p225.java

/* 
 * Solution to Project Euler problem 225
 * By Nayuki Minase
 * 
 * http://nayuki.eigenstate.org/page/project-euler-solutions
 * https://github.com/nayuki/Project-Euler-solutions
 */


public final class p225 implements EulerSolution {
	
	public static void main(String[] args) {
		System.out.println(new p225().run());
	}
	
	
	private static final int INDEX = 124;  // 1-based
	
	public String run() {
		int count = 0;
		for (int i = 1; ; i += 2) {
			if (!hasMultiple(i)) {
				count++;
				if (count == INDEX)
					return Integer.toString(i);
			}
		}
	}
	
	
	private static boolean hasMultiple(int modulus) {
		// Floyd's cycle-finding algorithm
		Tribonacci slow = new Tribonacci(modulus);
		Tribonacci fast = new Tribonacci(modulus);
		while (true) {
			if (slow.hasMultiple())
				return true;
			slow.next();
			fast.next();
			fast.next();
			if (slow.equals(fast))
				return false;
		}
	}
	
	
	
	private static class Tribonacci {
		
		public final int modulus;
		
		public int a;
		public int b;
		public int c;
		
		
		public Tribonacci(int mod) {
			a = 1 % mod;
			b = 1 % mod;
			c = 1 % mod;
			modulus = mod;
		}
		
		
		public void next() {
			int d = (a + b + c) % modulus;
			a = b;
			b = c;
			c = d;
		}
		
		
		public boolean hasMultiple() {
			return a == 0 || b == 0 || c == 0;
		}
		
		
		public boolean equals(Tribonacci other) {
			return a == other.a
			    && b == other.b
			    && c == other.c
			    && modulus == other.modulus;
		}
		
	}
	
}