Elemental Names

Form names using the initials of chemical elements

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        - "I like Liam."
        — "Lithium. Americium. Perfect."

        - "What about Nora?"
        — "Nitrogen. Oxygen. Radium. That works."

        - "Emma is a nice name too."
        — "Hmm... no. That doesn't work."

They can't keep checking names by hand. They need an automated way to spot elemental names.

Guessing is not enough. They need a way to validate elemental names.

Elemental Name!

14 one-letter elements and 104 two-letter elements

So now we know "Erica" is elemental. But how do we validate this in a systematic way? Let's start from the left. "E" does not exist. So we try two letters. "Er". That works. We move forward. Now we have "ica". "I" works. Iodine. We move forward again. Now we have "ca". "C" works. Carbon. We move forward. Now we have "a". "A" does not exist. So this fails. If we stop here, we conclude that "Erica" does not work. But that conclusion is wrong.

The mistake happened earlier. When we matched "C", we had another valid option. Instead of taking "C", we could have taken "Ca". Calcium. And that would have finished the name. The question is not whether we take one or two letters. We need to try both. If we commit too early and never go back, we can miss a valid solution.

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Some names do not branch much. Sophia There is only one valid path. "Coco" is different. At every step, there are two valid choices. Co. Or C and O. This creates a very wide tree. So why is a very long repetition of "Coco" still fast?

The algorithm explores one branch at a time. As soon as it finds a valid one, it stops. In this case, the first branch succeeds. But when we add an "A" at the end, none of them works. Now it has to explore the entire tree. That's why it explodes.

If instead we end with "Ca", a valid path appears again. The algorithm stops early. It's not about how many branches exist. It's about how many we must explore before we can stop.

At first glance, this looks unavoidable. If the tree grows wide, we must explore all possibilities. But not necessarily. If we look closely, many branches are actually the same. We are solving the same subproblems again and again. We can be smarter.

We can save the result for each remaining name. If we reach the same position again, we reuse the result. This technique is called memoization. With memoization, each position is solved only once. The algorithm becomes much faster. Even for names with many possibilities.

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