## Problem:

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1

Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.

Find the value of d [<] 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.

983

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{

public String run();

}
/*
* Solution to Project Euler problem 26
* By Nayuki Minase
*
* http://nayuki.eigenstate.org/page/project-euler-solutions
* https://github.com/nayuki/Project-Euler-solutions
*/

import java.util.HashMap;
import java.util.Map;

public final class p026 implements EulerSolution {

public static void main(String[] args) {
System.out.println(new p026().run());
}

public String run() {
int bestNumber = 0;
int bestLength = 0;
for (int i = 1; i <= 1000; i++) {
int len = getCycleLength(i);
if (len > bestLength) {
bestNumber = i;
bestLength = len;
}
}
return Integer.toString(bestNumber);
}

private static int getCycleLength(int n) {
Map<Integer,Integer> stateToIter = new HashMap<Integer,Integer>();
int state = 1;
int iter = 0;
while (!stateToIter.containsKey(state)) {
stateToIter.put(state, iter);
state = state * 10 % n;
iter++;
}
return iter - stateToIter.get(state);
}

}