Project Euler Problem #25

February 9, 2010

Read the details of the problem here

Summary

What is the first term in the Fibonacci sequence to contain 1000 digits?

Solution

I just took the brute-force naive approach for this as Java, with BigInteger support, makes it just too tempting not do so. Note that it’s quicker (by about 30%) to check the length of the string representation rather than comparing it to a terminal value.

def (fib1, fib2, answer) = [ 1G, 2G, 3 ]

while (fib2.toString().size() < 1000) {
    (fib1, fib2, answer) = [ fib2, fib1+fib2, answer+1 ]
}

This runs in 2.94 seconds. There are cleverer ways to do this using the Golden Ratio relationships to derive the value of the term mathematically but this took seconds to write and is obviously correct!

Conclusion

Groovy, with automatic support for Java’s BigInteger, made this very quick and simple to write.

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