hdu 4398 多校联合赛 第九场 X mod f(x) 数论

X mod f(x)

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 174    Accepted Submission(s): 42

Problem Description

Here is a function f(x):　　　int f ( int x ) {　　　    if ( x == 0 ) return 0;　　　    return f ( x / 10 ) + x % 10;　　　}

　　　Now, you want to know, in a given interval [A, B] (1 <= A <= B <= 10⁹), how many integer x that mod f(x) equal to 0.

 

Input

　　　The first line has an integer T (1 <= T <= 50), indicate the number of test cases.
　　　Each test case has two integers A, B.

 

Output

　　　For each test case, output only one line containing the case number and an integer indicated the number of x.

 

SampleInput

21 1011 20

 

SampleOutput

Case 1: 10Case 2: 3

 

Author

WHU

题意：

输入n m  从n到m算出满足x%f(x)的数的个数  

思路：

一开始找规律 没有规律可循 

后来想到了 部分暴力 就是说 写打表 

把从1分别到

1*200000

2*200000

3*200000

。。。。。

10^9

的满足题意的个数全部给打表打出来打进文件 再复制进数组里

然后：比如 对于一个输入的n=620000

那么由于1-600000的个数已经打表知道了 只要暴力600000+1到620000 即可

ac代码   下面有打表代码

#include<stdio.h>#include<string.h>int a[5050]={0,23038,43691,62344,79494,95428,117251,136926,154753,171215,186561,207319,226142,243273,259122,273964,293749,311777,328266,343560,357923,376842,394196,410102,424906,438795,456935,473705,489121,503491,516988,534432,550627,565578,579518,592666,609471,625153,639668,653243,666027,682185,697359,711460,724669,737096,752684,767362,781082,793957,806095,827912,847505,865348,881829,897228,917958,936644,953748,969593,984457,1004246,1022150,1038599,1053893,1068251,1087182,1104383,1120224,1134999,1148898,1167083,1183663,1198988,1213284,1226769,1244283,1260310,1275181,1289050,1302141,1319012,1334553,1348965,1362477,1375194,1391506,1406579,1420620,1433752,1446173,1461907,1476483,1490129,1502903,1514990,1530199,1544339,1557612,1570094,1581855,1602519,1621202,1638352,1654240,1669171,1688855,1706723,1723174,1738471,1752886,1771743,1788901,1804751,1819529,1833499,1851587,1868075,1883358,1897646,1911166,1928604,1944532,1959309,1973139,1986220,2003059,2018498,2032861,2046299,2059035,2075318,2090283,2104235,2117319,2129704,2145464,2159997,2173585,2186330,2198383,2213611,2227715,2240925,2253328,2265047,2279834,2293525,2306406,2318480,2329984,2349563,2367444,2383947,2399319,2413838,2432533,2449651,2465529,2480347,2494379,2512304,2528778,2544072,2558405,2571992,2589245,2605125,2619881,2633724,2646896,2663574,2678924,2693224,2706624,2719392,2735522,2750405,2764291,2777339,2789743,2805369,2819833,2833334,2846056,2858080,2873233,2887292,2900473,2912873,2924630,2939314,2952939,2965768,2977813,2989257,3003491,3016763,3029225,3040992,3052160,3070810,3087935,3103866,3118775,3132961,3150784,3167212,3182541,3196945,3210653,3227800,3243650,3258456,3272346,3285645,3302173,3317444,3331742,3345157,3358037,3374014,3388829,3402658,3415677,3428135,3443601,3457971,3471414,3484045,3496170,3511200,3525126,3538227,3550533,3562323,3576928,3590511,3603263,3615293,3626798,3640941,3654135,3666545,3678248,3689474,3703248,3716068,3728163,3739560,3750525,3768368,3784857,3800280,3814795,3828640,3845731,3861558,3876416,3890413,3903809,3920254,3935541,3949897,3963419,3976405,3992271,4007043,4020913,4033968,4046550,4061913,4076225,4089680,4102288,4114501,4129399,4143282,4156326,4168604,4180462,4194923,4208446,4221125,4233077,4244641,4258729,4271874,4284236,4295907,4307251,4320953,4333726,4345745,4357099,4368127,4381443,4393918,4405618,4416724,4427492,4444608,4460526,4475477,4489698,4503070,4519477,4534790,4549222,4562954,4575951,4591795,4606580,4620542,4633801,4646413,4661706,4675988,4689473,4702274,4714477,4729282,4743148,4756221,4768606,4780451,4794821,4808276,4820985,4832996,4844581,4858557,4871639,4883959,4895644,4906971,4920601,4933355,4945346,4956769,4967829,4981078,4993494,5005165,5016303,5027126,5040064,5052151,5063546,5074389,5084970,5101431,5116842,5131436,5145295,5158330,5174152,5188978,5203052,5216456,5229087,5244346,5258689,5272273,5285249,5297507,5312261,5326115,5339278,5351804,5363730,5378048,5391460,5404245,5416390,5427989,5441864,5454907,5467241,5479054,5490370,5503845,5516543,5528524,5540019,5551100,5564270,5576637,5588334,5599544,5610431,5623259,5635301,5646688,5657629,5668264,5680733,5692492,5703586,5714304,5724686,5740568,5755509,5769765,5783154,5795749,5811019,5825429,5839203,5852170,5864428,5879197,5893125,5906465,5919016,5930950,5945229,5958684,5971571,5983726,5995318,6009173,6022241,6034731,6046569,6057901,6071352,6084018,6096132,6107639,6118762,6131845,6144152,6155917,6167148,6178017,6190748,6202765,6214207,6225199,6235854,6248238,6259936,6271122,6281842,6292282,6304401,6315811,6326727,6337241,6347468,6362850,6377364,6391270,6404220,6416462,6431293,6445302,6458763,6471348,6483225,6497539,6511123,6524149,6536365,6547969,6561819,6574923,6587544,6599372,6610705,6624168,6636874,6649128,6660672,6671740,6684816,6697162,6709022,6720314,6731176,6743849,6755843,6767401,6778405,6789058,6801426,6813069,6824364,6835105,6845573,6857599,6868982,6879972,6890536,6900765,6912509,6923628,6934386,6944738,6954793,6976583,6996285,7014095,7030588,7045942,7066672,7085511,7102619,7118527,7133324,7153096,7171148,7187588,7202960,7217267,7236173,7253551,7269451,7284339,7298238,7316346,7333102,7348488,7362912,7376359,7393745,7409939,7424845,7438854,7451901,7468651,7484336,7498853,7512453,7525188,7541342,7556515,7570617,7583868,7596271,7611835,7626540,7640228,7653107,7665191,7680213,7694457,7707794,7720323,7732131,7752829,7771537,7788609,7804493,7819332,7839107,7857044,7873447,7888788,7903158,7922072,7939289,7955106,7969917,7983801,8001955,8018568,8033854,8048239,8061674,8079146,8095190,8110000,8123944,8137010,8153844,8169358,8183759,8197305,8209989,8226256,8241296,8255293,8268482,8280812,8296532,8311160,8324781,8337637,8349662,8364873,8379035,8392319,8404796,8416558,8431245,8444976,8457899,8470072,8481543,8501214,8519098,8535530,8550862,8565293,8584112,8601284,8617098,8631916,8645838,8663896,8680430,8695652,8709973,8723430,8740833,8756791,8771553,8785438,8798508,8815311,8830751,8845054,8858566,8871242,8887488,8902422,8916325,8929457,8941769,8957507,897202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f(int x){if(x==0) return 0;return f(x/10)+x%10;}int main(){      int cas,k,i,n,m,nn,nm,k1,k2;  scanf("%d",&cas);  for(k=1;k<=cas;k++)  {  scanf("%d %d",&n,&m);  n=n-1;   k1=n/200000;   k2=m/200000;           nn=a[k1];   nm=a[k2];   for(i=k1*200000+1;i<=n;i++)   if(i%f(i)==0) nn++;   for(i=k2*200000+1;i<=m;i++)   if(i%f(i)==0) nm++;    printf("Case %d: %d\n",k,nm-nn);  }  return 0;}

打表代码：

#include<stdio.h>int f (int x){if(x==0) return 0;return f(x/10)+x%10;}int main(){int i,cnt=0,num=0,cnt2=0;freopen("d://521.in","w",stdout);for(i=1;i<=1000000000;i++){if(i%f(i)==0){cnt++;}if(i%200000==0){printf("%d,",cnt);cnt2++;if(cnt2==10) {printf("\n");cnt2=0;}}}return 0;}

注意 打长度为1000的表 超时  长度为10000的表 限制代码长度 不让提交  打5000正好