F04051h1a1k0v1h0_0T0H0k0)0+0-0/0+0P0A0p0M0A0B0o0F0S0W0E180e0E0H0A0E0b1M0E0W0@050!0D0b0B1t0,0.011L1N1P1N0W1V1X1T0W0y1i1H0)140t0F0M0P0/0m011Z1v010x0$0B0P0M0l0B1T1^1`1 1#221X25270@0a0e0G0y0O0F0O0t0H170P0e0Y1?0y0y0B0I2s1a2a0P1i0v1H2F1/1;1:1U0T2c1w0H0P242p1T1q1s0*1!2P2R0P0O2V1T0F2y1i2D2F2,0`1_2t2X202#0y0~0b1T0M1K2y0x0/030f0f0I2$0B1P2!0O0o0g0o0U0@0e0U1a0M2-2:0^2/2b2=1#2@2_2{2}0B2 01313335372S3a0o1}040e0m3h3j1`3l2D2O013q0M2`1i2|0E2~3032340Y3A2#3C0u3e0u3I2C3k0_3M3o0/3P3R053T3V3w3X3z2Q3B3b0g3e0g3*1b3,3m2;1u3p0O2^3Q3s3U3u3W3y3Z3|3#3b0K3e0K422,3-2:3N3;4c3^3x3Y364i393b0n3e0n4o443.473:493r3S3t3v4w3{383C0z3e0z4F3K4q3n4I3O4K4b4M4d4O3`4h4R3b0r3e0r4W2E4Y462Y4#4a3=3@4e3_4g4y4-0o0d3e0d4=3L4r3/4`4L3?4N4f4x3!4A3c0J0@0U0J574@4s4$4|5e4 5g4z3C0U3d045y5o455q4{4u4~4P4,3}3c3E0U3H0v3i3+4X5D5a4t4(4v4+515K0U3%5A3)5P3J4?5T4!5V5d4)5f4Q5!3 5A415)5R5+4H4_5.4}4*505h5x4l5A4n5`435S5}2?5r5G615v520U4C5A4E682.1n2*1a2V2I0T1;2N5a4x2U1r1i2)0B2+3k5{1i4x6D2b0H0T0/322D5x3s6K6M625w3b3d0e2g0B6S6g5!1T5`6b1#0Q0@0Y0x6F5,4_0s3e6/6)3:0x0@0W0O6|6@594!0?040c6 4Z5~0@19692E6:20720V0h6F0_7a6I2t6R016N2:3C3E5d7m5Y633b1}6X266Z7n6T527r6(706;3e0e7J754^200t0T0@020L0p6}0i7R7T0W7V7S7U0C2R0e0x182A0H1J0W361X0e7S1Y7g7j7i2.3M7t0f6O3b5$7s6L7B6#4j0o3%7y276!5=85805)7_6E7{827o1`3C5@818a5J853 887A7u6U3a6%5Q6^017O7I7J0o0e0N6|6|0c0J0V0N0e2y0P0k0O0H1Y0N02030u0d0i0J8V8X0i0N7h7L0e7|7~0o658n838b5i4l8s8o5Z858/7F767N7P3F7J0e8E8G6}0O0c0U8L8N248Q8S8F8#8Y8J0e0w0e8K9g8%8)7j5D8,7p4B6Q8i7C5K4C8^8;8p5i6j3*8z8B918D8F8H970m9a8O9d8T9n0c9i9k8K9j0e9U9l0V0V9n8(7^8*9s8k3b4T4M7|845i4T9A8u529.9F7G8 8C930e0Z0I0e0{0y0e7:0l0R270e2)2Q0I0=0B9p7`4r9+0P3C4/9/9w9;am1~6Y8_7v0oan3I8f3K9r9w8-54aoau8v549@9x85aE9{8~1#9H926Xa00t0W0e0p2t240;0Ba52o2q0;6.9)9q8h6S8-5m9vaG6h5kaJaq6V5k2F8y9|aP90aR7W7Ub27Yb40iah8gajaC9t3c5z8:9^5!6Wat9B8`5i5y8x3la,baa.bc5Na;bkavbua^8=5x7E3iaR7c6*0@0Ha*2,0ebF3:786FbL8z0O0@0j0jbPbM010l0H0@5nbqaO0/727@4p9*bb9,3c802|9:bA6V87bjbg855#boaRbE8z6+042y0W0p0y79bKbX0t5z9n8!8W8Yb8aAa-7Ba/8mb=apb@3c8rb`aKbm8m5)c0a~0/c2360tagb%7M1#b*ch7bcj8jal6V8/cna=5!8@csa_3c8|bDb 7K8z0P0@0l6}bIbWbRbTc*cy3O6{968*5a7274cE4sbO7jbQc.bS040oc-b(bYb!5Ac=710@0VcI7k8+b.cM3c9EcPbw8v6ias7zcQb|9EcwcYc}d3c2c4c6c83kdtcF0/cb7Qcf0i0c9nd2dB01c 0wdJc`04c%a)dO5adMdT4!dD049n9XdIc|bXdVd%c!c$c(bJdzd(0@dNd*c.dY9n9$dFdb1a6H1l6p0v6r1a0W6te32L2G0M1W6C6q6z7i0Y0!0$0t04.

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

Évaluations restantes : 5/5

.9888.128013A_4:2!-.Sw3/]7bçpPiqoF1tl(9 ;=vTm6u8RsèCfrgàe[hcDé05a,nkydx)050+0U0z0$0u0A0N0D0X0A0$0N0N0F010z0u0s010406050N0K0I0I0$0R0*040k0w0A0K110w0(0D020$0I0s0E0D0M0U1b0R0v0K0U0N050n181a1c1e160s04051J1C1M0n1J160+0u0G0_0{0}0 0{0(0S0K0$0S0U0i0s0*0z0W1l0D0W0u0S0W0A1=0W0z14050;0q0A0U1V0|0~011;1?1^1?0z1~201|0z0R1K1-0_1h0N0s0$0(0 0g01221X010Q0?0U0(1p0U1|2k2m2r242u202x0I2z040b0D0t0R0w0s0w0N0u1k1m0/2i0R0R0U0X2U1C2B0(1K0n1-2*2e2g2f1}0+2D1Y0u0(2w2R1|1S1U0`232@2_0(0w2}1|0s2Z1K2(2*3a172l1m2 2s330R1b0A1|0$1:2Z0Q0 030d0d0X340U1^320w0i0#0i0y140D0y1C0$3b3e153d2C3g243i3k3m3o0U3q013s3u3w3y2`3B0i2p040D0g3I3K2m3M2(2?013R0$3l1K3n0W3p3r3t3v0/3#333%0m3F0m3-2%3L163;3P0 3@3_053{3}3X3 3!2^3$3C0e3F0e481D4a3N3f1W3Q0w3j3^3T3|3V3~3Z414n433C0#3F0#4t3a4b3e3=4f4D4j3Y403x4J3A3C0J3F0J4P4v4c4y4e4A3S3`3U3W4X4m3z3%0p3F0p4*3/4R3O4-3?4/4C4;4E4?4l4I4_3C0L3F0L4~2)504x30534B4g4i4F4k4H4Z5b0i0C3F0C5g3:4S4d5l4:4h4=4G4Y424#3D0!140y0!5y1N381C2}2-0+2g2=5B4Y2|1T1K370U393L493/054Y5)2C0u0+0 3t2(3%3E4;5;5?5r5I5_2q2H0U5}5H4!602*3J4w3=0)140/0Q5+2)6a5B0l3F6g5/5j3h0Q141A0z0d2l3y0+2O2I6m6i5213040B6A4,5k0(140I0w0z6G5A6C140-0f6m164u5,3;5|015@3e3%3)5E6Z595s4o3(612y644^6-6(0n696H2s6k3*0D6~6O515k0N0+14021y6M0E760K787a780Y0Z0z0U3j4n0D2S0D6L0z0D6s0D0K1m6v2^6x0w2I7d0z79777B7A0E6U701m6*0d5^3C455{5=6!5~667N6/2I6;5a6-7O3-6V3c6Y7Q6#2m3%4q7P7X6,4K0i4q0D627/5 4p1|6^6}6 6`246c040u6f6W2)0D6B6I0q142G7I3=6D6F866n4T6K6M8e5B6D0-6m88800 0w750A7B8r892s0I0u143,8i8A246D6T8i7$5*7(5}7M3B3T7K655t4M7@6:7R8U6-4M687~6~8)8H0 822Z0z0K0R0(8z8t010)0X140H0R1z7H8G8O7R8Q4%7.8Z6=7;4%8X7W967Y987|3J8)8s6P5k823x0N0U8n6Q048K4Q8e7K8Q4{956+7`0i4{9a639c7:5J9x3-9h9h8+8^14848?9j3h8l6N909R8I140V9p5k8C145O9V712s6D0o9Q9*248v040h0F9.6o3Q9T9!9+9Y9|9:140i9 0 9$043H9)9_0 9,9s4va80D9v6$5c8S7)7S5t5d9D7_7T0i5d8%9Kau9i9/8,148.8:8=8iawa98^8`040x3^9n8 7%4Sag7+3C5v9yal6-5vao9F9AaS9Jav9M9l0@9oae8o14ac4 9uak8Q5Najap5ta?aX9zaqa?atav9L8@8-0:aB9^8k046s6u3^7w6ya*aNax018ga33?9{a+9q9Zbm9#8Da6bj8Jbj9;a2bp8Bbra7bfaF9,8q8L6A0n5.5Q5(5S5#1C0z5VbO2:2+0$1 bL0n5T1I8j5B2Z0I0d0Q0$0)0U0d0W7O1u1w1y1A0Da.6h1P3M0/0;0?0^5B337h0D0+0Z0s1^0Z2z0D2P2w8u0s2w144b191w1e0c1j2Z2X2Z2#0u1/2Q0}0ubV2%ci1Gb{1T3=1Z1#1%1)1+1-1/261@1_1{b!522F2w2y140t1,1.aC3c5%6n3.6hbJ917*0(0i0J3Da@aY66c,3Ea{aU43c;2q575G973Ac_8%a%6d3Vbj6|88by3Q6qb80N6t7v0(7x6zd7aa148hbCb77obt6Rb^3MaeaPc*c,6(3n8Tc}c+6.c?8!c^dBc{5qdDc~6.d08@0N3)7F7f7h7j2_7l0u7n6M7qdb7s7ubbdebd7FaM8NaOa;6$c,7!dxakdIdA45dCdzd/c`4Wa|4_d{8%8M6Xd,8Pd.7=c.d~3$c,7?7^c/d e75FdHd`e7a 7 9Way83853aaE4T8b048ddhbhdjbj6J04dnex8pb65B9;028x7GaD9Ma58Fdla,9rd*e35:d-7+c,8$6)d=ej8Wede9dE8WdG4@9ddJeZ7}b0d104aA8;eG528_8{8}beaddldtdA94e!a^eac+7V9Ee)dJ99e,fbf39f8(e?9me eUbDa-eT6hc(7Le69Id;f6dE9Ce(c@dJ9CfefAdA9Ie;a$b2azb4e_eM8@eBeDeQbnbja59(fR5k9,e`5k9;0F9@fNenbkeC8meE9~exbwfTbAdo049-f(bg0w6|2m0+fZ9Sdadcd$dfflfqf)biexfPf,fW9}04bogc24a5bBd+bgbuf/a1f;5Mf?0obF9t8GbI3w2*cZbM0G3M1Jb:1c770(0^b=0D0{c30U0K0,0u0O2I0D2l0R11210+0K885.f}1C5.0D6F5.b9ddg40B7o0V0y0f3Dgsg%gx0-7@219n0R3n0Z0G3^0Kc87q1mcUcI1mgJ7m5-gxg:0!0o0Df$dW0z0Vg@g_0/3*7rh1h30Z0D0Tg!gx8|8~gwhpg)hs1i0$2UgT1c1A9n0K9n0-0j1Ndrb|0=0@cA2~520$0+6L0(2Tcr1m0l1ch#1!cg1L3=hYh!h$1l0i110z2c04gE1xhA1Q1L040a0D0P0:c20N1h1jh%hv0D0q0|gX213v0s0uif0D010N1^0X1A2q0B2e2m0X0Wb?2w0D0Qg 0(0r0=0Ng{0(007r2l0^3V2u0X0$ip0%7@0whM0D0G7i2OgHgT1i0^0;0R2=7t210I7g1.2Wc6iUiM0uiOip0D0$iW0XgKb?7wi?1AhPb`6VbY5S0:hT0N04.

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 !

Python

def 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

Évaluations restantes : 20/20

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Crédits⚓︎

Franck Chambon