2016 ACM/ICPC Asia Regional Qingdao Online 1001

题目大意：给一个数字n，求出大于等于n的第一个满足如下条件的数：2^a*3^b*5^c*7^d;

解题思路：一般这种类型的题目思路有两种：1、提前打表，当输入n后在打好的表中进行查询；2、按照题目描述进行模拟，即从n开始，判断每一个数字是否符合条件

对于本题，若采用第二种思路会TLE，因此应采用第一种思路，而第一种思路中包含两个过程，打表和查询，需要分别最这两个过程进行效率优化，否则同样会TLE。

我使用的方法是首先用一个程序跑出10^9以内所有满足条件的数字，然后手动建立数组进行查询，而查询使用的是STL模板中的lower_bound()函数，该函数使用二分查找，找到大于等于指定数字的第一个数字的位置。

//用来跑数据的函数，将所有符合条件的数字输出到1.txt文件中，然后手动建立数组，经程序统计，10^9以内共5194个符合条件的数字。
#include 
#include 
#include 
using namespace std;
int main()
{
    ofstream outfile;
    outfile.open("1.txt");
    int t;
    long long n;
    long long result;
    long long num;
    long long sum=0;
    for(int i=1; i<=1000000005; i++)
    {
        num=i;
        while((num%2==0)||(num%3==0)||(num%5)==0||(num%7==0))
        {
            if(num%2==0)
            {
                num = num>>1;
            }
            if(num%3==0)
            {
                num /= 3;
            }
            if(num%5==0)
            {
                num /= 5;
            }
            if(num%7==0)
            {
                num /= 7;
            }
        }
        if(num==1)
        {
            outfile<

AC代码：

#include 
#include 
using namespace std;
int num[]={1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,25,27,28,30,32,35,36,40,42,45,48,49,50,54,56,60,63,64,70,72,75,80,81,84,90,96,98,100,105,108,112
,120,125,126,128,135,140,144,147,150,160,162,168,175,180,189,192,196,200,210,216,224,225,240,243,245,250,252,256,270,280,288,294,300,315,320,324,336,343
,350,360,375,378,384,392,400,405,420,432,441,448,450,480,486,490,500,504,512,525,540,560,567,576,588,600,625,630,640,648,672,675,686,700,720,729,735,750
,756,768,784,800,810,840,864,875,882,896,900,945,960,972,980,1000,1008,1024,1029,1050,1080,1120,1125,1134,1152,1176,1200,1215,1225,1250,1260,1280,1296
,1323,1344,1350,1372,1400,1440,1458,1470,1500,1512,1536,1568,1575,1600,1620,1680,1701,1715,1728,1750,1764,1792,1800,1875,1890,1920,1944,1960,2000,2016
,2025,2048,2058,2100,2160,2187,2205,2240,2250,2268,2304,2352,2400,2401,2430,2450,2500,2520,2560,2592,2625,2646,2688,2700,2744,2800,2835,2880,2916,2940
,3000,3024,3072,3087,3125,3136,3150,3200,3240,3360,3375,3402,3430,3456,3500,3528,3584,3600,3645,3675,3750,3780,3840,3888,3920,3969,4000,4032,4050,4096
,4116,4200,4320,4374,4375,4410,4480,4500,4536,4608,4704,4725,4800,4802,4860,4900,5000,5040,5103,5120,5145,5184,5250,5292,5376,5400,5488,5600,5625,5670
,5760,5832,5880,6000,6048,6075,6125,6144,6174,6250,6272,6300,6400,6480,6561,6615,6720,6750,6804,6860,6912,7000,7056,7168,7200,7203,7290,7350,7500,7560
,7680,7776,7840,7875,7938,8000,8064,8100,8192,8232,8400,8505,8575,8640,8748,8750,8820,8960,9000,9072,9216,9261,9375,9408,9450,9600,9604,9720,9800,10000
,10080,10125,10206,10240,10290,10368,10500,10584,10752,10800,10935,10976,11025,11200,11250,11340,11520,11664,11760,11907,12000,12005,12096,12150,12250
,12288,12348,12500,12544,12600,12800,12960,13122,13125,13230,13440,13500,13608,13720,13824,14000,14112,14175,14336,14400,14406,14580,14700,15000,15120
,15309,15360,15435,15552,15625,15680,15750,15876,16000,16128,16200,16384,16464,16800,16807,16875,17010,17150,17280,17496,17500,17640,17920,18000,18144
,18225,18375,18432,18522,18750,18816,18900,19200,19208,19440,19600,19683,19845,20000,20160,20250,20412,20480,20580,20736,21000,21168,21504,21600,21609
,21870,21875,21952,22050,22400,22500,22680,23040,23328,23520,23625,23814,24000,24010,24192,24300,24500,24576,24696,25000,25088,25200,25515,25600,25725
,25920,26244,26250,26460,26880,27000,27216,27440,27648,27783,28000,28125,28224,28350,28672,28800,28812,29160,29400,30000,30240,30375,30618,30625,30720
,30870,31104,31250,31360,31500,31752,32000,32256,32400,32768,32805,32928,33075,33600,33614,33750,34020,34300,34560,34992,35000,35280,35721,35840,36000
,36015,36288,36450,36750,36864,37044,37500,37632,37800,38400,38416,38880,39200,39366,39375,39690,40000,40320,40500,40824,40960,41160,41472,42000,42336
,42525,42875,43008,43200,43218,43740,43750,43904,44100,44800,45000,45360,45927,46080,46305,46656,46875,47040,47250,47628,48000,48020,48384,48600,49000
,49152,49392,50000,50176,50400,50421,50625,51030,51200,51450,51840,52488,52500,52920,53760,54000,54432,54675,54880,55125,55296,55566,56000,56250,56448
,56700,57344,57600,57624,58320,58800,59049,59535,60000,60025,60480,60750,61236,61250,61440,61740,62208,62500,62720,63000,63504,64000,64512,64800,64827
,65536,65610,65625,65856,66150,67200,67228,67500,68040,68600,69120,69984,70000,70560,70875,71442,71680,72000,72030,72576,72900,73500,73728,74088,75000
,75264,75600,76545,76800,76832,77175,77760,78125,78400,78732,78750,79380,80000,80640,81000,81648,81920,82320,82944,83349,84000,84035,84375,84672,85050
,85750,86016,86400,86436,87480,87500,87808,88200,89600,90000,90720,91125,91854,91875,92160,92610,93312,93750,94080,94500,95256,96000,96040,96768,97200
,98000,98304,98415,98784,99225,100000,100352,100800,100842,101250,102060,102400,102900,103680,104976,105000,105840,107163,107520,108000,108045,108864,
109350,109375,109760,110250,110592,111132,112000,112500,112896,113400,114688,115200,115248,116640,117600,117649,118098,118125,119070,120000,120050,
120960,121500,122472,122500,122880,123480,124416,125000,125440,126000,127008,127575,128000,128625,129024,129600,129654,131072,131220,131250,131712,
132300,134400,134456,135000,136080,137200,137781,138240,138915,139968,140000,140625,141120,141750,142884,143360,144000,144060,145152,145800,147000,
147456,148176,150000,150528,151200,151263,151875,153090,153125,153600,153664,154350,155520,156250,156800,157464,157500,158760,160000,161280,162000,
163296,163840,164025,164640,165375,165888,166698,168000,168070,168750,169344,170100,171500,172032,172800,172872,174960,175000,175616,176400,177147,
178605,179200,180000,180075,181440,182250,183708,183750,184320,185220,186624,187500,188160,189000,190512,192000,192080,193536,194400,194481,196000,
196608,196830,196875,197568,198450,200000,200704,201600,201684,202500,204120,204800,205800,207360,209952,210000,211680,212625,214326,214375,215040,
216000,216090,217728,218700,218750,219520,220500,221184,222264,224000,225000,225792,226800,229376,229635,230400,230496,231525,233280,234375,235200,
235298,236196,236250,238140,240000,240100,241920,243000,244944,245000,245760,246960,248832,250000,250047,250880,252000,252105,253125,254016,255150,
256000,257250,258048,259200,259308,262144,262440,262500,263424,264600,268800,268912,270000,272160,273375,274400,275562,275625,276480,277830,279936,
280000,281250,282240,283500,285768,286720,288000,288120,290304,291600,294000,294912,295245,296352,297675,300000,300125,301056,302400,302526,303750,
306180,306250,307200,307328,308700,311040,312500,313600,314928,315000,317520,320000,321489,322560,324000,324135,326592,327680,328050,328125,329280,
330750,331776,333396,336000,336140,337500,338688,340200,343000,344064,345600,345744,349920,350000,351232,352800,352947,354294,354375,357210,358400,
360000,360150,362880,364500,367416,367500,368640,370440,373248,375000,376320,378000,381024,382725,384000,384160,385875,387072,388800,388962,390625,
392000,393216,393660,393750,395136,396900,400000,401408,403200,403368,405000,408240,409600,411600,413343,414720,416745,419904,420000,420175,421875,
423360,425250,428652,428750,430080,432000,432180,435456,437400,437500,439040,441000,442368,444528,448000,450000,451584,453600,453789,455625,458752,
459270,459375,460800,460992,463050,466560,468750,470400,470596,472392,472500,476280,480000,480200,483840,486000,489888,490000,491520,492075,493920,
496125,497664,500000,500094,501760,504000,504210,506250,508032,510300,512000,514500,516096,518400,518616,524288,524880,525000,526848,529200,531441,
535815,537600,537824,540000,540225,544320,546750,546875,548800,551124,551250,552960,555660,559872,560000,562500,564480,567000,571536,573440,576000,
576240,580608,583200,583443,588000,588245,589824,590490,590625,592704,595350,600000,600250,602112,604800,605052,607500,612360,612500,614400,614656,
617400,622080,625000,627200,629856,630000,635040,637875,640000,642978,643125,645120,648000,648270,653184,655360,656100,656250,658560,661500,663552,
666792,672000,672280,675000,677376,680400,686000,688128,688905,691200,691488,694575,699840,700000,702464,703125,705600,705894,708588,708750,714420,
716800,720000,720300,725760,729000,734832,735000,737280,740880,746496,750000,750141,752640,756000,756315,759375,762048,765450,765625,768000,768320,
771750,774144,777600,777924,781250,784000,786432,787320,787500,790272,793800,800000,802816,806400,806736,810000,816480,819200,820125,823200,823543,
826686,826875,829440,833490,839808,840000,840350,843750,846720,850500,857304,857500,860160,864000,864360,870912,874800,875000,878080,882000,884736,
885735,889056,893025,896000,900000,900375,903168,907200,907578,911250,917504,918540,918750,921600,921984,926100,933120,937500,940800,941192,944784,
945000,952560,960000,960400,964467,967680,972000,972405,979776,980000,983040,984150,984375,987840,992250,995328,1000000,1000188,1003520,1008000,100
8420,1012500,1016064,1020600,1024000,1029000,1032192,1036800,1037232,1048576,1049760,1050000,1053696,1058400,1058841,1062882,1063125,1071630,1071875,
1075200,1075648,1080000,1080450,1088640,1093500,1093750,1097600,1102248,1102500,1105920,1111320,1119744,1120000,1125000,1128960,1134000,1143072,1146880,
1148175,1152000,1152480,1157625,1161216,1166400,1166886,1171875,1176000,1176490,1179648,1180980,1181250,1185408,1190700,1200000,1200500,1204224,1209600,
1210104,1215000,1224720,1225000,1228800,1229312,1234800,1240029,1244160,1250000,1250235,1254400,1259712,1260000,1260525,1265625,1270080,1275750,1280000,
1285956,1286250,1290240,1296000,1296540,1306368,1310720,1312200,1312500,1317120,1323000,1327104,1333584,1344000,1344560,1350000,1354752,1360800,1361367,
1366875,1372000,1376256,1377810,1378125,1382400,1382976,1389150,1399680,1400000,1404928,1406250,1411200,1411788,1417176,1417500,1428840,1433600,1440000,
1440600,1451520,1458000,1469664,1470000,1474560,1476225,1481760,1488375,1492992,1500000,1500282,1500625,1505280,1512000,1512630,1518750,1524096,1530900,
1531250,1536000,1536640,1543500,1548288,1555200,1555848,1562500,1568000,1572864,1574640,1575000,1580544,1587600,1594323,1600000,1605632,1607445,1612800,
1613472,1620000,1620675,1632960,1638400,1640250,1640625,1646400,1647086,1653372,1653750,1658880,1666980,1679616,1680000,1680700,1687500,1693440,1701000,
1714608,1715000,1720320,1728000,1728720,1741824,1749600,1750000,1750329,1756160,1764000,1764735,1769472,1771470,1771875,1778112,1786050,1792000,1800000,
1800750,1806336,1814400,1815156,1822500,1835008,1837080,1837500,1843200,1843968,1852200,1866240,1875000,1881600,1882384,1889568,1890000,1905120,1913625,
1920000,1920800,1928934,1929375,1935360,1944000,1944810,1953125,1959552,1960000,1966080,1968300,1968750,1975680,1984500,1990656,2000000,2000376,2007040,
2016000,2016840,2025000,2032128,2041200,2048000,2058000,2064384,2066715,2073600,2074464,2083725,2097152,2099520,2100000,2100875,2107392,2109375,2116800,
2117682,2125764,2126250,2143260,2143750,2150400,2151296,2160000,2160900,2177280,2187000,2187500,2195200,2204496,2205000,2211840,2222640,2239488,2240000,
2250000,2250423,2257920,2268000,2268945,2278125,2286144,2293760,2296350,2296875,2304000,2304960,2315250,2322432,2332800,2333772,2343750,2352000,2352980,
2359296,2361960,2362500,2370816,2381400,2400000,2401000,2408448,2419200,2420208,2430000,2449440,2450000,2457600,2458624,2460375,2469600,2470629,2480058,
2480625,2488320,2500000,2500470,2508800,2519424,2520000,2521050,2531250,2540160,2551500,2560000,2571912,2572500,2580480,2592000,2593080,2612736,2621440,
2624400,2625000,2634240,2646000,2654208,2657205,2667168,2679075,2688000,2689120,2700000,2701125,2709504,2721600,2722734,2733750,2734375,2744000,2752512,
2755620,2756250,2764800,2765952,2778300,2799360,2800000,2809856,2812500,2822400,2823576,2834352,2835000,2857680,2867200,2880000,2881200,2893401,2903040,
2916000,2917215,2939328,2940000,2941225,2949120,2952450,2953125,2963520,2976750,2985984,3000000,3000564,3001250,3010560,3024000,3025260,3037500,3048192,
3061800,3062500,3072000,3073280,3087000,3096576,3110400,3111696,3125000,3136000,3145728,3149280,3150000,3161088,3175200,3176523,3188646,3189375,3200000,
3211264,3214890,3215625,3225600,3226944,3240000,3241350,3265920,3276800,3280500,3281250,3292800,3294172,3306744,3307500,3317760,3333960,3359232,3360000,
3361400,3375000,3386880,3402000,3429216,3430000,3440640,3444525,3456000,3457440,3472875,3483648,3499200,3500000,3500658,3512320,3515625,3528000,3529470,
3538944,3542940,3543750,3556224,3572100,3584000,3600000,3601500,3612672,3628800,3630312,3645000,3670016,3674160,3675000,3686400,3687936,3704400,3720087,
3732480,3750000,3750705,3763200,3764768,3779136,3780000,3781575,3796875,3810240,3827250,3828125,3840000,3841600,3857868,3858750,3870720,3888000,3889620,
3906250,3919104,3920000,3932160,3936600,3937500,3951360,3969000,3981312,4000000,4000752,4014080,4032000,4033680,4050000,4064256,4082400,4084101,4096000,
4100625,4116000,4117715,4128768,4133430,4134375,4147200,4148928,4167450,4194304,4199040,4200000,4201750,4214784,4218750,4233600,4235364,4251528,4252500,
4286520,4287500,4300800,4302592,4320000,4321800,4354560,4374000,4375000,4390400,4408992,4410000,4423680,4428675,4445280,4465125,4478976,4480000,4500000,
4500846,4501875,4515840,4536000,4537890,4556250,4572288,4587520,4592700,4593750,4608000,4609920,4630500,4644864,4665600,4667544,4687500,4704000,4705960,
4718592,4723920,4725000,4741632,4762800,4782969,4800000,4802000,4816896,4822335,4838400,4840416,4860000,4862025,4898880,4900000,4915200,4917248,4920750,
4921875,4939200,4941258,4960116,4961250,4976640,5000000,5000940,5017600,5038848,5040000,5042100,5062500,5080320,5103000,5120000,5143824,5145000,5160960,
5184000,5186160,5225472,5242880,5248800,5250000,5250987,5268480,5292000,5294205,5308416,5314410,5315625,5334336,5358150,5359375,5376000,5378240,5400000,
5402250,5419008,5443200,5445468,5467500,5468750,5488000,5505024,5511240,5512500,5529600,5531904,5556600,5598720,5600000,5619712,5625000,5644800,5647152,
5668704,5670000,5715360,5734400,5740875,5760000,5762400,5764801,5786802,5788125,5806080,5832000,5834430,5859375,5878656,5880000,5882450,5898240,5904900,
5906250,5927040,5953500,5971968,6000000,6001128,6002500,6021120,6048000,6050520,6075000,6096384,6123600,6125000,6144000,6146560,6174000,6193152,6200145,
6220800,6223392,6250000,6251175,6272000,6291456,6298560,6300000,6302625,6322176,6328125,6350400,6353046,6377292,6378750,6400000,6422528,6429780,6431250,
6451200,6453888,6480000,6482700,6531840,6553600,6561000,6562500,6585600,6588344,6613488,6615000,6635520,6667920,6718464,6720000,6722800,6750000,6751269,
6773760,6804000,6806835,6834375,6858432,6860000,6881280,6889050,6890625,6912000,6914880,6945750,6967296,6998400,7000000,7001316,7024640,7031250,7056000,
7058940,7077888,7085880,7087500,7112448,7144200,7168000,7200000,7203000,7225344,7257600,7260624,7290000,7340032,7348320,7350000,7372800,7375872,7381125,
7408800,7411887,7440174,7441875,7464960,7500000,7501410,7503125,7526400,7529536,7558272,7560000,7563150,7593750,7620480,7654500,7656250,7680000,7683200,
7715736,7717500,7741440,7776000,7779240,7812500,7838208,7840000,7864320,7873200,7875000,7902720,7938000,7962624,7971615,8000000,8001504,8028160,8037225,
8064000,8067360,8100000,8103375,8128512,8164800,8168202,8192000,8201250,8203125,8232000,8235430,8257536,8266860,8268750,8294400,8297856,8334900,8388608,
8398080,8400000,8403500,8429568,8437500,8467200,8470728,8503056,8505000,8573040,8575000,8601600,8605184,8640000,8643600,8680203,8709120,8748000,8750000,
8751645,8780800,8817984,8820000,8823675,8847360,8857350,8859375,8890560,8930250,8957952,8960000,9000000,9001692,9003750,9031680,9072000,9075780,9112500,
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600000,453789000,455196672,455625000,457228800,457419312,458752000,459165024,459270000,459375000,460800000,460992000,461184080,462422016,462944160,463050000,464486400,464679936,465010875,466560000,466754400,466948881,468730962,468750000,468838125,469762048,470292480,470400000,470596000,471859200,472055808,472392000,472500000,472588830,472696875,474163200,474360768,474609375,476171136,476280000,476478450,477757440,478296900,478406250,478515625,480000000,480090240,480200000,481689600,481890304,482233500,482343750,483729408,483840000,484041600,484243284,486000000,486091368,486202500,487710720,488281250,489888000,490000000,490092120,491520000,491724800,492075000,492187500,493807104,493920000,494125800,495452160,496011600,496125000,497664000,497871360,500000000,500094000,501645312,501760000,502211745,503316480,503884800,504000000,504094752,504210000,505774080,506250000,506345175,508032000,508243680,509607936,510183360,510300000,510512625,512000000,512096256,512578125,513802240,514382400,514500000,514596726,514714375,516096000,516311040,516560652,516678750,516796875,518400000,518616000,518832090,520224768,520812180,520931250,522547200,522764928,524288000,524880000,525000000,525098700,525218750,526848000,527067520,527343750,528482304,529079040,529200000,529420500,530841600,531062784,531441000,531562500,533433600,533655864,535692528,535815000,535937500,536870912,537477120,537600000,537824000,539492352,540000000,540101520,540225000,541900800,542126592,544195584,544320000,544546800,546750000,546852789,546875000,548674560,548800000,550502400,550731776,551124000,551250000,551353635,552960000,553190400,553420896,553584375,555532992,555660000,555891525,557383680,558013050,558140625,559872000,560000000,560105280,561971200,562500000,562605750,562734375,564350976,564480000,564715200,564950498,566231040,566870400,567000000,567106596,567236250,568995840,569531250,571536000,571774140,573308928,573440000,573956280,574087500,574218750,576000000,576108288,576240000,576480100,578027520,578680200,578812500,580608000,580849920,583200000,583443000,585252864,585937500,587202560,587865600,588000000,588110544,588245000,589824000,590069760,590490000,590625000,592704000,592950960,594542592,595213920,595350000,597196800,597445632,597871125,600000000,600112800,600250000,600362847,602112000,602362880,602654094,602791875,603979776,604661760,604800000,605052000,605304105,606928896,607500000,607614210,607753125,609638400,609892416,612220032,612360000,612500000,612615150,614400000,614656000,615093750,615234375,616562688,617258880,617400000,617657250,619315200,619573248,620014500,620156250,622080000,622339200,622598508,624974616,625000000,625117500,627056640,627200000,629145600,629407744,629856000,630000000,630118440,630262500,632217600,632481024,632812500,634894848,635040000,635304600,637009920,637729200,637875000,640000000,640120320,642252800,642978000,643125000,644972544,645120000,645388800,645657712,645700815,648000000,648121824,648270000,650280960,651015225,653184000,653456160,655360000,656100000,656250000,656373375,658409472,658560000,658834400,660602880,661348800,661500000,661624362,661775625,663552000,663828480,664301250,664453125,666792000,667069830,668860416,669615660,669768750,669921875,671088640,671846400,672000000,672126336,672280000,674365440,675000000,675126900,675281250,677376000,677658240,679477248,680244480,680400000,680683500,682795008,683437500,683593750,685843200,686000000,686128968,688128000,688414720,688747536,688905000,689062500,691200000,691488000,691776120,693633024,694416240,694575000,696729600,697019904,699840000,700000000,700131600,702464000,703096443,703125000,704643072,705438720,705600000,705894000,707788800,708083712,708588000,708750000,708883245,711244800,711541152,714256704,714420000,714717675,716636160,716800000,717445350,717609375,719323136,720000000,720135360,720300000,720600125,722534400,722835456,723350250,723515625,725594112,725760000,726062400,726364926,729000000,729137052,729303750,731566080,732421875,734003200,734832000,735000000,735138180,735306250,737280000,737587200,737894528,738112500,738281250,740710656,740880000,741188700,743178240,744017400,744187500,746496000,746807040,750000000,750141000,750312500,752467968,752640000,752953600,754974720,755827200,756000000,756142128,756315000,758661120,759375000,762048000,762365520,764411904,765275040,765450000,765625000,768000000,768144384,768320000,770703360,771573600,771750000,771895089,774144000,774466560,774840978,775018125,777600000,777924000,778248135,780337152,781218270,781250000,781396875,783820800,784000000,784147392,786432000,786759680,787320000,787500000,787648050,787828125,790272000,790601280,791015625,792723456,793618560,793800000,794130750,796262400,796594176,797161500,797343750,800000000,800150400,800483796,802816000,803538792,803722500,803906250,805306368,806215680,806400000,806736000,807072140,809238528,810000000,810152280,810337500,812851200,813189888,816293376,816480000,816820200,819200000,820125000,820312500,822083584,823011840,823200000,823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int main()
{
    int t;
    int n;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        int p = lower_bound(num, num+5194, n) - num;
        printf("%d\n",num[p]);
    }
    return 0;
}

不过这道题用程序来打表好像也能过，关键在于二分查找对效率的提高。