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Rezolvare de nota 20

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Salut!

Azi am vazut pe .campion subiectele de la finala de anul trecut, si am zis sa ma uit putin peste ele.

Am rezolvat una din probleme, dar am vrut sa vad cum au facut-o altii mai experimantati.

Din intamplare, am intrat pe folderul cu nr. 5. Problema suna in felul urmator:

Fie k un numãr natural strict pozitiv. Numãrul natural n se numeºte k-factorizabil dacã poate fi scris ca un produs de numere naturale ? k.
Cerinþã
Pentru un k dat ºi un interval [a, b] specificat, sã se determine câte numere k-factorizabile se aflã în intervalul [a, b].
Restricþii
2 ? k ? 100 000
1 ? a ? b ? 2 000 000 000
b-a ? 5 000 000

Si rezolvarea "1337" a tipului:

#include <stdio.h>
const int prim[9594]={2,3,5,7,11,13,17,19,23
,29,31,37,41,43,47,53,59,61,67
,71,73,79,83,89,97,101,103,107,109
,113,127,131,137,139,149,151,157,163,167
,173,179,181,191,193,197,199,211,223,227
,229,233,239,241,251,257,263,269,271,277
,281,283,293,307,311,313,317,331,337,347
,349,353,359,367,373,379,383,389,397,401
,409,419,421,431,433,439,443,449,457,461
,463,467,479,487,491,499,503,509,521,523
,541,547,557,563,569,571,577,587,593,599
,601,607,613,617,619,631,641,643,647,653
,659,661,673,677,683,691,701,709,719,727
,733,739,743,751,757,761,769,773,787,797
,809,811,821,823,827,829,839,853,857,859
,863,877,881,883,887,907,911,919,929,937
,941,947,953,967,971,977,983,991,997,1009
,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063
,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129
,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217
,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289
,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367
,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447
,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499
,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579
,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637
,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723
,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801
,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879
,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979
,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039
,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113
,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207
,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281
,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351
,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417
,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521
,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609
,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683
,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731
,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803
,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897
,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971
,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067
,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169
,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253
,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329
,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407
,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499
,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559
,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637
,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719
,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803
,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889
,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967
,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051
,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133
,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229
,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289
,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397
,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483
,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567
,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651
,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733
,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817
,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933
,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999
,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081
,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171
,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273
,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381
,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441
,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519
,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623
,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689
,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783
,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851
,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927
,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047
,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131
,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217
,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299
,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361
,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469
,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569
,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661
,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737
,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829
,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911
,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991
,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079
,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193
,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283
,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393
,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489
,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559
,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639
,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717
,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823
,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907
,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011
,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101
,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209
,8219,8221,8231,8233,8237,8243,8263,8269,8273,8287
,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377
,8387,8389,8419,8423,8429,8431,8443,8447,8461,8467
,8501,8513,8521,8527,8537,8539,8543,8563,8573,8581
,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669
,8677,8681,8689,8693,8699,8707,8713,8719,8731,8737
,8741,8747,8753,8761,8779,8783,8803,8807,8819,8821
,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923
,8929,8933,8941,8951,8963,8969,8971,8999,9001,9007
,9011,9013,9029,9041,9043,9049,9059,9067,9091,9103
,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187
,9199,9203,9209,9221,9227,9239,9241,9257,9277,9281
,9283,9293,9311,9319,9323,9337,9341,9343,9349,9371
,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437
,9439,9461,9463,9467,9473,9479,9491,9497,9511,9521
,9533,9539,9547,9551,9587,9601,9613,9619,9623,9629
,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721
,9733,9739,9743,9749,9767,9769,9781,9787,9791,9803
,9811,9817,9829,9833,9839,9851,9857,9859,9871,9883
,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973
,10007,10009,10037,10039,10061,10067,10069,10079,10091,10093
,10099,10103,10111,10133,10139,10141,10151,10159,10163,10169
,10177,10181,10193,10211,10223,10243,10247,10253,10259,10267
,10271,10273,10289,10301,10303,10313,10321,10331,10333,10337
,10343,10357,10369,10391,10399,10427,10429,10433,10453,10457
,10459,10463,10477,10487,10499,10501,10513,10529,10531,10559
,10567,10589,10597,10601,10607,10613,10627,10631,10639,10651
,10657,10663,10667,10687,10691,10709,10711,10723,10729,10733
,10739,10753,10771,10781,10789,10799,10831,10837,10847,10853
,10859,10861,10867,10883,10889,10891,10903,10909,10937,10939
,10949,10957,10973,10979,10987,10993,11003,11027,11047,11057
,11059,11069,11071,11083,11087,11093,11113,11117,11119,11131
,11149,11159,11161,11171,11173,11177,11197,11213,11239,11243
,11251,11257,11261,11273,11279,11287,11299,11311,11317,11321
,11329,11351,11353,11369,11383,11393,11399,11411,11423,11437
,11443,11447,11467,11471,11483,11489,11491,11497,11503,11519
,11527,11549,11551,11579,11587,11593,11597,11617,11621,11633
,11657,11677,11681,11689,11699,11701,11717,11719,11731,11743
,11777,11779,11783,11789,11801,11807,11813,11821,11827,11831
,11833,11839,11863,11867,11887,11897,11903,11909,11923,11927
,11933,11939,11941,11953,11959,11969,11971,11981,11987,12007
,12011,12037,12041,12043,12049,12071,12073,12097,12101,12107
,12109,12113,12119,12143,12149,12157,12161,12163,12197,12203
,12211,12227,12239,12241,12251,12253,12263,12269,12277,12281
,12289,12301,12323,12329,12343,12347,12373,12377,12379,12391
,12401,12409,12413,12421,12433,12437,12451,12457,12473,12479
,12487,12491,12497,12503,12511,12517,12527,12539,12541,12547
,12553,12569,12577,12583,12589,12601,12611,12613,12619,12637
,12641,12647,12653,12659,12671,12689,12697,12703,12713,12721
,12739,12743,12757,12763,12781,12791,12799,12809,12821,12823
,12829,12841,12853,12889,12893,12899,12907,12911,12917,12919
,12923,12941,12953,12959,12967,12973,12979,12983,13001,13003
,13007,13009,13033,13037,13043,13049,13063,13093,13099,13103
,13109,13121,13127,13147,13151,13159,13163,13171,13177,13183
,13187,13217,13219,13229,13241,13249,13259,13267,13291,13297
,13309,13313,13327,13331,13337,13339,13367,13381,13397,13399
,13411,13417,13421,13441,13451,13457,13463,13469,13477,13487
,13499,13513,13523,13537,13553,13567,13577,13591,13597,13613
,13619,13627,13633,13649,13669,13679,13681,13687,13691,13693
,13697,13709,13711,13721,13723,13729,13751,13757,13759,13763
,13781,13789,13799,13807,13829,13831,13841,13859,13873,13877
,13879,13883,13901,13903,13907,13913,13921,13931,13933,13963
,13967,13997,13999,14009,14011,14029,14033,14051,14057,14071
,14081,14083,14087,14107,14143,14149,14153,14159,14173,14177
,14197,14207,14221,14243,14249,14251,14281,14293,14303,14321
,14323,14327,14341,14347,14369,14387,14389,14401,14407,14411
,14419,14423,14431,14437,14447,14449,14461,14479,14489,14503
,14519,14533,14537,14543,14549,14551,14557,14561,14563,14591
,14593,14621,14627,14629,14633,14639,14653,14657,14669,14683
,14699,14713,14717,14723,14731,14737,14741,14747,14753,14759
,14767,14771,14779,14783,14797,14813,14821,14827,14831,14843
,14851,14867,14869,14879,14887,14891,14897,14923,14929,14939
,14947,14951,14957,14969,14983,15013,15017,15031,15053,15061
,15073,15077,15083,15091,15101,15107,15121,15131,15137,15139
,15149,15161,15173,15187,15193,15199,15217,15227,15233,15241
,15259,15263,15269,15271,15277,15287,15289,15299,15307,15313
,15319,15329,15331,15349,15359,15361,15373,15377,15383,15391
,15401,15413,15427,15439,15443,15451,15461,15467,15473,15493
,15497,15511,15527,15541,15551,15559,15569,15581,15583,15601
,15607,15619,15629,15641,15643,15647,15649,15661,15667,15671
,15679,15683,15727,15731,15733,15737,15739,15749,15761,15767
,15773,15787,15791,15797,15803,15809,15817,15823,15859,15877
,15881,15887,15889,15901,15907,15913,15919,15923,15937,15959
,15971,15973,15991,16001,16007,16033,16057,16061,16063,16067
,16069,16073,16087,16091,16097,16103,16111,16127,16139,16141
,16183,16187,16189,16193,16217,16223,16229,16231,16249,16253
,16267,16273,16301,16319,16333,16339,16349,16361,16363,16369
,16381,16411,16417,16421,16427,16433,16447,16451,16453,16477
,16481,16487,16493,16519,16529,16547,16553,16561,16567,16573
,16603,16607,16619,16631,16633,16649,16651,16657,16661,16673
,16691,16693,16699,16703,16729,16741,16747,16759,16763,16787
,16811,16823,16829,16831,16843,16871,16879,16883,16889,16901
,16903,16921,16927,16931,16937,16943,16963,16979,16981,16987
,16993,17011,17021,17027,17029,17033,17041,17047,17053,17077
,17093,17099,17107,17117,17123,17137,17159,17167,17183,17189
,17191,17203,17207,17209,17231,17239,17257,17291,17293,17299
,17317,17321,17327,17333,17341,17351,17359,17377,17383,17387
,17389,17393,17401,17417,17419,17431,17443,17449,17467,17471
,17477,17483,17489,17491,17497,17509,17519,17539,17551,17569
,17573,17579,17581,17597,17599,17609,17623,17627,17657,17659
,17669,17681,17683,17707,17713,17729,17737,17747,17749,17761
,17783,17789,17791,17807,17827,17837,17839,17851,17863,17881
,17891,17903,17909,17911,17921,17923,17929,17939,17957,17959
,17971,17977,17981,17987,17989,18013,18041,18043,18047,18049
,18059,18061,18077,18089,18097,18119,18121,18127,18131,18133
,18143,18149,18169,18181,18191,18199,18211,18217,18223,18229
,18233,18251,18253,18257,18269,18287,18289,18301,18307,18311
,18313,18329,18341,18353,18367,18371,18379,18397,18401,18413
,18427,18433,18439,18443,18451,18457,18461,18481,18493,18503
,18517,18521,18523,18539,18541,18553,18583,18587,18593,18617
,18637,18661,18671,18679,18691,18701,18713,18719,18731,18743
,18749,18757,18773,18787,18793,18797,18803,18839,18859,18869
,18899,18911,18913,18917,18919,18947,18959,18973,18979,19001
,19009,19013,19031,19037,19051,19069,19073,19079,19081,19087
,19121,19139,19141,19157,19163,19181,19183,19207,19211,19213
,19219,19231,19237,19249,19259,19267,19273,19289,19301,19309
,19319,19333,19373,19379,19381,19387,19391,19403,19417,19421
,19423,19427,19429,19433,19441,19447,19457,19463,19469,19471
,19477,19483,19489,19501,19507,19531,19541,19543,19553,19559
,19571,19577,19583,19597,19603,19609,19661,19681,19687,19697
,19699,19709,19717,19727,19739,19751,19753,19759,19763,19777
,19793,19801,19813,19819,19841,19843,19853,19861,19867,19889
,19891,19913,19919,19927,19937,19949,19961,19963,19973,19979
,19991,19993,19997,20011,20021,20023,20029,20047,20051,20063
,20071,20089,20101,20107,20113,20117,20123,20129,20143,20147
,20149,20161,20173,20177,20183,20201,20219,20231,20233,20249
,20261,20269,20287,20297,20323,20327,20333,20341,20347,20353
,20357,20359,20369,20389,20393,20399,20407,20411,20431,20441
,20443,20477,20479,20483,20507,20509,20521,20533,20543,20549
,20551,20563,20593,20599,20611,20627,20639,20641,20663,20681
,20693,20707,20717,20719,20731,20743,20747,20749,20753,20759
,20771,20773,20789,20807,20809,20849,20857,20873,20879,20887
,20897,20899,20903,20921,20929,20939,20947,20959,20963,20981
,20983,21001,21011,21013,21017,21019,21023,21031,21059,21061
,21067,21089,21101,21107,21121,21139,21143,21149,21157,21163
,21169,21179,21187,21191,21193,21211,21221,21227,21247,21269
,21277,21283,21313,21317,21319,21323,21341,21347,21377,21379
,21383,21391,21397,21401,21407,21419,21433,21467,21481,21487
,21491,21493,21499,21503,21517,21521,21523,21529,21557,21559
,21563,21569,21577,21587,21589,21599,21601,21611,21613,21617
,21647,21649,21661,21673,21683,21701,21713,21727,21737,21739
,21751,21757,21767,21773,21787,21799,21803,21817,21821,21839
,21841,21851,21859,21863,21871,21881,21893,21911,21929,21937
,21943,21961,21977,21991,21997,22003,22013,22027,22031,22037
,22039,22051,22063,22067,22073,22079,22091,22093,22109,22111
,22123,22129,22133,22147,22153,22157,22159,22171,22189,22193
,22229,22247,22259,22271,22273,22277,22279,22283,22291,22303
,22307,22343,22349,22367,22369,22381,22391,22397,22409,22433
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char v[5000000];
int t, i, sol, j, o, k, a, b;
int main()
{
freopen("kfactor.in","r",stdin);
freopen("kfactor.out","w",stdout);
scanf("%d %d %d",&k, &a, &;
for (i = 0; prim[i] <= k; ++ i)
;
o=i-1;
for (i = a; i <= b; ++ i)
if (!v[i-a])
{
t=i;
for (j = 0; j <= o && t!= 1; ++ j)
while (t%prim[j] == 0)
t/=prim[j];
if (t == 1)
{
sol++;
v[i-a] = 1;
for (j = 0; j <= o && i*prim[j]<=b; ++j)
if (!v[i*prim[j]-a])
{
v[i*prim[j]-a] = 1;
++sol;
}
}
}
else
{
for (j = 0; j <= o && i*prim[j] <= b; ++ j)
if (!v[i*prim[j]-a])
{
v[i*prim[j]-a] = 1;
++sol;
}
}
printf("%d\n",sol);
return 0;
}

So ... ce parere aveti :)) ?

Posted
Ma doare creierul... destept tipul, ce mai.

esti un prost. n-ai inteles nimic

tehnica aceasta se folosea foarte des la olimpiada.

aveai sa zicem 3 probleme de rezolvat. si vedeai ca una se poate rezolva cu o metoda mai neconventionala.

prin generarea tuturor solutiilor sau solutiilor partiale. faza e ca ti-ar fi iesit din timp la testele propriu-zise.

asa ca faci un program care iti genereaza (cum este in acest caz) numerele prime pana la limita specificata in problema. si il lasi in background sa ruleze cat timp rezolvi alta problema.

spre sfarsitul concursului cand vezi ca a terminat de rezolvat si ai terminat si tu celelalte 2 probleme, iei datele si le incluzi in sursa.

cu aceste date iti garantezi punctaj maxim cu timp de exeecutie de invidiat.

acesta a fost din gama Tips & Tricks pentru olimpiada nationala de informatica marca moubik.

(vedeti nu eram singurul care "optimiza" rezolvarea problemelor in acest mod)

Posted

a precalculat bravo lui.

orice problema se poate rezolva cu un backtracking sau ceva cu o complexitate mai mare si introfuceti apoi in program.deaia sunt limite de lungime a sursei pe unele siteuri gen infoarena.merge bine pe problemele ce cer sa gasesti anumite numere dintr un interval dat cu o anumita prop etc

oricum ce te pasa pe tine ce a facut el?

Posted
cu aceste date iti garantezi punctaj maxim cu timp de exeecutie de invidiat.

Timpul de executie al programului e de tot cacatul.

Pentru unul din teste, ia 4 secunde si pentru un altul, acces violation (am incercat doar pe trei teste, din care doar 1 a mers cum trebuie) 8).

In plus, putea fi rezolvata mult mai usor (nu cred ca mi-a luat mai mult de 15 minute sa o rezolv) si cu timp de executie mai mic.

[quote=

Posted

tw8, eu am observat tehnica folosita si vorbeam despre tehnica.

@aghast: tu singur ai spus:

Ma doare creierul... destept tipul, ce mai.

1. spui public ca nu intelegi

2. nu intelegi

3. te bagi in seama total aiurea

unii oameni sunt prosti, altii sunt destepti.

problema este ca toti vor sa fie destepti. oricat de prosti ar fi ei nu pot sa accepte acest lucru.

Guest Kenpachi
Posted

problema e ca oamenii cu un intelect limitat vor sa para mai sus decat sunt.

Posted

Mi-a spus proful de info de mai de mult, ca a fost o problema la nationala, in care solutia oficiala era o smecherie de genu asta.

In prob respectiva se citea un singur nr N; astfel se facea usor un backtracking pt toate nr N posibile, si afisa in fisier solutia. Dadeai un copy paste si programul arata cam asa:

daca n==1 afiseaza(1223241,124214,434352 etc.)

daca n==2 ....

..

..

pana la limita din enunt.

Desigur pt problema aia exista si o rezolvare care sa intre in timp, fara smecheria asta; insa daca nu ai idei faci ca mai sus si iei 100 (sunt foarte rare problemele in care citesti 1,2 numere din intervale mici, din motivul asta).

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