2013
11-11

# Consecutive Digits

As a recruiting ploy, Google once posted billboards in Harvard Square and in the Silicon Valley area just stating “{first 10-digit prime found in consecutive digits of e}.com”. In other words, find that 10-digit sequence and then connect to the web site — and find out that Google is trying to hire people who can solve a particular kind of problem.

Not to be outdone, Gaggle (a loosy-goosy fuzzy logic search firm), has devised its own recruiting problem. Consider the base 7 expansion of a rational number. For example, the first few digits of the base 7 expansion of 1/510 = 0.12541…7, 33/410 = 11.15151…7, and 6/4910 = 0.06000…7, From this expansion, find the digits in a particular range of positions to the right of the “decimal” point.

The input file begins with a line containing a single integer specifying the number of problem sets in the file. Each problem set is specified by four base 10 numbers on a single line, n d b e, where n and d are the numerator and denominator of the rational number and 0 <= n <= 5,000 and 1 <= d <= 5,000. b and e are the beginning and ending positions for the desired range of digits, with 0 <= b,e <= 250 and 0 <= (e-b) <= 20. Note that 0 is the position immediately to the right of the decimal point.

Each problem set will be numbered (beginning at one) and will generate a single line:
Problem set k: n / d, base 7 digits b through e: result

where k is replaced by the problem set number, result is your computed result, and the other values are the corresponding input values.

4
1 5 0 0
6 49 1 3
33 4 2 7
511 977 122 126


Problem set 1: 1 / 5, base 7 digits 0 through 0: 1
Problem set 2: 6 / 49, base 7 digits 1 through 3: 600
Problem set 3: 33 / 4, base 7 digits 2 through 7: 151515
Problem set 4: 511 / 977, base 7 digits 122 through 126: 12425


//* @author: ccQ.SuperSupper
import java.util.*;
import java.math.*;
public class Main {
public static void main(String []args) throws Exception{

int t,cs=1,left,right,i,j;
BigInteger a,b,seven;
String str1,str2;

seven = BigInteger.valueOf(1);
for(i=0;i< 10000;++i)
seven = seven.multiply(BigInteger.valueOf(7));

Scanner cin = new Scanner(System.in);

t = cin.nextInt();
while(t--!=0){
str1 = cin.next();
str2 = cin.next();
left = cin.nextInt();
right = cin.nextInt();

a = new BigInteger(str1);
a = a.multiply(seven);
a = a.divide(new BigInteger(str2));

b = new BigInteger(str1);
b = b.divide(new BigInteger(str2));
b = b.multiply(seven);

a = a.subtract(b);
}