POJ-1338 Ugly Numbers 打表 Or 递推

该题题意很简单,题目中定义了丑数的概念,即这个数只有2,3,5这几个因子,现在要我们输出前1500个丑数的任意一个.

前面没想到好的方法,直接想着打表了,前面700个能够在线跑出来,后面的就打了个表.

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
using namespace std;

bool is(int x) {
    while (x % 2 == 0) x /= 2;
    while (x % 3 == 0) x /= 3;
    while (x % 5 == 0) x /= 5;
    return x == 1;
}

int rec[850] = {
5904900, 5971968, 6000000, 6075000, 6144000, 6220800, 6250000, 6291456, 6298560, 6328125, 6377292, 6400000, 6480000, 6553600, 6561000, 6635520, 6718464, 6750000, 6834375, 6912000, 6998400, 7031250, 7077888, 7085880, 7200000, 7290000, 7372800, 7381125, 7464960, 7500000, 7558272, 7593750, 7680000, 7776000, 7812500, 7864320, 7873200, 7962624, 7971615, 8000000, 8100000, 8192000, 8201250, 8294400, 8388608, 8398080, 8437500, 8503056, 8640000, 8748000, 
8847360, 8857350, 8957952, 9000000, 9112500, 9216000, 9331200, 9375000, 9437184, 9447840, 9565938, 9600000, 9720000, 9765625, 9830400, 9841500, 9953280, 10000000, 10077696, 10125000, 10240000, 10368000, 10485760, 10497600, 10546875, 10616832, 10628820, 10800000, 10935000, 11059200, 11197440, 11250000, 11337408, 11390625, 11520000, 11664000, 11718750, 11796480, 11809800, 11943936, 12000000, 12150000, 12288000, 12301875, 12441600, 12500000, 12582912, 12597120, 12656250, 12754584, 
12800000, 12960000, 13107200, 13122000, 13271040, 13286025, 13436928, 13500000, 13668750, 13824000, 13996800, 14062500, 14155776, 14171760, 14348907, 14400000, 14580000, 14745600, 14762250, 14929920, 15000000, 15116544, 15187500, 15360000, 15552000, 15625000, 15728640, 15746400, 15925248, 15943230, 16000000, 16200000, 16384000, 16402500, 16588800, 16777216, 16796160, 16875000, 17006112, 17280000, 17496000, 17578125, 17694720, 17714700, 17915904, 18000000, 18225000, 18432000, 18662400, 18750000, 
18874368, 18895680, 18984375, 19131876, 19200000, 19440000, 19531250, 19660800, 19683000, 19906560, 20000000, 20155392, 20250000, 20480000, 20503125, 20736000, 20971520, 20995200, 21093750, 21233664, 21257640, 21600000, 21870000, 22118400, 22143375, 22394880, 22500000, 22674816, 22781250, 23040000, 23328000, 23437500, 23592960, 23619600, 23887872, 23914845, 24000000, 24300000, 24576000, 24603750, 24883200, 25000000, 25165824, 25194240, 25312500, 25509168, 25600000, 25920000, 26214400, 26244000, 
26542080, 26572050, 26873856, 27000000, 27337500, 27648000, 27993600, 28125000, 28311552, 28343520, 28697814, 28800000, 29160000, 29296875, 29491200, 29524500, 29859840, 30000000, 30233088, 30375000, 30720000, 31104000, 31250000, 31457280, 31492800, 31640625, 31850496, 31886460, 32000000, 32400000, 32768000, 32805000, 33177600, 33554432, 33592320, 33750000, 34012224, 34171875, 34560000, 34992000, 35156250, 35389440, 35429400, 35831808, 36000000, 36450000, 36864000, 36905625, 37324800, 37500000, 
37748736, 37791360, 37968750, 38263752, 38400000, 38880000, 39062500, 39321600, 39366000, 39813120, 39858075, 40000000, 40310784, 40500000, 40960000, 41006250, 41472000, 41943040, 41990400, 42187500, 42467328, 42515280, 43046721, 43200000, 43740000, 44236800, 44286750, 44789760, 45000000, 45349632, 45562500, 46080000, 46656000, 46875000, 47185920, 47239200, 47775744, 47829690, 48000000, 48600000, 48828125, 49152000, 49207500, 49766400, 50000000, 50331648, 50388480, 50625000, 51018336, 51200000, 
51840000, 52428800, 52488000, 52734375, 53084160, 53144100, 53747712, 54000000, 54675000, 55296000, 55987200, 56250000, 56623104, 56687040, 56953125, 57395628, 57600000, 58320000, 58593750, 58982400, 59049000, 59719680, 60000000, 60466176, 60750000, 61440000, 61509375, 62208000, 62500000, 62914560, 62985600, 63281250, 63700992, 63772920, 64000000, 64800000, 65536000, 65610000, 66355200, 66430125, 67108864, 67184640, 67500000, 68024448, 68343750, 69120000, 69984000, 70312500, 70778880, 70858800, 
71663616, 71744535, 72000000, 72900000, 73728000, 73811250, 74649600, 75000000, 75497472, 75582720, 75937500, 76527504, 76800000, 77760000, 78125000, 78643200, 78732000, 79626240, 79716150, 80000000, 80621568, 81000000, 81920000, 82012500, 82944000, 83886080, 83980800, 84375000, 84934656, 85030560, 86093442, 86400000, 87480000, 87890625, 88473600, 88573500, 89579520, 90000000, 90699264, 91125000, 92160000, 93312000, 93750000, 94371840, 94478400, 94921875, 95551488, 95659380, 96000000, 97200000, 
97656250, 98304000, 98415000, 99532800, 100000000, 100663296, 100776960, 101250000, 102036672, 102400000, 102515625, 103680000, 104857600, 104976000, 105468750, 106168320, 106288200, 107495424, 108000000, 109350000, 110592000, 110716875, 111974400, 112500000, 113246208, 113374080, 113906250, 114791256, 115200000, 116640000, 117187500, 117964800, 118098000, 119439360, 119574225, 120000000, 120932352, 121500000, 122880000, 123018750, 124416000, 125000000, 125829120, 125971200, 126562500, 127401984, 127545840, 128000000, 129140163, 129600000, 
131072000, 131220000, 132710400, 132860250, 134217728, 134369280, 135000000, 136048896, 136687500, 138240000, 139968000, 140625000, 141557760, 141717600, 143327232, 143489070, 144000000, 145800000, 146484375, 147456000, 147622500, 149299200, 150000000, 150994944, 151165440, 151875000, 153055008, 153600000, 155520000, 156250000, 157286400, 157464000, 158203125, 159252480, 159432300, 160000000, 161243136, 162000000, 163840000, 164025000, 165888000, 167772160, 167961600, 168750000, 169869312, 170061120, 170859375, 172186884, 172800000, 174960000, 
175781250, 176947200, 177147000, 179159040, 180000000, 181398528, 182250000, 184320000, 184528125, 186624000, 187500000, 188743680, 188956800, 189843750, 191102976, 191318760, 192000000, 194400000, 195312500, 196608000, 196830000, 199065600, 199290375, 200000000, 201326592, 201553920, 202500000, 204073344, 204800000, 205031250, 207360000, 209715200, 209952000, 210937500, 212336640, 212576400, 214990848, 215233605, 216000000, 218700000, 221184000, 221433750, 223948800, 225000000, 226492416, 226748160, 227812500, 229582512, 230400000, 233280000, 
234375000, 235929600, 236196000, 238878720, 239148450, 240000000, 241864704, 243000000, 244140625, 245760000, 246037500, 248832000, 250000000, 251658240, 251942400, 253125000, 254803968, 255091680, 256000000, 258280326, 259200000, 262144000, 262440000, 263671875, 265420800, 265720500, 268435456, 268738560, 270000000, 272097792, 273375000, 276480000, 279936000, 281250000, 283115520, 283435200, 284765625, 286654464, 286978140, 288000000, 291600000, 292968750, 294912000, 295245000, 298598400, 300000000, 301989888, 302330880, 303750000, 306110016, 
307200000, 307546875, 311040000, 312500000, 314572800, 314928000, 316406250, 318504960, 318864600, 320000000, 322486272, 324000000, 327680000, 328050000, 331776000, 332150625, 335544320, 335923200, 337500000, 339738624, 340122240, 341718750, 344373768, 345600000, 349920000, 351562500, 353894400, 354294000, 358318080, 358722675, 360000000, 362797056, 364500000, 368640000, 369056250, 373248000, 375000000, 377487360, 377913600, 379687500, 382205952, 382637520, 384000000, 387420489, 388800000, 390625000, 393216000, 393660000, 398131200, 398580750,
400000000, 402653184, 403107840, 405000000, 408146688, 409600000, 410062500, 414720000, 419430400, 419904000, 421875000, 424673280, 425152800, 429981696, 430467210, 432000000, 437400000, 439453125, 442368000, 442867500, 447897600, 450000000, 452984832, 453496320, 455625000, 459165024, 460800000, 466560000, 468750000, 471859200, 472392000, 474609375, 477757440, 478296900, 480000000, 483729408, 486000000, 488281250, 491520000, 492075000, 497664000, 500000000, 503316480, 503884800, 506250000, 509607936, 510183360, 512000000, 512578125, 516560652, 
518400000, 524288000, 524880000, 527343750, 530841600, 531441000, 536870912, 537477120, 540000000, 544195584, 546750000, 552960000, 553584375, 559872000, 562500000, 566231040, 566870400, 569531250, 573308928, 573956280, 576000000, 583200000, 585937500, 589824000, 590490000, 597196800, 597871125, 600000000, 603979776, 604661760, 607500000, 612220032, 614400000, 615093750, 622080000, 625000000, 629145600, 629856000, 632812500, 637009920, 637729200, 640000000, 644972544, 645700815, 648000000, 655360000, 656100000, 663552000, 664301250, 671088640, 
671846400, 675000000, 679477248, 680244480, 683437500, 688747536, 691200000, 699840000, 703125000, 707788800, 708588000, 716636160, 717445350, 720000000, 725594112, 729000000, 732421875, 737280000, 738112500, 746496000, 750000000, 754974720, 755827200, 759375000, 764411904, 765275040, 768000000, 774840978, 777600000, 781250000, 786432000, 787320000, 791015625, 796262400, 797161500, 800000000, 805306368, 806215680, 810000000, 816293376, 819200000, 820125000, 829440000, 838860800, 839808000, 843750000, 849346560, 850305600, 854296875, 859963392,     
};

int online[705];

void prep() {
    int cnt = 0;
    for (int i = 1; ; ++i) {
        if (is(i)) {
            online[++cnt] = i;
            if (cnt == 705) break;
        }     
    }
}

int main() {
    int N;
    prep();
    while (scanf("%d", &N), N) {
        if (N <= 700) printf("%d\n", online[N]);
        else printf("%d\n", rec[N-701]);    
    }
    return 0;    
}

 

还有一种方法就是通过递推来求解了. 我们能够得到这样一个结论,那就是所有的丑数,一定是从前面比它小的丑数中乘上一个2,3或者是5的因子来构成一个新的丑数.因此,我们便记录下2,3,5分别和哪个数相乘得到当前一个最小的丑数.如果得到这个丑数是有乘以3得来的,那么我们就直接就把乘三这个下标往后面移一位.

代码如下:

#include <cstdlib>
#include <cstring>
#include <cstdio>
#include <iostream>
#include <algorithm>
using namespace std;

int num[1505];

void prep() {
    num[1] = 1;
    int p2 = 1, p3 = 1, p5 = 1, cnt = 1;
    while (cnt < 1500) {
        int x = min(num[p2]*2, min(num[p3]*3, num[p5]*5));
        num[++cnt] = x;
        if (x == num[p2]*2) ++p2;
        if (x == num[p3]*3) ++p3;
        if (x == num[p5]*5) ++p5;
        // 这里不能过使用if和else的搭配,这样写能够去重 
    }
}

int main() {
    int N;
    prep();
    while (scanf("%d", &N), N) {
        printf("%d\n", num[N]);
    }
    return 0;    
}