1-condition
2-while
3-maths
5-difficile
Exercice 4 - Persistance multiplicative
Partons d'un nombre entier par exemple 243.
On fait le produit de ses chiffres : 2 × 4 × 3 = 24.
On fait de même pour le résultat obtenu : 2 × 4 = 8 et on ne peut pas continuer plus longtemps, car on a obtenu un nombre à un seul chiffre.
On dit que la persistance multiplicative de 243 est 2.
Indication
Pour extraire les différents chiffres d’un nombre, il peut être intéressant de le voir comme une chaîne de caractères.
Il peut donc être intéressant d'effectuer du transtypage (du cast en anglais).
1. Déterminer la persistance multiplicative
Compléter la fonction persistance_multiplicative
qui permet de déterminer la persistance multiplicative de l'entier en paramètre.
.128013="mI_eh(+yaplq37)dRunC sSé':6w
gPi1vkr.,908-t2è5*;f4Lbcîo/030m0a0N0f0C0h0s0r0X0h0f0s0s05060N0C0g06020z030s0o07070f0G0e020t0Z0h0o0@0Z0p0r000f070g0S0r0n0a110G0i0o0a0s030!0~1012140|0g02031z1s1C0!1z0|0m0C0E0,0.0:0=0.0p0A0o0f0A0a0M0g0e0N0b1b0r0b0C0A0b0h1'0b0N0`030'0W0h0a1L0/0;061%1(1*1(0N1:1=1.0N0G1A1Z0,170s0g0f0p0=0O061@1N060T0)0a0p1f0a1.292b2g1_2j1=2m072o02040r0B0G0Z0g0Z0s0C1a1c0$270G0G0a0X2J1s2q0p1A0!1Z2V2325241/0m2s1O0C0p2l2G1.1I1K0-1^2(2*0p0Z2.1.0g2O1A2T2V2~0}2a1c2:2h2@0G110h1.0f1$2O0T0=0109090X2^0a1*2?0Z0M0K0M0D0`0r0D1s0f2 320{312r341_36383a3c0a3e063g3i3k3m2+3p0M2e020r0O3w3y2b3A2T2'063F0f391A3b0b3d3f3h3j0$3P2@3R0j3t0j3X2S3z0|3#3D0=3'3)033+3-3L3/3O2)3Q3q0U3t0U3{1t3}3B331M3E0Z373(3H3,3J3.3N3;4a3?3q0Q3t0Q4g2~3~323$424q463M3:3l4w3o3q0x3t0x4C4i3 4l414n3G3*3I3K4K493n3R0k3t0k4T3Z4E3C4W3%4Y4p4!4r4$484v4(3q0L3t0L4-2U4/4k2;4=4o43454s474u4M4}0M0J3t0J523!4F40574Z444#4t4L3=4O3r0K0`0D0K5k544G4?595r5c5t4N3R0D3s025L5B4j5D584I5b4%4|4b3r3T0D3W0!3x3|4.5Q5n4H4^4J4{5e5X0D3^5N3`5$3Y535)4;5+5q4_5s4'5:4d5N4f5^5'5`4V565}5a4`5d5u5K4z5N4B664h5(69355E5T6d5I5f0D4Q5N4S6k4D5{6a6p5,5U5.6f3q0D4*5N4,6y4U5m5|6C5~5-6e5J6H4 5N516M6m6O6B5S6D6r614x3r5h5N5j6Z686#6o6%6R6E6T5f0O5x026{5P6n4m6?6c605W6*0O5M775k1D2|1s2.2Y0m252%5n4L2-1J1A2{0a2}3z671A4L7q2r0C0m0=3h2T5K3H7x7z6_5:2f2w0a7F6s7H2V5%700=0F0`0$0T7s0r6A350T0`070o0h0@0g1*0X0f2J3i1%0T0T2O7s7Y1_0_020c7?7Q3%0`0X0b0(2*7|6;7^0`0l0w7s0|6l2U5Q7E067A323R3T5q8f6F6U3S7I2n7L6)5v8k667}0y3t0r8A844:560s0m0`00010j0J0S8I8K8M8J8L8a8C1c8m097B3q5=8l7y8g7G6*3^0r7J8s755v8Z8w850=8F8z8A0q0%0N1?0s0Z0o0+070u1Z3k0r2O0p0E0Z0C1?1=0r2{2^0o2I0r0$1r8c3A9k8e8#8h2b3R638!8+5/6*4d8)8r8$7M9w1.8/8D2h8=3U8A0,7/7;1q271g2G2b0N0+9b2@070W7=9k8b303#8V8X0M6h9t9A8t3R4z9y2x9u6G9(9D7P8:069H9J0r2l9c121f0P230a8S9m9$9o8W8i4P7Da89B5v4Q9/7K9+8,3R6v3{7}9{9J8N8Lar8P8Oa59#4F9%aa0M6J9*8n5f4*ah9;8oaC5^9|7@410`2O0~7'7WaN060Z0`05aT7}070C5yaw7ra77F9'6WaD8%5v4 aHaj9va/9@9I8B7}7S020T4naZ9_0p7 9L9Y2~7X7}0Z8y022)b09F3Eb382a4a69_7_899Z8T0raz9q3q6,a-ae3R5ha;aE5XbtaL9|9JaU0X5M010r0V1?800C7:2O9}0s0N0r0o2*9K0f0YbV2L7+0G0f2Q0PaQ0Ha'3Z9na*aA5zacaI6t5xbya.5K6|3XbDbE7}bG0`bI080h0r0T0f190r9b001o0Z0N0S7+bR0a0Gcb0ocd1i9~2)0Nb*bnbj7wa89'5Lb;a=9=cxb^bv6H5Mb|b}b7b1aP1q7%0Nbd552haW020RaY9kcIbe410W0`cpbo5n7_7{ctcPbf02bMbObiaxcX067_0lb+8da)8$cw8k3b8VcD5Y8q9:cz8o5!a^aMa{cK0N0o0G0pcO4GcKaRcNcsc:8Ucvb/8Zc~ad9,6H8(8*d46t8.3x9!a(aydnbr3r9sdqb=62d2aibz6*0D9s5^dAb,c`9p0p6gcydM5v0D9.dvdYdW7O7vc*7R7T3Jdf5*7!020gci2HbR2b0X0a097$7'0^7*7,1Jc/dBc;c'c$5|0`dec)3$c?bm6zebbqdV6HamdHdw5:agd$b_ejd7b~cJc,814ad.4;cRcUb6aU0pcZ02bR0Ge756e6eb5*e9eJ2hc?c^d)bpdDei3raCeld%6HaGepd06Iesa`euaQcMey56eAe.2ha#0`5Adke4dmb.dE0Da,eZeq3ra:e%dsf2e)cWd*06a|0y1%1=e;3EeF2veP867`fjaOevbhfmc=87ff0=cR000Aceft06e?5NfqbleSb-c{b/btf0e'bxf4ak6HbB3xcHf8dg02e,aScVaUcR0deB3zfT5nfB3ve_dSdCe|eW6{dXf1f:cCf5f:d(fSeDbgexfYb8aXfzeE0`eHfD0`c(dlfUd}7(e07-c-9Mg6fleMe8fof~g9c%87c@f+c_f-fHdE77f;d0gwf@fO3ScFbCe*c;a|2Odbddg2dhe-gr2V7u7b7p7d7m1s0N7ggV2#2W0f1;gS0!7e1yeT5n2O0709c60Fd{0b5=1k1m1o9Nee7r1F3A2.3$0f0m071b2I0C1#2)a~0`1yh0h2h42J0M0@0N2102080pa~4o2Rg}g)080X0C0Ibpc41qbS230P0+2{e1g_0r0c110ChC0/0r0Z1;1'7,982O0l9hbL0G0ucibTbVa~0p2Qh68U0p8`370u1I0(2Ohv037ugbd 0C7+geb4bi7uhv1o0C942l97i09b9d0m9fbS9i9KbN9M0+0m0vbU8)0Z9WbP0m1b0p0ucr1GgT0E9l0$0'0)0s02.
2. Plus petit entier
Compléter la fonction inverse_persistance_multiplicative
renvoyant le plus petit entier dont la persistance multiplicative est au moins l'entier n
en paramètre.
.128013="m_eh(+3yapl)7qdàuné sS:j6w
gPi1vkr.908O-t25f;4bco/030l090L0f0A0h0r0q0S0h0f0r0r05060L0A0g06020x030r0n07070f0E0e020s0T0h0n0.0T0o030U0^0`0|0~0?0g02031e171h0U1e0?0l0A0C0%0(0*0,0(0o0y0n0f0y090K0g0e0L0a150q0a0A0y0a0h1J0a0L0;030Y0R0h091q0)0+061I1K1M1K0L1S1U1Q0L0E1f1E0%110r0g0f0o0,0M061W1s060O0!090o0f07091Q1;1?1{1Y1~1U21230;040q0z0E0T0g0T0r0A140o0q0W1/0E0E090S2o17260o1f0U1E2B1+1-1,1R0l281t0A0o202l1Q1n1p0'1X2L2N0o0T2R1Q0g2u1f2z2B2'0@1=2p2T1|2X0E0{0h1Q0f1H2u0O0,0108080S2Y091M2W0T0K0B350;0B170f2(2+0=2*272-1Y2/2;2?2^092`062|2~30322O350K1_020M3a3c1?3e2z2K063j0f2=1f2@0a2_2{2}2 0W3t2X3v0d0;0d3A2y3d0?3E3h0,3H3J033L3N3p3P3s2M3u360Q0;0Q3Y183!3f2,1r3i0T2:3I3l3M3n3O3r3R3:3T360N0;0N3_2'3#2+3F3(433,3q3Q314934360v0;0v4f3{3$3~3'403k3K3m3o4n3/333v0j0;0j4w3C4h3g4z3G4B424D444F3.484I360I0;0I4N2A1i2$172R2E0l1-2J3%064o2Q1o1f2#092%3d3Z3C034o4}270A0l0,2}2z3v0B3l5557474p4!370q2c095e4o3S4r372B3b3|3F0D0;0W0O4 2A0q5t4=0o0O0;2M0C090E0r09080g5J2m0r0Y0o0S5M070n0h0.0g1M0S0f0.5I5z533}2U060:020b5)5C4R0o0;163`504y5,5.0i0t5)0?5`4)3E5d06582+3v3x3*0q664Y5g3;3w1`5k5m4H6h6b0U3b0q6r5B5|1|0S5b02010q0J2,0a5J0S6D0q0(0q5!0n0$5O0.0L1V0C3I090n0E2q1V0h00010d0G0P200.5J0q2u0^5Y2q150L6H2@5O5K0A5R1?5U0q5W5Y0/5#5%1o1V095R0q0^0g0p0E0A6T2u0q0T0n0q0p0y6S0q0m5j0F615;6556670859363V4D6e5f5o3U6j225l7t5n4q7C5r026s6t4i4=6w0;6z6B1/0`206{7m0H0q0F7#7p635*6d7s681?3v3?7y7*7A7I3=7D236l4Z6h7.3A7M5=5,5@026+5X0L5)7N4Q5,0T0;05867 1|070A0;0H7%2)7r5e7v0K4c7/7_6g4a8p7@7F6f7B4b1Q6p7L6s8e1Y5v020w1I1U8d6u3i0;6?5Q5S5U086}5Z705'097q7O4R5.5:7'8F3'0;835Y8!881|5~8M8#890;005Y0P8=8/8O025_8l8?8:0;607'6291547:8o4t8r7G6m8u4t5j7E8s8z0K9c7}7M8E8N0,7Q6y7!7#0q0X7e2p0f0n1z070o6P6W0q0B0q0u6L0k0n6Z6#0P7m1+7f5I0E7o968.2p7z8o4K9d8y7=0K4K9i7^9e7`8u9%9o9p875+2.8+74848|9^1Y8a020c8c7'9@3F8g388k4~8m7t8o4$9'7;5h4$9,8xag6hae9=a54=8H2u0L6U903dap5?9`6,859Y8(0U524*4|4,4_170L4/aK2H2C0f1TaH0U4-620W0Y0!0r02.
# Tests
(insensible à la casse)(Ctrl+I)