HDU 4937 Lucky Number
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Lucky Number
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)Total Submission(s): 1542 Accepted Submission(s): 453
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.
“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.
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: 1Hint10 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.
题意:输入一个十进制数字n,用一个k进制数表示,每个数只能包含3 4 5 6,问这样的k有多少个
#include <iostream>#include <stdio.h>#include <string>#include <cstring>#include <algorithm>#include <cmath>#include <queue>#include <map>using namespace std;typedef long long ll;int main(){ int T; scanf("%d",&T); for(int ca=1;ca<=T;ca++) { ll n; scanf("%I64d",&n); printf("Case #%d: ",ca); if(n>=3&&n<=6)//只有3 4 5 6是无限多种进制可以表示,10以上数字会用'A'表示 { puts("-1"); continue; } int num=0; for(int i=3;i<=6;i++)//两位的时候 for(int j=3;j<=6;j++) { if((n-j)%i==0 && (n-j)/i>i && (n-j)/i>j) { num++; } } for(int i=3;i<=6;i++)//三位组成的时候 for(int j=3;j<=6;j++) for(int k=3;k<=6;k++) { ll m=j*j-4*(k-n)*i; ll f=sqrt(m); if(f*f==m) { ll tt=(f-j)%(2*i); ll ff=(f-j)/(2*i); if(tt==0 && ff>i && ff>j && ff>k) { num++; } } } for(int i=4;i<=10000;i++)//大于等于四位的时候,此时进制数最大不会超过10000 { ll t=n; int flag=0; int cnt=0; while(t) { ll f=t%i; if(f<3 || f>6) { flag=1; break; } t/=i; cnt++;//判断有几位,小于4位前面已经出现过,会重复 } if(flag==0 && cnt>3) { num++; } } printf("%d\n",num); } return 0;}
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