这真是一道很神的题，看起来似乎只能暴搜，但是暴搜的话又没法解决出现了大质数因子的问题，所以我蛋疼了一下午还是写了个骗分+暴力，但没想到竟然A了！
后来我看了题解，感到很不满意，因为题解根本就没有处理存在大质数的问题。
让我们先来看看所谓的正解：
本题的要求是，求出一个给定区间内的含因子数最多的整数。
首先，有必要明确一下如何求一个数的因子数。若一个数N满足N=P1N1·P2N2·P3N3·…·PmNm，其中P1, P2, …, Pm是N的m个质因子。则N的约数个数为(N1+1)·(N2+1)·(N3+1)·…·(Nm+1)。这一公式可以通过乘法原理来证明。
有了求因子数的公式后，最容易想到的算法就是，枚举区间内的每个整数，统计它们的约数个数。这个算法很容易实现，但是时间复杂度却相当高。因为区间中整数的范围是1～1000000000，整个枚举一遍并计算因子数的代价约为109×(109)0.5=1013.5。这个规模是无法忍受的。所以，我们需要尽量优化时间。
分析一下枚举的过程就会发现，如果我们分别枚举两个数n和p·n（p为一相对较大的质数），那么我们将重复计算两次n的因子数。其实，如果枚举顺序得当的话，完全可以在n的基础上去计算p·n，而如果能在n的基础上计算p·n，就相当于计算p·n的因子数只用了O(1)的时间。这是一个比较形象的例子，类似的（可能相对更复杂一些）重复计算在枚举过程中应该是普遍存在的。这就是枚举效率低的根本所在。为了解决这一重复，我们可以选取另一种搜索顺序——枚举质因子。这样的搜索顺序可以避免前面所说了类似n和p·n的重复计算。
定义number为当前搜索到的数。初始时，令number=1，然后从最小的质数2开始枚举，枚举因子中包含0个2、1个2、2个2、…、k个2的情况……直至number·2k大于区间的上限(max)。对于每个“2k的情况”，令number:=number*2k，在这个基础上，再枚举因子3索的过程，搜索的过程中，利用前面提到的求因子数的公式可以算出当前的number的因子数供下一层枚举继承。当number大于等于区间下限(min)时，我们就找到了一个区间内的数(枚举的过程已保证number不超过上界)。所有枚举得到的区间内的数中，因子数的最大值就是我们要求的目标。
这样的枚举完全去除了重复计算，但是这还是不够的，因为光1～1000000000内的数每枚举一遍就有109个单位的操作。所以，我们还需要找到一些剪枝的方法，进一步优化时间。
我们看到，如果当前搜索状态为(from, number, total)，其中，from是指当前枚举到的质因子（按从小到大枚举），total是指number中包含的因子数。那么剩下的因子数最多为q=logfrommax/number，这些因子组成的因子个数最大为2q。因此，当前所能取到的（理想情况）最大约数个数就是total·2q。如果这个数仍然无法超过当前最优解，则这一分支不可能产生最优解，可以剪去。
此外，如果[(min-1)/number]=[max/number]，则表示以当前状态搜索下去，结果肯定不在区间内了，就无法产生合法解，也可剪去。不过，这一剪枝作用不是很大，因为即使不剪，再搜索一层也就退出了。
以上两个剪枝，前一个是最优化剪枝，后一个是合法性剪枝。相比较而言，前一个剪枝的作用要大得多。
下面我们用平摊分析的方法来讨论一下搜索的复杂度。由于枚举的过程中没有重复计算，每枚举一个质因子，都可以得到一个不同的number(number≤max)，所以可以将每一个单位的枚举质因子的代价与一个不超过max的number对应，并且还可在两者之间建立双射。不同的number最多只有max个，所以枚举的总代价不超过O(max)，max≤109。
加上了剪枝以后，计算总代价就远远小于O(max)了。从运行效果来看，即便是最大数据，也可以很快出解。
从本题的解决过程中可以看到，最关键的有两步：
（1）采用合理的搜索顺序，避免重复计算；
（2）利用最优化剪枝和合法性剪枝，剪去一些不可能产生最优解或合法解的分支。
这两种优化的方法在搜索中的地位是极其重要的，当然可能在本题中的重要性体现得格外突出。
这不是扯淡么！就这么俩小破剪枝，而且根本就处理不了最后搜得剩一个大质数的问题啊！
那该怎么办呢？。。与其耗费脑力和体力剪一个DFS，还不如先来讲讲怎么骗分。
一、骗分？
1、我们可以挑出这样一些数ai,其中每一个数都使得f(ai)=max{f(aj)},j∈[1,ai],那么显然该数列是个严格不下降序列，那么显然，若询问区间与该数列有交集的话，那么答案必来自交集之中，但是该数列是不太密集的，到最后其两个数之间的差距甚至达到了10^8左右。。所以出错的概率还是相当高的。。
2、但是！我们这样想啊，假如我是出题人的话，我会出哪些数据呢？
随机数据，特殊数据。
如果是随机数据的话，它们之间差很大的概率还是很大的；如果是特殊数据的话，它们之间的差应该比较小。
差比较小，这可怎么办？
3、暴力！对于差比较小的情况，我们完全可以暴力分解每一个数的质因子，复杂度O(10^4.5*(R-L)).
4、于是。。我们就把这道神搜索题A掉啦A掉啦！
#include
using namespace std;
#include
#include
#include
#include
#include
const int MAXN=31622;
bool b[31622];
int prime[20000],a[200]={1,2,3,4,6,8,10,12,18,20,24,30,36,48,60,72,84,90,96,108,120,168,180,240,336,360,420,480,504,540,600,630,660,672,720,840,1080,1260,1440,1680,2160,2520,3360,3780,3960,4200,4320,4620,4680,5040,7560,9240,10080,12600,13860,15120,18480,20160,25200,27720,30240,32760,36960,37800,40320,41580,42840,43680,45360,50400,55440,65520,75600,83160,98280,110880,131040,138600,151200,163800,166320,196560,221760,262080,277200,327600,332640,360360,393120,415800,443520,471240,480480,491400,498960,554400,655200,665280,720720,831600,942480,982800,997920,1053360,1081080,1330560,1413720,1441440,1663200,1801800,1884960,1965600,2106720,2162160,2827440,2882880,3326400,3603600,4324320,5405400,5654880,5765760,6126120,6320160,6486480,7207200,8648640,10810800,12252240,12972960,13693680,14137200,14414400,17297280,18378360,20540520,21621600,24504480,27387360,28274400,28828800,30270240,30630600,31600800,32432400,36756720,41081040,43243200,49008960,54774720,56548800,60540480,61261200,64864800,68468400,73513440,82162080,86486400,91891800,98017920,99459360,102702600,107442720,108108000,109549440,110270160,122522400,136936800,147026880,164324160,183783600,205405200,220540320,232792560,245044800,273873600,294053760,328648320,349188840,367567200,410810400,465585120,490089600,497296800,514594080,537213600,547747200,551350800,616215600,698377680,735134400,821620800,931170240,994593600},divsum[200]={1,2,2,3,4,4,4,6,6,6,8,8,9,10,12,12,12,12,12,12,16,16,18,20,20,24,24,24,24,24,24,24,24,24,30,32,32,36,36,40,40,48,48,48,48,48,48,48,48,60,64,64,72,72,72,80,80,84,90,96,96,96,96,96,96,96,96,96,100,108,120,120,120,128,128,144,144,144,144,144,160,160,168,168,180,180,192,192,192,192,192,192,192,192,200,216,216,224,240,240,240,240,240,240,256,256,256,288,288,288,288,288,288,320,320,336,336,360,384,384,384,384,384,384,400,432,448,480,480,480,480,480,504,512,512,512,576,576,576,576,576,576,576,576,600,640,640,672,672,672,672,672,720,720,720,768,768,768,768,768,768,768,768,768,768,800,864,864,896,896,960,960,960,960,1008,1008,1024,1024,1024,1152,1152,1152,1152,1152,1152,1152,1152,1200,1200,1280,1344,1344,1344,1344};
int main(){
freopen("divisors.in","r",stdin);
freopen("divisors.out","w",stdout);
int i,j,x,tot=194,ans,tmpsum,maxans=0,L,R,maxi;
prime[0]=1;
for(i=2;i2500){
x=upper_bound(a,a+tot,R)-a-1;
while(x&&divsum[x]==divsum[x-1]&&a[x-1]>=L)--x;
printf("Between %d and %d, %d has a maximum of %d divisors.",L,R,a[x],divsum[x]);
return 0;
}
for(i=L;i<=R;++i){
ans=1,x=i;
for(j=1;jmaxans){
maxans=ans;
maxi=i;
}
}
printf("Between %d and %d, %d has a maximum of %d divisors.",L,R,maxi,maxans);
}
二、DFS
1、上述两个可行性剪枝和最优化剪枝都是显然要有的。
只不过有一个要更正的地方，就是可行性剪枝剪掉的并不是什么再搜一层就退出的枝，而是很多条很粗的枝干，其还是非常必要的；
再者就是我们还要处理大质数的问题，就是说最优解来自于一个有大质数的数，这显然是可以构造出来的。
2、那么该怎么办呢？
考虑我们在分解质因数时的优化：prime[j]*prime[j]<=x.
是不是灵感顿生了呢！
对于DFS中的三元组(nowsum,nowdis,nowans)分别表示当前乘积，当前搜索的是第几个质因子，当前乘积的因子数。
那么当R/nowsum
这样的话，不仅仅是解决了乘以大质数的问题，而且还剪掉了一部分枝叶。
3、但是吧，在这些剪枝中，如果都采用实数运算是比较方便的，但如果采用整数运算，虽然牺牲了编程复杂度，但却会削减常数。所以我的Code比Nill的跑得慢好多。。按理说我应该调一下的。。但是吧。。实在是懒得调了。
#include
using namespace std;
#include
#include
int L,R,ans=1,num=1,prime[]={3402,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783,8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601,9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007,10009,10037,10039,10061,10067,10069,10079,10091,10093,10099,10103,10111,10133,10139,10141,10151,10159,10163,10169,10177,10181,10193,10211,10223,10243,10247,10253,10259,10267,10271,10273,10289,10301,10303,10313,10321,10331,10333,10337,10343,10357,10369,10391,10399,10427,10429,10433,10453,10457,10459,10463,10477,10487,10499,10501,10513,10529,10531,10559,10567,10589,10597,10601,10607,10613,10627,10631,10639,10651,10657,10663,10667,10687,10691,10709,10711,10723,10729,10733,10739,10753,10771,10781,10789,10799,10831,10837,10847,10853,10859,10861,10867,10883,10889,10891,10903,10909,10937,10939,10949,10957,10973,10979,10987,10993,11003,11027,11047,11057,11059,11069,11071,11083,11087,11093,11113,11117,11119,11131,11149,11159,11161,11171,11173,11177,11197,11213,11239,11243,11251,11257,11261,11273,11279,11287,11299,11311,11317,11321,11329,11351,11353,11369,11383,11393,11399,11411,11423,11437,11443,11447,11467,11471,11483,11489,11491,11497,11503,11519,11527,11549,11551,11579,11587,11593,11597,11617,11621,11633,11657,11677,11681,11689,11699,11701,11717,11719,11731,11743,11777,11779,11783,11789,11801,11807,11813,11821,11827,11831,11833,11839,11863,11867,11887,11897,11903,11909,11923,11927,11933,11939,11941,11953,11959,11969,11971,11981,11987,12007,12011,12037,12041,12043,12049,12071,12073,12097,12101,12107,12109,12113,12119,12143,12149,12157,12161,12163,12197,12203,12211,12227,12239,12241,12251,12253,12263,12269,12277,12281,12289,12301,12323,12329,12343,12347,12373,12377,12379,12391,12401,12409,12413,12421,12433,12437,12451,12457,12473,12479,12487,12491,12497,12503,12511,12517,12527,12539,12541,12547,12553,12569,12577,12583,12589,12601,12611,12613,12619,12637,12641,12647,12653,12659,12671,12689,12697,12703,12713,12721,12739,12743,12757,12763,12781,12791,12799,12809,12821,12823,12829,12841,12853,12889,12893,12899,12907,12911,12917,12919,12923,12941,12953,12959,12967,12973,12979,12983,13001,13003,13007,13009,13033,13037,13043,13049,13063,13093,13099,13103,13109,13121,13127,13147,13151,13159,13163,13171,13177,13183,13187,13217,13219,13229,13241,13249,13259,13267,13291,13297,13309,13313,13327,13331,13337,13339,13367,13381,13397,13399,13411,13417,13421,13441,13451,13457,13463,13469,13477,13487,13499,13513,13523,13537,13553,13567,13577,13591,13597,13613,13619,13627,13633,13649,13669,13679,13681,13687,13691,13693,13697,13709,13711,13721,13723,13729,13751,13757,13759,13763,13781,13789,13799,13807,13829,13831,13841,13859,13873,13877,13879,13883,13901,13903,13907,13913,13921,13931,13933,13963,13967,13997,13999,14009,14011,14029,14033,14051,14057,14071,14081,14083,14087,14107,14143,14149,14153,14159,14173,14177,14197,14207,14221,14243,14249,14251,14281,14293,14303,14321,14323,14327,14341,14347,14369,14387,14389,14401,14407,14411,14419,14423,14431,14437,14447,14449,14461,14479,14489,14503,14519,14533,14537,14543,14549,14551,14557,14561,14563,14591,14593,14621,14627,14629,14633,14639,14653,14657,14669,14683,14699,14713,14717,14723,14731,14737,14741,14747,14753,14759,14767,14771,14779,14783,14797,14813,14821,14827,14831,14843,14851,14867,14869,14879,14887,14891,14897,14923,14929,14939,14947,14951,14957,14969,14983,15013,15017,15031,15053,15061,15073,15077,15083,15091,15101,15107,15121,15131,15137,15139,15149,15161,15173,15187,15193,15199,15217,15227,15233,15241,15259,15263,15269,15271,15277,15287,15289,15299,15307,15313,15319,15329,15331,15349,15359,15361,15373,15377,15383,15391,15401,15413,15427,15439,15443,15451,15461,15467,15473,15493,15497,15511,15527,15541,15551,15559,15569,15581,15583,15601,15607,15619,15629,15641,15643,15647,15649,15661,15667,15671,15679,15683,15727,15731,15733,15737,15739,15749,15761,15767,15773,15787,15791,15797,15803,15809,15817,15823,15859,15877,15881,15887,15889,15901,15907,15913,15919,15923,15937,15959,15971,15973,15991,16001,16007,16033,16057,16061,16063,16067,16069,16073,16087,16091,16097,16103,16111,16127,16139,16141,16183,16187,16189,16193,16217,16223,16229,16231,16249,16253,16267,16273,16301,16319,16333,16339,16349,16361,16363,16369,16381,16411,16417,16421,16427,16433,16447,16451,16453,16477,16481,16487,16493,16519,16529,16547,16553,16561,16567,16573,16603,16607,16619,16631,16633,16649,16651,16657,16661,16673,16691,16693,16699,16703,16729,16741,16747,16759,16763,16787,16811,16823,16829,16831,16843,16871,16879,16883,16889,16901,16903,16921,16927,16931,16937,16943,16963,16979,16981,16987,16993,17011,17021,17027,17029,17033,17041,17047,17053,17077,17093,17099,17107,17117,17123,17137,17159,17167,17183,17189,17191,17203,17207,17209,17231,17239,17257,17291,17293,17299,17317,17321,17327,17333,17341,17351,17359,17377,17383,17387,17389,17393,17401,17417,17419,17431,17443,17449,17467,17471,17477,17483,17489,17491,17497,17509,17519,17539,17551,17569,17573,17579,17581,17597,17599,17609,17623,17627,17657,17659,17669,17681,17683,17707,17713,17729,17737,17747,17749,17761,17783,17789,17791,17807,17827,17837,17839,17851,17863,17881,17891,17903,17909,17911,17921,17923,17929,17939,17957,17959,17971,17977,17981,17987,17989,18013,18041,18043,18047,18049,18059,18061,18077,18089,18097,18119,18121,18127,18131,18133,18143,18149,18169,18181,18191,18199,18211,18217,18223,18229,18233,18251,18253,18257,18269,18287,18289,18301,18307,18311,18313,18329,18341,18353,18367,18371,18379,18397,18401,18413,18427,18433,18439,18443,18451,18457,18461,18481,18493,18503,18517,18521,18523,18539,18541,18553,18583,18587,18593,18617,18637,18661,18671,18679,18691,18701,18713,18719,18731,18743,18749,18757,18773,18787,18793,18797,18803,18839,18859,18869,18899,18911,18913,18917,18919,18947,18959,18973,18979,19001,19009,19013,19031,19037,19051,19069,19073,19079,19081,19087,19121,19139,19141,19157,19163,19181,19183,19207,19211,19213,19219,19231,19237,19249,19259,19267,19273,19289,19301,19309,19319,19333,19373,19379,19381,19387,19391,19403,19417,19421,19423,19427,19429,19433,19441,19447,19457,19463,19469,19471,19477,19483,19489,19501,19507,19531,19541,19543,19553,19559,19571,19577,19583,19597,19603,19609,19661,19681,19687,19697,19699,19709,19717,19727,19739,19751,19753,19759,19763,19777,19793,19801,19813,19819,19841,19843,19853,19861,19867,19889,19891,19913,19919,19927,19937,19949,19961,19963,19973,19979,19991,19993,19997,20011,20021,20023,20029,20047,20051,20063,20071,20089,20101,20107,20113,20117,20123,20129,20143,20147,20149,20161,20173,20177,20183,20201,20219,20231,20233,20249,20261,20269,20287,20297,20323,20327,20333,20341,20347,20353,20357,20359,20369,20389,20393,20399,20407,20411,20431,20441,20443,20477,20479,20483,20507,20509,20521,20533,20543,20549,20551,20563,20593,20599,20611,20627,20639,20641,20663,20681,20693,20707,20717,20719,20731,20743,20747,20749,20753,20759,20771,20773,20789,20807,20809,20849,20857,20873,20879,20887,20897,20899,20903,20921,20929,20939,20947,20959,20963,20981,20983,21001,21011,21013,21017,21019,21023,21031,21059,21061,21067,21089,21101,21107,21121,21139,21143,21149,21157,21163,21169,21179,21187,21191,21193,21211,21221,21227,21247,21269,21277,21283,21313,21317,21319,21323,21341,21347,21377,21379,21383,21391,21397,21401,21407,21419,21433,21467,21481,21487,21491,21493,21499,21503,21517,21521,21523,21529,21557,21559,21563,21569,21577,21587,21589,21599,21601,21611,21613,21617,21647,21649,21661,21673,21683,21701,21713,21727,21737,21739,21751,21757,21767,21773,21787,21799,21803,21817,21821,21839,21841,21851,21859,21863,21871,21881,21893,21911,21929,21937,21943,21961,21977,21991,21997,22003,22013,22027,22031,22037,22039,22051,22063,22067,22073,22079,22091,22093,22109,22111,22123,22129,22133,22147,22153,22157,22159,22171,22189,22193,22229,22247,22259,22271,22273,22277,22279,22283,22291,22303,22307,22343,22349,22367,22369,22381,22391,22397,22409,22433,22441,22447,22453,22469,22481,22483,22501,22511,22531,22541,22543,22549,22567,22571,22573,22613,22619,22621,22637,22639,22643,22651,22669,22679,22691,22697,22699,22709,22717,22721,22727,22739,22741,22751,22769,22777,22783,22787,22807,22811,22817,22853,22859,22861,22871,22877,22901,22907,22921,22937,22943,22961,22963,22973,22993,23003,23011,23017,23021,23027,23029,23039,23041,23053,23057,23059,23063,23071,23081,23087,23099,23117,23131,23143,23159,23167,23173,23189,23197,23201,23203,23209,23227,23251,23269,23279,23291,23293,23297,23311,23321,23327,23333,23339,23357,23369,23371,23399,23417,23431,23447,23459,23473,23497,23509,23531,23537,23539,23549,23557,23561,23563,23567,23581,23593,23599,23603,23609,23623,23627,23629,23633,23663,23669,23671,23677,23687,23689,23719,23741,23743,23747,23753,23761,23767,23773,23789,23801,23813,23819,23827,23831,23833,23857,23869,23873,23879,23887,23893,23899,23909,23911,23917,23929,23957,23971,23977,23981,23993,24001,24007,24019,24023,24029,24043,24049,24061,24071,24077,24083,24091,24097,24103,24107,24109,24113,24121,24133,24137,24151,24169,24179,24181,24197,24203,24223,24229,24239,24247,24251,24281,24317,24329,24337,24359,24371,24373,24379,24391,24407,24413,24419,24421,24439,24443,24469,24473,24481,24499,24509,24517,24527,24533,24547,24551,24571,24593,24611,24623,24631,24659,24671,24677,24683,24691,24697,24709,24733,24749,24763,24767,24781,24793,24799,24809,24821,24841,24847,24851,24859,24877,24889,24907,24917,24919,24923,24943,24953,24967,24971,24977,24979,24989,25013,25031,25033,25037,25057,25073,25087,25097,25111,25117,25121,25127,25147,25153,25163,25169,25171,25183,25189,25219,25229,25237,25243,25247,25253,25261,25301,25303,25307,25309,25321,25339,25343,25349,25357,25367,25373,25391,25409,25411,25423,25439,25447,25453,25457,25463,25469,25471,25523,25537,25541,25561,25577,25579,25583,25589,25601,25603,25609,25621,25633,25639,25643,25657,25667,25673,25679,25693,25703,25717,25733,25741,25747,25759,25763,25771,25793,25799,25801,25819,25841,25847,25849,25867,25873,25889,25903,25913,25919,25931,25933,25939,25943,25951,25969,25981,25997,25999,26003,26017,26021,26029,26041,26053,26083,26099,26107,26111,26113,26119,26141,26153,26161,26171,26177,26183,26189,26203,26209,26227,26237,26249,26251,26261,26263,26267,26293,26297,26309,26317,26321,26339,26347,26357,26371,26387,26393,26399,26407,26417,26423,26431,26437,26449,26459,26479,26489,26497,26501,26513,26539,26557,26561,26573,26591,26597,26627,26633,26641,26647,26669,26681,26683,26687,26693,26699,26701,26711,26713,26717,26723,26729,26731,26737,26759,26777,26783,26801,26813,26821,26833,26839,26849,26861,26863,26879,26881,26891,26893,26903,26921,26927,26947,26951,26953,26959,26981,26987,26993,27011,27017,27031,27043,27059,27061,27067,27073,27077,27091,27103,27107,27109,27127,27143,27179,27191,27197,27211,27239,27241,27253,27259,27271,27277,27281,27283,27299,27329,27337,27361,27367,27397,27407,27409,27427,27431,27437,27449,27457,27479,27481,27487,27509,27527,27529,27539,27541,27551,27581,27583,27611,27617,27631,27647,27653,27673,27689,27691,27697,27701,27733,27737,27739,27743,27749,27751,27763,27767,27773,27779,27791,27793,27799,27803,27809,27817,27823,27827,27847,27851,27883,27893,27901,27917,27919,27941,27943,27947,27953,27961,27967,27983,27997,28001,28019,28027,28031,28051,28057,28069,28081,28087,28097,28099,28109,28111,28123,28151,28163,28181,28183,28201,28211,28219,28229,28277,28279,28283,28289,28297,28307,28309,28319,28349,28351,28387,28393,28403,28409,28411,28429,28433,28439,28447,28463,28477,28493,28499,28513,28517,28537,28541,28547,28549,28559,28571,28573,28579,28591,28597,28603,28607,28619,28621,28627,28631,28643,28649,28657,28661,28663,28669,28687,28697,28703,28711,28723,28729,28751,28753,28759,28771,28789,28793,28807,28813,28817,28837,28843,28859,28867,28871,28879,28901,28909,28921,28927,28933,28949,28961,28979,29009,29017,29021,29023,29027,29033,29059,29063,29077,29101,29123,29129,29131,29137,29147,29153,29167,29173,29179,29191,29201,29207,29209,29221,29231,29243,29251,29269,29287,29297,29303,29311,29327,29333,29339,29347,29363,29383,29387,29389,29399,29401,29411,29423,29429,29437,29443,29453,29473,29483,29501,29527,29531,29537,29567,29569,29573,29581,29587,29599,29611,29629,29633,29641,29663,29669,29671,29683,29717,29723,29741,29753,29759,29761,29789,29803,29819,29833,29837,29851,29863,29867,29873,29879,29881,29917,29921,29927,29947,29959,29983,29989,30011,30013,30029,30047,30059,30071,30089,30091,30097,30103,30109,30113,30119,30133,30137,30139,30161,30169,30181,30187,30197,30203,30211,30223,30241,30253,30259,30269,30271,30293,30307,30313,30319,30323,30341,30347,30367,30389,30391,30403,30427,30431,30449,30467,30469,30491,30493,30497,30509,30517,30529,30539,30553,30557,30559,30577,30593,30631,30637,30643,30649,30661,30671,30677,30689,30697,30703,30707,30713,30727,30757,30763,30773,30781,30803,30809,30817,30829,30839,30841,30851,30853,30859,30869,30871,30881,30893,30911,30931,30937,30941,30949,30971,30977,30983,31013,31019,31033,31039,31051,31063,31069,31079,31081,31091,31121,31123,31139,31147,31151,31153,31159,31177,31181,31183,31189,31193,31219,31223,31231,31237,31247,31249,31253,31259,31267,31271,31277,31307,31319,31321,31327,31333,31337,31357,31379,31387,31391,31393,31397,31469,31477,31481,31489,31511,31513,31517,31531,31541,31543,31547,31567,31573,31583,31601,31607,31607};
inline bool prm(int x){
for(int i=1;i if(!(x%prime[i]))
return 0;
return 1;
}
inline void dfs(int nowsum,int nowdis,int nowans){
if(nowsum>=L&&(nowans>ans||nowans==ans&&nowsum if(nowans*pow((float)2,(log((float)R/nowsum)/log(prime[nowdis])))<=ans)return;//剪枝1
if(ceil((float)L/nowsum)*nowsum>R)return;//剪枝2
if(nowdis==prime[0]&&R/nowsum if(nowans<<1>=ans)
for(int tmp=max(ceil((float)L/nowsum),(float)prime[nowdis]),maxtmp=ans==nowans<<1?min((floor((float)R/nowsum)+1),(float)num/nowsum+1):floor((float)R/nowsum)+1;tmp if(prm(tmp)){
ans=nowans<<1;
num=tmp*nowsum;
break;
}
return;
}//边界
for(int i=log((double)R/nowsum)/log(prime[nowdis])+1;i;--i)dfs((int)(nowsum*pow(prime[nowdis],i-1)),nowdis+1,nowans*i);//To next depth
}
int main(){
freopen("divisors.in","r",stdin);
freopen("divisors.out","w",stdout);
scanf("%d%d",&L,&R);
dfs(1,1,1);
printf("Between %d and %d, %d has a maximum of %d divisors.\n",L,R,num,ans);
}
总结：
①这道题首先提高了我对DFS复杂度的分析，比如本题中对于DFS时间复杂度的分析就非常棒，是我一开始没有想到的，我误以为如果没有剪枝的话它会比暴力还慢，但实际上它显然不是这样，DFS是O(R)≈10^9，而暴力是O((R-L)*R^0.5)≈10^13.5的。
所以以后在分析时间复杂度的时候我一定要仔细认真思考，勇于DFS。
②尽量用位运算代替其他运算，尽量用整数运算代替实数运算。
