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

.1280137w4h)1(+5-_s3u:/S[ bn=ve08imL.tP]69p2drg;ylckfao050M0y0F0V0B0R0m0t0S0R0V0m0m0w010F0B0K010406050m0o0C0C0V0N0Q040r0W0R0o0;0W0v050q0{0}0 110_0K04051h1a1k0q1h0_0M0B0x0)0+0-0/0+0v0O0o0V0O0y0k0K0Q0F0e180t0e0B0O0e0R1M0e0F0@050!0u0R0y1t0,0.011L1N1P1N0F1V1X1T0F0N1i1H0)140m0K0V0v0/0L011Z1v010U0$0y0v0V0C0y1T1^1`1 1#221X25270@0a0t0G0N0W0K0W0m0B170v0t0Y1?0N0N0y0S2s1a2a0v1i0q1H2F1/1;1:1U0M2c1w0B0v242p1T1q1s0*1!2P2R0v0W2V1T0K2y1i2D2F2,0`1_2t2X202#0N0~0R1T0V1K2y0U0/030l0l0S2$0y1P2!0W0k0L0k0g0@0g1a0V2-2:0^2/2b2=1#2@2_2{2}0y2 01313335372S3a3a0@0L3g3i1`3k2D2O013p0V2`1i2|0e2~3032340Y3z2#3B0n0@0n3F2C3j0_3J3n0/3M3O053Q3S3v3U3y2Q3A3b0d0@0d3%1b3)3l2;1u3o0W2^3N3r3R3t3T3x3W3_3Y3b0j0@0j3 2,3*2:3K3.493=3w3V364f393b0I0@0I4l413+443-463q3P3s3u4t3^383B0b0@0b4C3H4n3m4F3L4H484J4a4L3@4e4O3b0A0@0A4T2E4V432Y4Y473/3;4b3?4d4v4*0k0J0@0J4/2F2)0y2F2V2I0M1;2N3,014u2U1r1i562+3j3(3H054u5l2b0B0M0/322D3B3d4J5t5v4}3X4x3c1~2g0y5C4u5E5y1T0q3h423K0T0@0Y0U5n2E5R5e0c0@0t5X5r4=2?0U0@0R181z0y0o0N5(5Z4X0?040h5@4E4?0v0@1,0y0V0o5}4o5e5`0p5(5%5~2?0u5-0B0m0F664W4?5`0f6b5^4?0W0@0k020O0F0P6p6d3o6f042Q6j405o6A0/695(0_6G5Y3J5B015w2:3B1}5A5u6R5D4w6U5H265J6Y5L6!3b6V3%6I015#040t6?5%6N5)3K0m0M0@016 6L6k2t6Q6S1`3Z3r746Z4 3!0t5I5K4N3`0k3!2F5Q6/6|5$6@0D2|0U182A0B1J2y0v0x0W0B1Y0+0t5.1y0o5;0N2u1Y6264716_5R795x3{786X4(4~7h3|7d6%7f4)7Y5O7l674X7n6=6@6 017O2.6P7V0l7S0k4i6W7$7X4g7{6$277~5M4h7)7.6?6q205T6D5W6_6c7+5 610V1W63658f8a1#6s040w0w6z8h205`0s0H6a6_6M7?4o7R6T4y7U846+0k4z7!836)7g804z7k886@896/8c2y0F5=198o6/0C0B0@0z7=5m7@5C7`4Q7}8Q7%804Q8O6(7W850k8?3F8W8p0/8c360m0y723K6K8C9a8G764+8J8^7 5F4,8|8K4 4,8U8W936/60047M8n8E6l208r0E9a5e9v2o0K9E5_0@0h6o9d7P8:6Y7`518@8~8L519n9j8 9T929s8X8w1#8Z0Z8$8v9A1#8*3e9.5*8q0@0i9?4p5-5/7H5=9J6m9La12?8j8l7N9P9)6J0@9N4m5@0q5q1l2*1a591a0F5bam2L2G8k1X585i6M0Y0!0$0m04.

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

.1280137w4xh)1(+5-,_s3u:/SC bqn=îèéve08im.tPN69p2drg;ylckfao050R0E0K0!0H0W0o0v0X0W0!0o0o0z010K0H0P010406050o0q0I0I0!0S0V040t0#0W0q0_0#0y050s101214160~0P04051m1f1p0s1m0~0R0H0D0.0:0=0@0:0y0T0q0!0T0E0l0P0V0K0f1d0v0f0H0T0f0W1R0f0K0|050)0w0W0E1y0;0?011Q1S1U1S0K1!1$1Y0K0S1n1M0.190o0P0!0y0@0Q011(1A010Z0+0E0y0!0I0E1Y1}1 241*271$2a2c0|0a0v0L0S0#0P0#0o0H1c0y0v0%1{0S0S0E0X2x1f2f0y1n0s1M2K1@1_1^1Z0R2h1B0H0y292u1Y1v1x0/1)2U2W0y0#2!1Y0P2D1n2I2K2;0 1~2y2$252*0S130W1Y0!1P2D0Z0@030n0n0X2+0E1U2)0#0l0p0l0h0|0h1f0!2=2^0}2@2g2`1*2|2~30320E340136383a3c2X3f0l22040Q3l3n1 3p2I2T013u0!2 1n310f333537390%3E2*3G0p0|0p3L2H3o0~3P3s0@3S3U053W3Y3A3!3D2V3F3g0d0|0d3-1g3/3q2_1z3t0#2}3T3w3X3y3Z3C3$3 3(3g0k0|0k452;3:2^3Q3@4f3{3B3#3b4l3e3g0N0|0N4r473;4a3?4c3v3V3x3z4z3~3d3G0b0|0b4I3N4t3r4L3R4N4e4P4g4R3}4k4U3g0G0|0G4Z2J4#492%4(4d3^3`4h3|4j4B4:0l0O0|0O4^2K2.0E2K2!2N0R1_2S3=014A2Z1w1n5c2:3o3.3N054A5r2g0H0R0@372I3G3i4P5z5B533%4D3h232l0E5I4A5K5E1Y0s3m483Q0Y0|0%0Z5t2J5X5k0c0|0v5%5x4{2{0Z0|2D0P0E0!0K5.5)4%0{040i5|4K4|0y0|1e465u63255 0r5.5-6a3t0w0|2V5{685(6g0@5 0m6e5}640|0K0e6l2?6o016c6s6A0y6i040o1@624u5k5 0g6D6L4%0#0|0l020T0K0U6P4$646G6I0S6Z5:1*6C6m3p6-5X5H015C2^3G3I3_0v6;4.54403H5N2b5P6=5J4C6^5U5W6A5+040v7d5-6/6A0o0R0|017l5.0~7g4u6|0n5D3g3*5G5A745R767u712c5Q4T6 7v3-7h7j7c7e0r1~0S2b0v0y0r2z1%0K0V5^0v290_0E0S0J0v0M0#0I0w2D7U0v0Z0#0H0-0x0q1%0W001O2D390P0H7`310X0f0!0A2W7/0X140!2F0B2D0o0J7n6K5y7x6?1 3G427w7E4/6 427R728r6~4m0l8p7I6Q4|7i5,7M7O7Q6w0K7T2A7W7Y6%7(0u853 898b8d8f0v7^7`7|2y0R7=0K0v0S0C0P0C0K7$8h6-7o6z7q8l7s6@4n3w7r7z554o8v7D7y7F8z4o2K798D258F7L7d7l018i7p8k5I7t0l4F8q958s8z4F93736}5S4E789e6f9b1*5Z040H5$6-9B6!2{666)3Q6S040z0z9N5k0I0H0|0F9T5~0|6d8?8j2y7r9m4W9p9w7A0l4W9u8x9x9:9z7e9`9J6*0@9E2D0K0q0S672;9|3Q0o5F00009i8^9k749m4=9-75554=9=9q8y5Lah3L9`6t259E3b0o0E9Z4|6,4s9(6{8`9m57ai906 57am9.55aHar9{7dat9D5?0(a2a43oa65k65048Kaz259P0ja)3taV5^5`aD6M0|619j9}3R9M9IaT0@9P0la-0@9V3ja=9!046ra}6E6v6xb6aA0|6O9%6/0s5w1q2/1f5f1f0K5hbq2Q2L0!1#5dbo5o7o0%0)0+0o04.

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

.1280137w4h)1(+5-_`s3u:/S bqn=êve08imtP69p2drgylckUfao050L0A0F0U0D0P0n0t0Q0P0U0n0n0x010F0D0J010406050n0p0E0E0U0M0O040s0V0P0p0:0V0w050r0`0|0~100^0J04051g191j0r1g0^0L0D0z0(0*0,0.0*0w0N0p0U0N0A0k0J0O0F0e170t0e0D0N0e0P1L0e0F0?050Z0u0P0A1s0+0-011K1M1O1M0F1U1W1S0F0M1h1G0(130n0J0U0w0.0K011Y1u010T0#0A0w0U0E0A1S1@1_1~1!211W24260?0a0t0G0M0V0J0V0n0D160w0t0X1=0M0M0A0Q2r19290w1h0r1G2E1.1:1/1T0L2b1v0D0w232o1S1p1r0)1Z2O2Q0w0V2U1S0J2x1h2C2E2+0_1^2s2W1 2!0M0}0P1S0U1J2x0T0.030l0l0Q2#0A1O2Z0V0k0d0k0g0?0t0g190U2,2/0@2.2a2;1!2?2^2`2|0A2~01303234362R390k1|040t0K3g3i1_3k2C2N013p0U2_1h2{0e2}2 31330X3z2!3B0o3d0o3H2B3j0^3L3n0.3O3Q053S3U3v3W3y2P3A3a0d3d0d3)1a3+3l2:1t3o0V2@3P3r3T3t3V3x3Y3{3!3a0j3d0j412+3,2/3M3:4b3@3w3X354h383a0H3d0H4n433-463/483q3R3s3u4v3`373B0b3d0b4E3J4p3m4H3N4J4a4L4c4N3_4g4Q3a0C3d0C4V2D4X452X4!493;3?4d3^4f4x4,0k0I3d0I4;3K4q3.4_4K3=4M4e4w3Z4z3b0B0?0g0B564?4r4#4{5d4~5f4y3B0g3c045x5n445p4`4t4}4O4+3|3b3D0g3G0r3h3*4W5C594s4%4u4*505J0g3$5z3(5O3I4=5S4Z5U5c4(5e4P5Z3~5z405(5Q5*4G4^5-4|4)4 5g5w4k5z4m5_425R5|2=5q5F605u510g4B5z4D672-1m2)192U2H0L1:2M594w2T1q1h2(0A2*3j5`1h4w6C2a0D0L0.312C5w3r6J6L615v3a3c0t2f0A6R6f5Z1S5_6a1!0R0?0X0T6E5+4^0c3d6.6(3/0T0?0F0V6{6?584Z0=040h6~4Y5}0?18682D6/1 710f0q6E0^796H2s6Q016M2/3B3D5c7l5X623a1|6W256Y7m6S517q6%6 6:3d0t7I744@1 0n0L0?017Q0S2Q0t0T172z0D1I0F351W0t0v0p1X7f7i7h2-3L7s0l6N3a5#7r6K7A6!4i0k3$7x266Z5;7|7@5(7-6D7/7_7n1_3B5?7^815I7|3~7 7z7t6T396$5P6@017N7H7I0k0t0m6{6{0h0B0f0m0t2x0w0z0V0D1X0m000B000m7g7K0t7:7=0k648e7`825h4k8j8f5Y7|8W7E757M7O3E7I0t8v8x6|0V0h0g8C8E238H8J8w008A0t0i0t8B8O8Q7i5C8T7o4A6P897B5J4B8$8Y8g5h6i3)8q8s8/8u8w8y8^0K8{8F8~8K9192948B930t9C950f0f977,8R9b8b3a4S4L7:7{5h4S9j8l519R9o7F8-8t8;0t0Y0Q0t0`0M0t7$0E0y260t2(2P0Q0;0A987.4q9O0w3B4.9S9f9Ua31}6X8%7u0ka43H863J9a9f8U53a5ab8m539X9g7|al9#8,1!9q8:6W9*0n0F0t0p2s230:0A9/2n2p0:6-9M99886R8U5l9ean6g5jaqa76U5j2E8p9$aw8.ay7Q019~87a0aj9c3b5y8X9Y5Z6Vaa9k8(5h5x8o3kaPa:aRa=5MaUa}acb7aY8Z5w7D3hay7b6)0?0DaN2+0tbi3/776Ebo8q0V0?0x0xbsbp010E0D0?5mb3av0.717+4o9Na;9P3b7@2{9Tbd6U7~a|a_7|5!b1aybh8q6*042x0F0p0M78bnbA0n5y8M00a.ahaQ7AaS8dbRa6bT3b8ibWara 8d5(b$a(0.b(350n9}bG7L1!bJb^7ab`8aa26U8Wb~aV5Z8#c3aZ3b8*bgb#7J8q0w0?0E6|blbzbubwcHc93N6`8@8R597173cf4rbr7ibtcLbv040kcKbHbBbD5zcP700?0fcj7j8SbNcn3b9ncqb98m6ha97ycrbY9nc7czcXc%b(b*b,b.3jd4cg0.b;0?91b@cWbAcZ0ic$dccM04cEaMdm3Mdkds59de04009Fdhb/cI04dldicBcDcFbmdadj0?dFdCcLdx009Kc/196G1k6o0r6q190F6sd#2K2F0U1V6B6p6y7h0X0Z0#0n04.

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

.128013.98887xh1ç5-s3:/SC nA!é0e.]RT2;cfaoàw4)D(,_u[qb=èv8imFtP69pdrgylk050(0v0Z0E0W0,0j0p0C0,0E0j0j0S010Z0W0%010406050j0O0X0X0E0)0+040n0F0,0O110F0q0p020E0X0%0B0p0y0v1b0)0Q0O0v0j050m181a1c1e160%04051J1C1M0m1J160(0W0U0_0{0}0 0{0q0*0O0E0*0v0i0%0+0Z0e1l0p0e0W0*0e0,1=0e0Z14050;0R0,0v1V0|0~011;1?1^1?0Z1~201|0Z0)1K1-0_1h0j0%0E0q0 0A01221X010D0?0v0q1p0v1|2k2m2r242u202x0X2z040a0p0!0)0F0%0F0j0W1k1m0/2i0)0)0v0C2U1C2B0q1K0m1-2*2e2g2f1}0(2D1Y0W0q2w2R1|1S1U0`232@2_0q0F2}1|0%2Z1K2(2*3a172l1m2 2s330)1b0,1|0E1:2Z0D0 030N0N0C340v1^320F0i0h0i0f140p0f1C0E3b3e153d2C3g243i3k3m3o0v3q013s3u3w3y2`3B0i2p040p0A3I3K2m3M2(2?013R0E3l1K3n0e3p3r3t3v0/3#333%0k3F0k3-2%3L163;3P0 3@3_053{3}3X3 3!2^3$3C0I3F0I481D4a3N3f1W3Q0F3j3^3T3|3V3~3Z414n433C0h3F0h4t3a4b3e3=4f4D4j3Y403x4J3A3C0#3F0#4P4v4c4y4e4A3S3`3U3W4X4m3z3%0c3F0c4*3/4R3O4-3?4/4C4;4E4?4l4I4_3C0V3F0V4~2)504x30534B4g4i4F4k4H4Z5b0i0$3F0$5g3:4S4d5l4:4h4=4G4Y424#3D0u140f0u5y1N381C2}2-0(2g2=5B4Y2|1T1K370v393L493/054Y5)2C0W0(0 3t2(3%3E4;5;5?5r5I5_2q2H0v5}5H4!602*3J4w3=0-140/0D5+2)6a5B0H3F6g5/5j3h0D141A0Z0N2l3y0(2O2I6m6i5213040L6A4,5k0q140X0F0Z6G5A6C140J0l6m164u5,3;5|015@3e3%3)5E6Z595s4o3(612y644^6-6(0m696H2s6k3*0p6~6O515k0j0(1401760K0t0Z0v3j4n0p2S0p6L0Z0p6s0p0O1m6v2^6x0F2I76016U701m6*0N5^3C455{5=6!5~667B6/2I6;5a6-7C3-6V3c6Y7E6#2m3%4q7D7L6,4K0i4q0p627Z5 4p1|6^6}6 6`246c040W6f6W2)0p6B6I0R142G7w3=6D6F7`6n4T6K6M825B6D0J6m7|7;0 0F14020,0Z0B8f7}2s0X0W143,868q246D6T867Q5*7S5}7A3B3T7y655t4M7(6:7F8K6-4M687/6~8V8x0 7?2Z0Z0O0)0q8p8h010-0C140z0)1z7v8w8E7F8G4%7Y8P6=7#4%8N7K8|7M8~7-3J8V8g6P5k7?3x0j0v8b6Q048A4Q827y8G4{8{6+7+0i4{9063927!5J9n3-97978X8+147^8)993h896N8?9H8y140P9f5k8s145O9L712s6D0x9G9W248j040s0S9!6o3Q9J9Q9X9O9/9$140i9=0 9S043H9V9,0 9Y9i4v9~0p9l6$5c8I7T7G5t5d9t7*7H0i5d8T9Aak989#8Y148!8$8(86am9 8+8-040Y3^9d8=7R4Sa67V3C5v9oab6-5vae9v9qaI9zal9C9b0@9ea48c14a24 9kaa8G5Na9af5ta)aN9paga)ajal9B8*8Z0:ar9+88046s6u3^7p6yaWaDan01849_3?9.aX9g9Pbc9R8t9|b98zb99%9^bf8rbh9}b5av9Y8e8B6A0m5.5Q5(5S5#1C0Z5VbE2:2+0E1 bB0m5T1I875B2Z0X0N0D0E0-0v0N0e7C1u1w1y1A0pa!6h1P3M0/0;0?0^5B337a0p0(0t0%1^0t2z0p2P2w8i0%2w144b191w1e0r1j2Z2X2Z2#0W1/2Q0}0WbL2%c81Gb.1T3=1Z1#1%1)1+1-1/261@1_1{bQ522F2w2y140!1,1.as3c5%6n3.6hbz8@7U0q0i0#3Da*aO66cY3Ea.aK43c%2q575G8}3Ac,8TaT6d3Vb96|7|bo3Q6qa~0j6t7o0q7q6zc}a01485bsa}7hbj6Rb+3Ma4aFcWcY6(3n8Jc:cX6.c)8Qc+drc.5qdtc;6.c?8*0j3)01787a7c2_7e0W7g6M7jd17l7nb1d4b37ubwdia%6$cY7Odnaadydq45dsdpd!c-4Wa/4_d-8T8C6XaEdY7VcY7X6)d%d,7$7J9ud:3$d|d.5p4@93dzd}7.a@9Mao7@7_3aau4T7 0481d7b7d9b96J04ddep8da|5B9%8l8ney529{8vdbaY9haC8Dd_8FdZ8HaJd(cY8M7)c#d;8H5Fdxe08SaRakc@04aq8%eD9aax8/8;dWdbdjdq8`d~a+e5cXe2e`du8 dwe99we@958Ue(9cb4eLb6bke;fa7xd`dk9rc!e4du9seUfkdz9sf1fodq9yedaSa^apa`e+at9CeteveHbdb99{9UfF5k9Ye,2s9%0S9*fB8*fD8aew9;epbmfHbqde049ZfSef010F6|2m0(fN9-d0d2dSd5f9d^fberepfU9KfK9:04beg0249{brfe83aZbl9@f!5Mf$0xbv9j8wby3w2*cPbC0U3M1Jb$1c1y1l0^b(0p0{b_0v0O0d0W0T2I0p2l0)11210(0O7|5.f.1C5.0p6F5.a d3f^0L7h0P0f0l3DgggRgl0J7(219d0)3n0t0U3^0Ob~7j1mcKcy1mgx7f5-glg!0u0x0pfQdM0Z0Pg(g*0/3*7kg=g@0t0p0GgOgle/aWgS0Lhg1i0E2UgH1c1A9d0O9d0J0w1Ndhb/0=0@cq2~520E0(6L0q2Tch1m0H1chO1!c61L3=hLhNhP1l0i110Z2c04gs1xe:1Q1L040b0p0o0:b^0j1h1jhQhj0p0R0|gL213v0%0Wi20p010j1^0C1A2q0L2e2m0C0eb)2w0p0Dg:0q0g0=0jg,0q007k2l0^3V2u0C0Eic0M7(0Fhz0p0U7b2O0q0^b|iH0;0)2=7m210X791.2WiOiy0DiAiC210EiJ0Cgyb)7p0Wic0jhCb-6VbO5S0:hG0j04.

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