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

.128013.128073Ta3=gvuth0x[/q8k).Féb6r7 +pcR5l:Sf(Cms1_i2n]ow;eyd4I9P,-050Z0X0j0d0Q0G0N0A0D0G0d0N0N0f010j0Q0C010406050N0i0M0M0d0y0Y040I0U0G0i0}0U0S0A020d0M0C0W0A0E0X170y0p0i0X0N050o1416181a120C04051F1y1I0o1F120Z0Q0h0=0@0_0{0@0S0g0i0d0g0X0)0C0Y0j0k1h0A0k0Q0g0k0G1.0k0j10050-0w0G0X1R0^0`011-1/1;1/0j1`1|1^0j0y1G1)0=1d0N0C0d0S0{0R011~1T010J0/0X0S1l0X1^2g2i2n202q1|2t0M2v040a0A0%0y0U0C0U0N0Q1g1i0+2e0y0y0X0D2Q1y2x0S1G0o1)2$2a2c2b1_0Z2z1U0Q0S2s2N1^1O1Q0?1 2:2=0S0U2_1^0C2V1G2!2$36132h1i2{2o2 0y170G1^0d1,2V0J0{030P0P0D300X1;2~0U0)0l0)0O100A0O1y0d373a11392y3c203e3g3i3k0X3m013o3q3s3u2?3x0)2l040A0R3E3G2i3I2!2/013N0d3h1G3j0k3l3n3p3r0+3X2 3Z0e3B0e3)2Z3H123-3L0{3:3=053@3_3T3{3W2;3Y3y0!3B0!441z463J3b1S3M0U3f3;3P3^3R3`3V3}4j3 3y0F3B0F4p36473a3.4b4z4f3U3|3t4F3w3y0x3B0x4L4r484u4a4w3O3?3Q3S4T4i3v3Z0z3B0z4$3+4N3K4)3/4+4y4-4A4/4h4E4=3y0q3B0q4`2#4|4t2|4 4x4c4e4B4g4D4V570)0$3B0$5c3,4O495h4,4d4.4C4U3~4X3z0l100O0l5u5e4P505j5B5m5D4W3Z0O3A045V5L4s5N5i4R5l4:564k3z3#0O3(0o3F454{5!5x4Q524S555o5+0O415X435:3*5d5@4~5_5A535C4;5~4m5X4o635=654(5g685k545n5E5U4I5X4K6h4q5?6k3d5O5%6o5S5p0O4Z5X4#6v381L341y2_2)0Z2c2.5x4U2^1P1G330X353H6i1G4U6!2y0Q0Z0{3p2!5U3P6+6-6p5T3y3A0A2D0X6?6D5~1^6h6y200r100+0J6$665g0V3B79734a0J102V0D0k0X0y7k0X7e5w4~0 040K7q4}6l100:0j7w5f2o7t0(6$0A7a3d100m7C3.7t0s0H6$126w2#5!6=016.3a3Z3#5A7X5|6q3y2l6{2u6~6c4G3!715;7f017c3$0A7|7N5x0N0Z10021u0U0j0W830i858784867S7N7(0P6/3y607%6,7Y6@5p417-2E7/5*7;8k727r5g803B7|0A0L0,0j1}0J1h2X0Q1+2V0S0h0U0Q1}0c0y1v0A2O0A0m0A1w0j0A0Z2i0;7A0(8!8$0u3;0N1}2O2 0S8e7U6)1i8g8i0)6e8l8t5}7;4m8r6}8n6 947?8{3.8A7{7|2J0v3r0S1O2Q0A0H8Y9n0A2;0j8,7A9q1;0N8$0,0A2a0Q0v1}2s0A4w0Z2V0=2K0Q0_2i7B8`7T383-8}7!4H6;8m7)6^0)4I96927*9$9b7J209e8C2I2N0j9j9l8L1i9o0D8F8H8J9m8N8P8R8%0i9B0Y0C1}0w0U1d9E8^9R8f9Z8h9W0)6G91987:5F4Z9(an8uap9,7^9/8C888aaz86aB0W8_9T4O9V2i4?9Y9)9#4@ar9!5p4@2$3F9S6#9Uah8~594-8g995F59aP8o5+a!3)9:9-0{75040Q788`7I7^0S0w7z2s7~7s107v8`a:3/7z9yb05g7P7Hb50U100f0fbc7^0M0Q105Kb47^7t7RafboaHaYaj5ra#aha%3Z5ra*bA3ybxa.9:8Cb5a=2V0j0i0yae36a`8y2o0r0D108/0:7pbsaG6*bvaJ6_5HbyaM6E5HbDao5Ub+bH7}a{100MbibT20be04bha_b5a|a~bQaWb}0{7tb3b$7D3Mb79Qcc7O100sb|7x2ob 0o0oclcd0{bk105/4Mag6?8~5VaLas935FcBb:at5U5Wb@bScm7410a@cr4Pcfb97E100ncUce04b{btcNc9100TcR5xb bgc+677LcYc(04brcxc$8|b(0S5U7$3ja$b;6_7,6|b-5~7$63bIbJ7^bL0,bOc63+cMcs01bV108T1vaFc7b%czaj5 cCaQ5~8qd5cD9*duaT9fdi3.a=4Va^bRc3cTc`ci04cXdN5^b`c=017tc*c27^b 020G8ddYc8b6047MdRb1c@dp3+7Wc|5U90d0bzd23z95dzdw7;0O90d9dadF5xddbNbPc/7y047j7l7n7ldUcadU0SdMch5x7tdQemc:c!eacn100Bet20cu5Xeh100H0T7Gd(c%d*d,eqbacjd:7VaXdsb)3z6samd cF9%d~a+e0eTe3b^d)dHbZeBd/b#dqc{eQc}6_ald_d6e0aqeYbE3zale$bIbK7idee9eGdjekec2Wee7oe+cbe.cS047Ae+0nc^fedSesd-eL04eEex4ac;focV04cke-d;0o6(1J6M0o6O1y0j6QfH2,2%0d1{6Z6N6W1E9c5x2V0M0P0J0d0r0X0P0k601q1s1u1w9n791L3I1F0b0A0#0G0A170S1u0.8$1|0;056(bMdf1y6(0A0tg81J3IfF0,0.0:04.

Exercice 2 : parité⚓︎

Parité

Compléter la fonction suivante qui doit être une fonction récursive.

⚠️ Il est interdit d'utiliser %

Évaluations restantes : 5/5

.1280136Tra37 =pcgvu5l:EtShf0(Cx/ms1_iq2n8owke)y4d;F9P,éb-050R0N0s0e0F0p0C0h0k0p0e0C0C0i010s0F0j010406050C0n0B0B0e0d0P040t0K0p0n0@0K0I050A0~1012140|0j04051k1d1n0A1k0|0R0F0m0,0.0:0=0.0I0l0n0e0l0N0Z0j0P0s0u1b0h0u0F0l0u0p1P0u0s0`050%0Y0p0N1w0/0;011O1Q1S1Q0s1Y1!1W0s0d1l1K0,170C0j0e0I0=0H011$1y010v0)0N0I0e0B0N1W1{1}221(251!282a0`0a0h0V0d0K0j0K0C0F1a0I0h0#1_0d0d0N0k2v1d2d0I1l0A1K2I1=1@1?1X0R2f1z0F0I272s1W1t1v0-1%2S2U0I0K2Y1W0j2B1l2G2I2/0}1|2w2!232(0d110p1W0e1N2B0v0=030E0E0k2)0N1S2%0K0Z0D3d0`0h0D1d0e2:2?0{2=2e2^1(2`2|2~300N32013436383a2V3d0Z20040h0H3j3l1}3n2G2R013s0e2}1l2 0u313335370#3C2(3E0f3g0f3K2F3m0|3O3q0=3R3T053V3X3y3Z3B2T3D3e0Q3g0Q3,1e3.3o2@1x3r0K2{3S3u3W3w3Y3A3#3~3%3e0o3g0o442/3/2?3P3?4e3`3z3!394k3c3e0b3g0b4q463:493=4b3t3U3v3x4y3}3b3E0g3g0g4H3M4s3p4K3Q4M4d4O4f4Q3|4j4T3e0J3g0J4Y2H4!482#4%4c3@3_4g3{4i4A4/0Z0U3g0U4@3N4t3;4|4N3^4P4h4z3$4C3d0w0`0D0w594_4u4(4~5g515i4B3E0D0D5n3i0A3k3-4Z475s4}4w504R4.3 3d3G0D3J5E3L4^5I5c4v4*4x4-535P0D3)045)5q5X4$5Z5f4+5h4S5(415+435U5G5W4J4{5:4 4,525j5z4n5+4p5|455H5 2_5t5L635x540D4E5+4G6a4r5.606f5!5M5$653e0D4V5+4X6o4I5b5/6s5;5#645y6x4;5+4?6C6c6E6r5K6t6h5@4l3d565+586P5~6R6e6T6H6u6J540H5m046/5-6d4a6*625?5O6X0H5B6;5D5F6b6%4#6S5e6`5w6W5k0H3G7c591o2-1d2Y2L0R1@2Q5c4z2X1u1l2,0N2.3m5}1l4z7v2e0F0R0=352G5z3u7C7E6-5(212j0N7K6i7M2I5F6@0=0M0`0#0v7x6q230L3g7#7V3Q0v0`0N0C0s0E1|0F0d7*6(1(0_040x7_752_0`1c737A4`237|0q7x0h7$3r0Y0`2T0s7 867{0`0O8a8c0=0K0`0Z020l0s0S8n7+0I8e040Y0K178i3P887x0|845I7J017F2?3E3G5f8M6v6K3F7N297P8N7L6}1W5|7+7(3H0h8,8F5c0C0R0`020G0n0K8v8?8^8`8@8_8w848J2;3O8T0E7G3e5*8S7D8!7R6X3)0h7O7Q7a3(8%7U7`0=8:3g8,0h0y0$0s1#0v1b2D0F1M2B0I0m0K0F1#0c0d0n1#2t9g0h7/0s0h7?0d0W0h0T3S0C9L2T1b8I8F95970Z5_9a9i6|5k419g8Y9-5%6X9+8(9n019p8+8,2o0X370I1t2v0q9N9P0h0n2w270@0N0d9R2s2u0F0v0h0K0n9g0n0p9$8K949b8O1}3E679,9c9j4m8X2a9?6w0Zay9`801(9}9r2n2s0sa2a49A0Ia60.0h0m3S0N0naf2B0sam0d0I0X1#a82y0s0P0j1#8C17a,836pas4t9(8P4D7Iau8#5k4E9;aEaA9.3E6l3,7+aM9r0r0z0N0B0j1!0h89919%b29)6zaz8U544Vb68Zbu5Pbs5U927wat7K9)6Mbtb33E4;bxaF8VbIaJ8j9o8;9~0h8t8`8u0SbX0S9O7:7=0(0d0x0Q8mboa|7Bbqa 55b1bO5456bNb89@5k6Zbc9{be8,9I9Kar93a}b=aw6x6:bJ9d5k5oaDbybKcc9l853Pc3bWbZb#b#b%7;9S0x0ob.a{c8b;bGb?5Ab^b}aGcFb|bz6XcF7Tcn8/bUaN9W0*0Nc7bEc9cDcb5QcGcLcg20cKckc#cO8o9|cR9rcscrbZcub)7@0x0wcz46b:2wa~c!5)c$c+d3c*cf5z99bRcoc:c49JcVb/cBd0ca0I5z9+2 95d86x9:9hcH8V0D9_3kbD3M8Ldk66d4dq3d4nd7aBdGcmc.cp8{8 dO8}8|90cAcXcC8!9)6kdEdJdZdIb96xbb5UaNc.7X041%ae8h848b8y828x9{8q04b#0id`aK0=0B0F0`5pd?c.7|0W8.4$0C6 02030f0U0Sab7:a9ab0Iadaf2r2t0@akamao0pefehdTc~di0hd1dl6xbsdob2dF6ycib_5(bB3kd,7+d.aje0bS3Qd_e77+d|0id eZ9{e3e5eb4{8HdhdVdjcZeF3dbIeIeNcMbMdtc%5zbQeQaN9rd-0`a%a#a`3md@9{0M0k0`c5dgdUdAbFdXcEc0e_du6jb{e}d5c0d+f3eS7.1S7!e(e1eX04f83MfafBe#e%2/fGeWe*5+e,870`bnfh2HdBe=8Qcdfne~3e6/eMfo5Pf$cOf2fvfbf50$f7eV3Pfc0`cT9YcWficYfkc!6~d!d(3F5Bd%b~8Q6 3KeRf.0439f`c 8GfRf{fUfjave?7cg1g6f#c)frdFgnf+f,fLf?f/0sf;fAeW0I7.b(9SfP8k7}gI3=eYfKc.d|0Zf=5cfN5TeC5c7|c}5H8K0A7z7g7u7i7r1d0s7lg,2O2J0e1Zg)0A7j8J0#0%0)0C04.

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

.1280136ra37 =+pcgvu5l:tShf0([/ms1_iq2n8]owLke)y4d;.9Péb-050R0N0r0d0D0p0A0g0k0p0d0A0A0h010r0D0j010406050A0n0z0z0d0c0P040s0J0p0n0?0J0G050y0}0 11130{0j04051j1c1m0y1j0{0R0D0m0+0-0/0;0-0G0l0n0d0l0N0Y0j0P0r0t1a0g0t0D0l0t0p1O0t0r0_050$0X0p0N1v0.0:011N1P1R1P0r1X1Z1V0r0c1k1J0+160A0j0d0G0;0F011#1x010u0(0N0G0d0z0N1V1`1|211%241Z27290_0a0g0V0c0J0j0J0A0D190G0g0!1^0c0c0N0k2u1c2c0G1k0y1J2H1;1?1=1W0R2e1y0D0G262r1V1s1u0,1$2R2T0G0J2X1V0j2A1k2F2H2.0|1{2v2Z222%0c100p1V0d1M2A0u0;030C0C0k2(0N1R2$0J0Y0F0Y0B0_0g0B1c0d2/2=0`2;2d2@1%2_2{2}2 0N3101333537392U3c3c3g0F3j3l1|3n2F2Q013s0d2|1k2~0t303234360!3C2%3E0e3g0e3I2E3m0{3M3q0;3P3R053T3V3y3X3B2S3D3d0Q3g0Q3*1d3,3o2?1w3r0J2`3Q3u3U3w3W3A3Z3|3#3d0o3g0o422.3-2=3N3;4c3^3z3Y384i3b3d0b3g0b4o443.473:493t3S3v3x4w3{3a3E0f3g0f4F3K4q3p4I3O4K4b4M4d4O3`4h4R3d0H3g0H4W2G4Y462!4#4a3=3@4e3_4g4y4-0Y0U3g0U4=3L4r3/4`4L3?4N4f4x3!4A3e0v0_0B0v571n2,1c2X2K0R1?2P5a4x2W1t1k2+0N2-3m3+3K054x5E2d0D0R0;342F3E3f4M5M5O505h5R202i0N5V5g4z5Y2H3k453N0M0_0!0u5G2G5,5a0K3g5=5K4^2^0u0_0p1a1B0N0n0c5{5@4!0^040w674H4_0G0_1.0N0d0n6d59690_0q5{0g686f0X600D0A0r6m4Z4_6a0O6r6t220J0_0Y020l0r0S6F6e2^6v042S6z435H6Q1%6a6q6W4?6A2v5U015P2=3E1 5T5N6+5W5(3d1 0g5!5$4Q3}3F5*5|3N5_040g756s6$715a0A0R0_020E0n0J6N7e7g7i7f7h6O780{785,6*6,1|3$3u7t6?523%6`285#6=5%7A1V0y5+6Y0;7b3g760L2~0u1a2C0D1L2A0G0m0J0D1!0-0g611A0n640c2w1!6i6k5{7q2:3M7y5Q3~7x6;4+516~3 7C296|4,807I7K6n4_7N74767j7n8e7l7k7o4p6(0g7_6-4k7|847 4j0Y4l827E7~5X8p70766s7L3O0_360j7#0C7:6l788D896H0_0h6P8P3r6S1R6y8l5a6a6c7r8E6g048L8Z6o046E8N6G1%0k5S032m0J656`1!1{0*0R0W1;0n0D2A0g8+7p8l8n7v4B8q7F6}8t4C8w8r8z0Y4C8B768;0;5.6T5;8:8(8G2p8J972.8O6B8Q040h8S9u8U0;6a0x0I6#8k8%4r9a0G4S9d8y6@0Y4T9i9e858t4T9n8C759p019r2A0r651b9H9C1%0z0D0_5n989P5L7}0C7`0Y4/6:9j9W4/9Z9V52a33I8C9+9r380A0N8,6C6p7=999 a154a49!8s5i54a87z6~aqac9)9*9v048H9y0d1Y6j8M7@9I016I040Taj2^0_2q0jaR6Z0_0w8/9OaL9~5Va15m9Uax8ta*aw7G6~a*9(9)ae0_9.9:8T9?0;9^5la|5}1%aO0ib14s60627+65aW9JaYbc8FaE9x0N8KaH1Z7;9}b2bd8.am7r0y5J5p5D5r5A1c0r5ubA2N2Iblbx0y5s7q0!0$0(0A04.

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

.1280136ra37 =Npcg+vèu5l:tShf(0Cxî/ms1_iq2n8owke)y4d;.9P,éb-050T0P0t0d0H0r0E0g0k0r0d0E0E0h010t0H0j010406050E0p0D0D0d0c0R040u0M0r0p0_0M0K050C101214160~0j04051m1f1p0C1m0~0T0H0n0.0:0=0@0:0K0l0p0d0l0P0#0j0R0t0v1d0g0v0H0l0v0r1R0v0t0|050)0!0r0P1y0;0?011Q1S1U1S0t1!1$1Y0t0c1n1M0.190E0j0d0K0@0J011(1A010w0+0P0K0d0D0P1Y1}1 241*271$2a2c0|0a0g0X0c0M0j0M0E0H1c0K0g0%1{0c0c0P0k2x1f2f0K1n0C1M2K1@1_1^1Z0T2h1B0H0K292u1Y1v1x0/1)2U2W0K0M2!1Y0j2D1n2I2K2;0 1~2y2$252*0c130r1Y0d1P2D0w0@030G0G0k2+0P1U2)0M0#0e0#0F0|0F1f0d2=2^0}2@2g2`1*2|2~30320P340136383a3c2X3f0#22040J3l3n1 3p2I2T013u0d2 1n310v333537390%3E2*3G0e0|0e3L2H3o0~3P3s0@3S3U053W3Y3A3!3D2V3F3g0S0|0S3-1g3/3q2_1z3t0M2}3T3w3X3y3Z3C3$3 3(3g0q0|0q452;3:2^3Q3@4f3{3B3#3b4l3e3g0b0|0b4r473;4a3?4c3v3V3x3z4z3~3d3G0f0|0f4I3N4t3r4L3R4N4e4P4g4R3}4k4U3g0L0|0L4Z2J4#492%4(4d3^3`4h3|4j4B4:0#0W0|0W4^2K2.0P2K2!2N0T1_2S3=014A2Z1w1n5c2:3o3.3N054A5r2g0H0T0@372I3G3i4P5z5B533%4D3h232l0P5I4A5K5E1Y0C3m483Q0O0|0%0w5t2J5X5k0N0|0g5%5x4{2{0w0|2D0j0P0d0t5.5)4%0{040x5|4K4|0K0|1e465u63255 0s5.5-6a3t0!0|2V5{685(6g0@5 0Y6e5}640|0t0A6l2?6o016c6s6A0K6i040E1@624u5k5 0Q6D6L4%0M0|0#020l0t0U6P4$646G6I0c6Z5:1*6C6m3p6-5X5H015C2^3G3I3_0g6;4.54403H5N2b5P6=5J4C6^5U5W6A5+040g7d5-6/6A0E0T0|020I0p0M6X7l7n7p7m7o6Y6-0~7g4u6|0G5D3g3*5G5A745R767D712c5Q4T6 7E3-7h7j7c7e0s1~0c2b0g0K0s2z1%0t0R5^0g290_0P0c0V0g0i0M0D0!2D7%0g0w0M0H0-7m1%0r02030e0W0U1O2D390j0H82310k0v0d0B2W7{0k140d2F0o2D0E0V5.7x6z7z7G6?1 3G427F7N4/6 427!728E6~4m0#8C7R6Q4|7i5,7V7X7Z6w0t7$2A7)7+6%7;0z8h3 8l8n8p8r0g810g8385871O0T7~0t0g0c0Z0j0Z0t7/8t7w6K5y8y7B6@4n3w7A7I554o8I7M7H7O8M4o2K798Q258S7U7d7q7u9u7s7r7v4s962y7A7C0#4F8D9j8F8M4F9h736}5S4E789s6f9p1*5Z040H5$6-9T6!2{666)3Q6S040h0h9)5k0D0H0|0y9/5~0|6d957y975I9E4W9H9O7J0#4W9M8K9Pa59R7eac9#6*0@9W2D0t0p0c672;ae3Q0E5F84860Uas878u9B6{989E4=a275554=a79I8L5LaC3Lac6t259W3b0E0P9^4|6,9A9}9CaA9a569c989e6 57aHa355579n9SaN6Aah0(akam3oao5k65048XaU259+0mb13t5?0P5^5`ay6M0|61aY4v9(9!aO1*9+0#b50@9;3jbb9_046rbi6E6v6xbraV0|6O9|2?0C5w1q2/1f5f1f0t5hbL2Q2L0d1#5dbJ5o7x0%0)0+0E04.

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

.1280136ra37 =+pcg`vu5l:tShf0(U/êms1_iq2n8owke)y4d;9Pb-050R0N0s0d0F0q0C0g0k0q0d0C0C0h010s0F0j010406050C0o0B0B0d0c0P040t0K0q0o0;0K0I050z0{0}0 110_0j04051h1a1k0z1h0_0R0F0n0)0+0-0/0+0I0l0o0d0l0N0W0j0P0s0u180g0u0F0l0u0q1M0u0s0@050!0V0q0N1t0,0.011L1N1P1N0s1V1X1T0s0c1i1H0)140C0j0d0I0/0H011Z1v010v0$0N0I0d0B0N1T1^1`1 1#221X25270@0a0g0U0c0K0j0K0C0F170I0g0Y1?0c0c0N0k2s1a2a0I1i0z1H2F1/1;1:1U0R2c1w0F0I242p1T1q1s0*1!2P2R0I0K2V1T0j2y1i2D2F2,0`1_2t2X202#0c0~0q1T0d1K2y0v0/030E0E0k2$0N1P2!0K0W0Q0W0D0@0g0D1a0d2-2:0^2/2b2=1#2@2_2{2}0N2 01313335372S3a0W1}040g0H3h3j1`3l2D2O013q0d2`1i2|0u2~3032340Y3A2#3C0e3e0e3I2C3k0_3M3o0/3P3R053T3V3w3X3z2Q3B3b0Q3e0Q3*1b3,3m2;1u3p0K2^3Q3s3U3u3W3y3Z3|3#3b0p3e0p422,3-2:3N3;4c3^3x3Y364i393b0b3e0b4o443.473:493r3S3t3v4w3{383C0f3e0f4F3K4q3n4I3O4K4b4M4d4O3`4h4R3b0J3e0J4W2E4Y462Y4#4a3=3@4e3_4g4y4-0W0T3e0T4=3L4r3/4`4L3?4N4f4x3!4A3c0w0@0D0w574@4s4$4|5e4 5g4z3C0D3d045y5o455q4{4u4~4P4,3}3c3E0D3H0z3i3+4X5D5a4t4(4v4+515K0D3%5A3)5P3J4?5T4!5V5d4)5f4Q5!3 5A415)5R5+4H4_5.4}4*505h5x4l5A4n5`435S5}2?5r5G615v520D4C5A4E682.1n2*1a2V2I0R1;2N5a4x2U1r1i2)0N2+3k5{1i4x6D2b0F0R0/322D5x3s6K6M625w3b3d0g2g0N6S6g5!1T5`6b1#0M0@0Y0v6F5,4_0L3e6/6)3:0v0@0s0K6|6@594!0?040x6 4Z5~0@19692E6:20720O0r6F0_7a6I2t6R016N2:3C3E5d7m5Y633b1}6X266Z7n6T527r6(706;3e0g7J754^200C0R0@020G0o6}0S7R7T0s7V7S7U0y2R0g0v182A0F1J0s361X0g7S1Y7g7j7i2.3M7t0E6O3b5$7s6L7B6#4j0W3%7y276!5=85805)7_6E7{827o1`3C5@818a5J853 887A7u6U3a6%5Q6^017O7I7J0W0g0m6|6|0x0w0O0m0g2y0I0n0K0F1Y0m02030e0T0S0w8V8X0S0m7h7L0g7|7~0W658n838b5i4l8s8o5Z858/7F767N7P3F7J0g8E8G6}0K0x0D8L8N248Q8S8F8#8Y8J0g0i0g8K9g8%8)7j5D8,7p4B6Q8i7C5K4C8^8;8p5i6j3*8z8B918D8F8H970H9a8O9d8T9n0x9i9k8K9j0g9U9l0O0O9n8(7^8*9s8k3b4T4M7|845i4T9A8u529.9F7G8 8C930g0Z0k0g0{0c0g7:0B0A270g2)2Q0k0=0N9p7`4r9+0I3C4/9/9w9;am1~6Y8_7v0Wan3I8f3K9r9w8-54aoau8v549@9x85aE9{8~1#9H926Xa00C0s0g0o2t240;0Na52o2q0;6.9)9q8h6S8-5m9vaG6h5kaJaq6V5k2F8y9|aP90aR7W7Ub27Yb40Sah8gajaC9t3c5z8:9^5!6Wat9B8`5i5y8x3la,baa.bc5Na;bkavbua^8=5x7E3iaR7c6*0@0Fa*2,0gbF3:786FbL8z0K0@0h0hbPbM010B0F0@5nbqaO0/727@4p9*bb9,3c802|9:bA6V87bjbg855#boaRbE8z6+042y0s0o0c79bKbX0C5z9n8!8W8Yb8aAa-7Ba/8mb=apb@3c8rb`aKbm8m5)c0a~0/c2360Cagb%7M1#b*ch7bcj8jal6V8/cna=5!8@csa_3c8|bDb 7K8z0I0@0B6}bIbWbRbTc*cy3O6{968*5a7274cE4sbO7jbQc.bS040Wc-b(bYb!5Ac=710@0OcI7k8+b.cM3c9EcPbw8v6ias7zcQb|9EcwcYc}d3c2c4c6c83kdtcF0/cb7Qcf0S0x9nd2dB01c 0idJc`04c%a)dO5adMdT4!dD049n9XdIc|bXdVd%c!c$c(bJdzd(0@dNd*c.dY9n9$dFdb1a6H1l6p0z6r1a0s6te32L2G0d1W6C6q6z7i0Y0!0$0C04.

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

.128013.9888DTa3=gvèuth0x[A/àq8kç).Féb6r7 pcR!5l:Sf(Cms1_i2n]ow;eyd49P,-050(0$0l0e0V0L0S0F0H0L0e0S0S0g010l0V0G010406050S0k0R0R0e0D0%040N0Z0L0k110Z0X0F020e0R0G0#0F0I0$1b0D0t0k0$0S050r181a1c1e160G04051J1C1M0r1J160(0V0i0_0{0}0 0{0X0h0k0e0h0$0-0G0%0l0m1l0F0m0V0h0m0L1=0m0l14050;0B0L0$1V0|0~011;1?1^1?0l1~201|0l0D1K1-0_1h0S0G0e0X0 0W01221X010O0?0$0X1p0$1|2k2m2r242u202x0R2z040a0F0+0D0Z0G0Z0S0V1k1m0/2i0D0D0$0H2U1C2B0X1K0r1-2*2e2g2f1}0(2D1Y0V0X2w2R1|1S1U0`232@2_0X0Z2}1|0G2Z1K2(2*3a172l1m2 2s330D1b0L1|0e1:2Z0O0 030U0U0H340$1^320Z0-0K0-0T140F0T1C0e3b3e153d2C3g243i3k3m3o0$3q013s3u3w3y2`3B0-2p040F0W3I3K2m3M2(2?013R0e3l1K3n0m3p3r3t3v0/3#333%0f3F0f3-2%3L163;3P0 3@3_053{3}3X3 3!2^3$3C0)3F0)481D4a3N3f1W3Q0Z3j3^3T3|3V3~3Z414n433C0K3F0K4t3a4b3e3=4f4D4j3Y403x4J3A3C0C3F0C4P4v4c4y4e4A3S3`3U3W4X4m3z3%0E3F0E4*3/4R3O4-3?4/4C4;4E4?4l4I4_3C0u3F0u4~2)504x30534B4g4i4F4k4H4Z5b0-0*3F0*5g3:4S4d5l4:4h4=4G4Y424#3D0n140T0n5y1N381C2}2-0(2g2=5B4Y2|1T1K370$393L493/054Y5)2C0V0(0 3t2(3%3E4;5;5?5r5I5_2q2H0$5}5H4!602*3J4w3=0v140/0O5+2)6a5B0!3F6g5/5j3h0O141A0l0U2l3y0(2O2I6m6i5213040P6A4,5k0X140R0Z0l6G5A6C140x0M6m164u5,3;5|015@3e3%3)5E6Z595s4o3(612y644^6-6(0r696H2s6k3*0F6~6O515k0S0(14021y6M0#760k787a780c0A0l0$3j4n0F2S0F6L0l0F6s0F0k1m6v2^6x0Z2I7d0l79777B7A0#6U701m6*0U5^3C455{5=6!5~667N6/2I6;5a6-7O3-6V3c6Y7Q6#2m3%4q7P7X6,4K0-4q0F627/5 4p1|6^6}6 6`246c040V6f6W2)0F6B6I0B142G7I3=6D6F866n4T6K6M8e5B6D0x6m88800 0Z750L7B8r892s0R0V143,8i8A246D6T8i7$5*7(5}7M3B3T7K655t4M7@6:7R8U6-4M687~6~8)8H0 822Z0l0k0D0X8z8t010v0H140d0D1z7H8G8O7R8Q4%7.8Z6=7;4%8X7W967Y987|3J8)8s6P5k823x0S0$8n6Q048K4Q8e7K8Q4{956+7`0-4{9a639c7:5J9x3-9h9h8+8^14848?9j3h8l6N909R8I140p9p5k8C145O9V712s6D0Y9Q9*248v040J0g9.6o3Q9T9!9+9Y9|9:140-9 0 9$043H9)9_0 9,9s4va80F9v6$5c8S7)7S5t5d9D7_7T0-5d8%9Kau9i9/8,148.8:8=8iawa98^8`040z3^9n8 7%4Sag7+3C5v9yal6-5vao9F9AaS9Jav9M9l0@9oae8o14ac4 9uak8Q5Najap5ta?aX9zaqa?atav9L8@8-0:aB9^8k046s6u3^7w6ya*aNax018ga33?9{a+9q9Zbm9#8Da6bj8Jbj9;a2bp8Bbra7bfaF9,8q8L6A0r5.5Q5(5S5#1C0l5VbO2:2+0e1 bL0r5T1I8j5B2Z0R0U0O0e0v0$0U0m7O1u1w1y1A0Fa.6h1P3M0/0;0?0^5B337h0F0(0A0G1^0A2z0F2P2w8u0G2w144b191w1e0q1j2Z2X2Z2#0V1/2Q0}0VbV2%ci1Gb{1T3=1Z1#1%1)1+1-1/261@1_1{b!522F2w2y140+1,1.aC3c5%6n3.6hbJ917*0X0-0C3Da@aY66c,3Ea{aU43c;2q575G973Ac_8%a%6d3Vbj6|88by3Q6qb80S6t7v0X7x6zd7aa148hbCb77obt6Rb^3MaeaPc*c,6(3n8Tc}c+6.c?8!c^dBc{5qdDc~6.d08@0S3)7F7f7h7j2_7l0V7n6M7qdb7s7ubbdebd7FaM8NaOa;6$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;0g9@fNenbkeC8meE9~exbwfTbAdo049-f(bg0Z6|2m0(fZ9Sdadcd$dfflfqf)biexfPf,fW9}04bogc24a5bBd+bgbuf/a1f;5Mf?0YbF9t8GbI3w2*cZbM0i3M1Jb:1c770X0^b=0F0{c30$0k0o0V0j2I0F2l0D11210(0k885.f}1C5.0F6F5.b9ddg40P7o0p0T0M3Dgsg%gx0x7@219n0D3n0A0i3^0kc87q1mcUcI1mgJ7m5-gxg:0n0Y0Ff$dW0l0pg@g_0/3*7rh1h30A0F0sg!gx8|8~gwhpg)hs1i0e2UgT1c1A9n0k9n0x0y1Ndrb|0=0@cA2~520e0(6L0X2Tcr1m0!1ch#1!cg1L3=hYh!h$1l0-110l2c04gE1xhA1Q1L040b0F0Q0:c20S1h1jh%hv0F0B0|gX213v0G0Vif0F010S1^0H1A2q0P2e2m0H0mb?2w0F0Og 0X0w0=0Sg{0X007r2l0^3V2u0H0eip0,7@0ZhM0F0i7i2OgHgT1i0^0;0D2=7t210R7g1.2Wc6iUiM0ViOip0F0eiW0HgKb?7wi?1AhPb`6VbY5S0:hT0S04.

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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Autres exercices :⚓︎

Exercices CodEx sur la récursivité

Crédits⚓︎

Franck Chambon