Question

We have started learning Java in school, and we have been given a few homeworks to do. I’ve managed to do 4 out of 5, but this last one is a real pain.

Basicly: Write a program that finds (in a 1000 places long number) the largest product of five
consecutive digits.

Here’s the number http://pastebin.com/PFgL6jcM

Do you have any ideas how to solve this ?

If this are unclear instruction, notify me and will try to explain to you again.

Answer 1

I’d say an optimized algorithm would look like this:

1) grab first five numbers

2) if current set contains a 0, grab the first five numbers after the 0. Do this until you reach a set that doesn’t contain a 0. (if all sets contain a 0 – unlikely – return 0).

3) compute the product of the 5 numbers ( x1, x2, x3, x4, x5 ) like so:

p1 = x5 * x4
p2 = x3 * p1
p3 = x2 * p2
p  = x1 * p3

4) if p is greater than the previous p, store it.

5) discard the first number and add the next one (x6).

p = x6 * p3

6) if the new p is greater than the old one, go to step 3)

You’re reducing the number of multiplications by a factor of 5, since you won’t keep multiplying 5 numbers, but 2.

Remember to discard sequences that contain a 0 and try to optimize the algorithm along these lines.