UVa 10624 - Super Number, Rujia Liu的神题(四)
链接：
http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=112&page=show_problem&problem=1565
原题：
Don't you think 162456723 very special? Look at the picture below if you are unable to find its speciality. (a | b means ‘b is divisible bya’)
Figure: Super Numbers
Given n, m (0 < n < m < 30), you are to find a m-digit positive integer X such that for every i (n <= i <= m), the first i digits of X is a multiple of i. If more than one such X exists, you should output the lexicographically smallest one. Note that the first digit of X should notbe 0.
Input
The first line of the input contains a single integer t(1 <= t <= 15), the number of test cases followed. For each case, two integers n and mare separated by a single space.
Output
For each test case, print the case number and X. If no such number, print -1.
样例输入：
2
1 10
3 29
样例输出：
Case 1: 1020005640
Case 2: -1
题目大意：
所谓的超级数字，就是指一个数字，从左边位数开始， 前i位能被i整数
输入n， m， 第n为开始要满足超级数字的要求。
分析与总结:
这种题很容易想到直接暴力回溯可以求出答案，但是也赤裸裸地TLE了。。。（据说网上有人暴力回溯也擦边过了， 膜拜）
由于没想到好的减枝方法， 于是打表水过
直接暴力回溯，TLE了。。。求大神的高效算法啊
#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int str[35];
int n, m, flag;
inline int mod(int *str,int num, int len){
int remainder=0;
for(int i=0;i<len;i++)
remainder=(remainder*10+str[i])%num;
return remainder;
}
void search(int cur){
if(flag) return;
if(cur==m){
flag=true; return;
}
for(int i=0; i<=9 && !flag; ++i){
if(cur==0 && i==0) continue;
str[cur] = i;
if(cur >= n-1){ // 大于等于n位的要求是倍数
if(mod(str, cur+1, cur+1)!=0) continue;
}
search(cur+1);
if(flag) return;
}
}
int main(){
int T, cas=1;
scanf("%d",&T);
while(T--){
scanf("%d%d",&n,&m);
memset(str, 0, sizeof(str));
flag = 0;
search(0);
printf("Case %d: ", cas++);
if(flag) {
for(int i=0; i<m; ++i)printf("%d", str[i]);
printf("\n");
}
else printf("-1\n");
}
return 0;
}
打表的,罪过啊罪过：
#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int str[35];
int n, m, flag;
typedef char BigNum[35];
BigNum ans[30][30]={
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"-1","-1","10","102","1020","10200","102000","1020005","10200056","102000564","1020005640","10200056405","102006162060","1020061620604","10200616206046","102006162060465","1020061620604656","10200616206046568","108054801036000018","1080548010360000180","10805480103600001800","123606009012225672009","1236060090122256720090","12360600901222567200901","144408645048225636603816","3608528850368400786036725","-1","-1","-1","-1",
"-1","-1","-1","102","1020","10200","102000","1020005","10200056","102000564","1020005640","10200056405","102006162060","1020061620604","10200616206046","102006162060465","1020061620604656","10200616206046568","108054801036000018","1080548010360000180","10805480103600001800","123606009012225672009","1236060090122256720090","12360600901222567200901","144408645048225636603816","3608528850368400786036725","-1","-1","-1","-1",
"-1","-1","-1","-1","1020","10200","102000","1020005","10200056","102000564","1020005640","10200056405","102006162060","1020061620604","10200616206046","102006162060465","1020061620604656","10200616206046568","108054801036000018","1080548010360000180","10805480103600001800","123606009012225672009","1236060090122256720090","12360600901222567200901","144408645048225636603816","3608528850368400786036725","75320424003636007240884008","753204240036360072408840084","7532042400363600724088400840","-1",
"-1","-1","-1","-1","-1","10000","100002","1000020","10000200","100002006","1000020060","10000200606","100002006060","1000027260128","10000272601284","100002726012840","1000027260128400","10000832402470569","101208807048720006","1016582400964208520","10165824009642085200","104052249072240066402","1040522490722400664022","10405224907224006640223","144408645048225636603816","1828022400607200846092400","18280224006072008460924002","753204240036360072408840084","7532042400363600724088400840","-1",
"-1","-1","-1","-1","-1","-1","100002","1000020","10000200","100002006","1000020060","10000200606","100002006060","1000027260128","10000272601284","100002726012840","1000027260128400","10000832402470569","100956888012540816","1016582400964208520","10165824009642085200","104052249072240066402","1040522490722400664022","10405224907224006640223","119952000084840030408408","1301587290367056900064800","13015872903670569000648008","528552567072465642000840006","7532042400363600724088400840","-1",
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"-1","-1","-1","-1","-1","-1","-1","-1","-1","100000008","1000000080","10000000802","100000008024","1000000080248","10000000802484","100000008024840","1000000080248400","10000072808446565","100001763072960030","1000017630729600301","10000344607246567820","100003446072465678204","1000034460724656782040","10003824006022562480160","100038240060225624801600","1000382400602256248016000","10003824006022562480160006","100038240060225624801600066","1015500060367808224022400608","10211576408418088880443254681",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","1000000080","10000000802","100000008024","1000000080248","10000000802484","100000008024840","1000000080248400","10000001704812002","100000179072360072","1000001880969008586","10000018809690085860","100000188096900858606","1000001880969008586064","10001501103622563080700","100015011036225630807000","1000150110362256308070000","10003824006022562480160006","100038240060225624801600066","1001385810724656966004325888","10101279606082569080443254680",
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"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","100000000104","1000000005485","10000000054856","100000000764300","1000000007643008","10000000087224007","100000004832000090","1000000073644656126","10000000736446561260","100000007364465612600","1000000122004800908046","10000001220048009080461","100000146732225624801456","1000004058963008284086000","10000155957610563000967256","100001559576105630009672561","1000023746761200244028400000","10000351372830084060967250126",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","1000000000207","10000000002076","100000000020765","1000000000805408","10000000008054089","100000000200105630","1000000002001056306","10000000020010563060","100000002384105660606","1000000023841056606060","10000000881654084060982","100000019772945648006240","1000000197729456480062400","10000007881248007860384004","100000093788420804006672546","1000000937884208040066725460","10000028419290081060024006085",
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"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","100000000000185","1000000000001856","10000000000018563","100000000000740852","1000000000015808227","10000000000438565400","100000000009140894201","1000000000091408942010","10000000001964009660049","100000000038825612600600","1000000000388256126006000","10000000106166087000943258","100000001748780810600072507","1000000029931056724086725040","10000000299310567240867250403",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","1000000000000208","10000000000006561","100000000000065618","1000000000000656183","10000000000027522820","100000000000635282009","1000000000006352820090","10000000000939521680145","100000000009395216801456","1000000000116752586006725","10000000001167525860067258","100000000061160048003000087","1000000004165856722072400216","10000000177423525880167258806",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","10000000000000169","100000000000006452","1000000000000064523","10000000000003042840","100000000000033650804","1000000000001744104022","10000000000021606220147","100000000000441656801480","1000000000004416568014800","10000000000044165680148008","100000000000441656801480087","1000000000484656388074325076","10000000012965287440500008129",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","100000000000000332","1000000000000003324","10000000000000033240","100000000000001016405","1000000000000010164056","10000000000000101640564","100000000000001016405648","1000000000004416568014800","10000000000044165680148008","100000000000441656801480087","1000000000011882960090000000","10000000000552924880760008767",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","1000000000000000265","10000000000000006260","100000000000000062606","1000000000000000626066","10000000000000006260668","100000000000001016405648","1000000000000019702046000","10000000000001107880743258","100000000000023444006480081","1000000000000273504056000848","10000000000010730620467258241",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","10000000000000000180","100000000000000039800","1000000000000000474024","10000000000000005880501","100000000000000123401432","1000000000000001234014325","10000000000000036280107256","100000000000001164602000024","1000000000000013964006000428","10000000000000635540300008128",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","100000000000000000005","1000000000000000000056","10000000000000000120243","100000000000000001202432","1000000000000000012024325","10000000000000000120243256","100000000000000001202432561","1000000000000002242010000420","10000000000000024060207252565",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","1000000000000000000056","10000000000000000008923","100000000000000000131096","1000000000000000010550000","10000000000000000105500008","100000000000000001055000087","1000000000000000047092400272","10000000000000000485667250123",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","10000000000000000000344","100000000000000000003440","1000000000000000000034400","10000000000000000001448008","100000000000000000014480081","1000000000000000006062725880","10000000000000000135423252801",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","100000000000000000000224","1000000000000000000006800","10000000000000000000068006","100000000000000000004592546","1000000000000000000045925468","10000000000000000007244006366",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","1000000000000000000000325","10000000000000000000015252","100000000000000000000392507","1000000000000000000003925076","10000000000000000001503258209",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","10000000000000000000000250","100000000000000000000017585","1000000000000000000000225268","10000000000000000000006750880",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","100000000000000000000000683","1000000000000000000000022492","10000000000000000000000224923",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","1000000000000000000000000624","10000000000000000000000141200",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","10000000000000000000000000086",
"-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1","-1"
};
int main(){
int T, cas=1;
scanf("%d", &T);
while(T--){
int n, m;
scanf("%d%d",&n,&m);
printf("Case %d: ",cas++);
printf("%s\n", ans[n][m]);
}
}
—— 生命的意义，在于赋予它意义。
原创 http://blog.csdn.net/shuangde800 ， By D_Double (转载请标明)