HDOJ 4937 Lucky Number

当进制转换后所剩下的为数较少时（2位，3位），对应的base都比较大，可以用数学的方法计算出来。

预处理掉转换后位数为3位后，base就小于n的3次方了，可以暴力计算。。。。

Lucky Number

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 521    Accepted Submission(s): 150

Problem Description

“Ladies and Gentlemen, It’s show time! ”

“A thief is a creative artist who takes his prey in style... But a detective is nothing more than a critic, who follows our footsteps...”

Love_Kid is crazy about Kaito Kid , he think 3(because 3 is the sum of 1 and 2), 4, 5, 6 are his lucky numbers and all others are not. 

Now he finds out a way that he can represent a number through decimal representation in another numeral system to get a number only contain 3, 4, 5, 6. 

For example, given a number 19, you can represent it as 34 with base 5, so we can call 5 is a lucky base for number 19. 

Now he will give you a long number n(1<=n<=1e12), please help him to find out how many lucky bases for that number. 

If there are infinite such base, just print out -1.

 

Input

There are multiply test cases.

The first line contains an integer T(T<=200), indicates the number of cases. 

For every test case, there is a number n indicates the number.

 

Output

For each test case, output “Case #k: ”first, k is the case number, from 1 to T , then, output a line with one integer, the answer to the query.

 

Sample Input

21019

 

Sample Output

Case #1: 0Case #2: 1
Hint
10 shown in hexadecimal number system is another letter different from ‘0’-‘9’, we can represent it as ‘A’, and you can extend to other cases.
 

 

Author

UESTC

 

Source

2014 Multi-University Training Contest 7

 

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <set>#include <cmath>using namespace std;typedef long long int LL;LL n;set<LL> ans;bool change(LL x,LL base){    bool flag=true;    while(x)    {        LL temp=x%base;        x/=base;        if(temp>=3LL&&temp<=6LL) continue;        else        {            flag=false;            break;        }    }    return flag;}int main(){    int T_T,cas=1;    scanf("%d",&T_T);    while(T_T--)    {        ans.clear();        cin>>n;        if(n>=3LL&&n<=6LL)        {           cout<<"Case #"<<cas++<<": -1"<<endl; continue;        }        for(LL a=3;a<=6;a++)        {            for(LL b=3;b<=6;b++)            {                LL limit=max(a,b);                if( (n-b)%a == 0 )                {                    if( (n-b)/a > limit)                    {                        ans.insert((n-b)/a);                    }                }            }        }        for(LL a=3;a<=6;a++)        {            for(LL b=3;b<=6;b++)            {                for(LL c=3;c<=6;c++)                {                    LL C=c-n;                    if(b*b >= 4LL*a*C )                    {                        LL deta=sqrt(b*b-4LL*a*C);                        LL base1=(-b+deta)/(2*a);                        LL base2=(-b-deta)/(2*a);                        LL limit=max(a,max(b,c));                        if(a*base1*base1+b*base1+c==n && base1>limit)                        {                            ans.insert(base1);                        }                        if(a*base2*base2+b*base2+c==n && base2>limit)                        {                            ans.insert(base2);                        }                    }                }            }        }        for(LL i=4;i*i*i<=n;i++)        {            if(change(n,i))            {                ans.insert(i);            }        }        cout<<"Case #"<<cas++<<": "<<ans.size()<<endl;    }    return 0;}