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p014.java
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p014.java
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/*
* Solution to Project Euler problem 14
* By Nayuki Minase
*
* http://nayuki.eigenstate.org/page/project-euler-solutions
* https://github.com/nayuki/Project-Euler-solutions
*/
import java.math.BigInteger;
public final class p014 implements EulerSolution {
public static void main(String[] args) {
System.out.println(new p014().run());
}
private static final int LIMIT = Library.pow(10, 6);
private static final BigInteger CACHE_SIZE = BigInteger.valueOf(LIMIT);
public String run() {
int maxArg = -1;
int maxChain = 0;
for (int i = 1; i < LIMIT; i++) {
int chainLen = collatzChainLength(BigInteger.valueOf(i));
if (chainLen > maxChain) {
maxArg = i;
maxChain = chainLen;
}
}
return Integer.toString(maxArg);
}
// Memoization
private int[] collatzChainLength = new int[CACHE_SIZE.intValue()];
private int collatzChainLength(BigInteger n) {
if (n.signum() < 0)
throw new IllegalArgumentException();
int index;
if (n.compareTo(CACHE_SIZE) < 0)
index = n.intValue();
else
index = -1;
if (index != -1 && collatzChainLength[index] != 0)
return collatzChainLength[index];
int result;
if (n.equals(BigInteger.ONE))
result = 1;
else if (!n.testBit(0)) // If n is even
result = collatzChainLength(n.shiftRight(1)) + 1;
else // Else n is odd
result = collatzChainLength(n.multiply(BigInteger.valueOf(3)).add(BigInteger.ONE)) + 1;
if (index != -1)
collatzChainLength[index] = result;
return result;
}
}