Palindrome Number: The Mirror Boutique

Steve's Approach (The Junior Way)

Steve says, "Easy. I'll take every tile out of the crate, one by one. I'll photocopy each one. I'll lay the photocopies out in reverse order on the floor. Then I'll walk down both rows and compare them."

The problem?

• Steve needs a massive floor.
• He needs a lot of paper for photocopies.
• If the crate has a million tiles, Steve needs space for a million photocopies.

This is what happens when you convert an integer to a String. You are "photocopying" the data into a new format, and it takes up a lot of "floor space" (Memory/RAM).

Mathilda's Approach (The Senior Way)

Mathilda says, "I don't need any paper. And I don't need to empty the crate."

1. She looks at the very last tile in the crate. She writes that number on a tiny sticky note.
2. Then she looks at the second-to-last tile. She does a little math in her head to combine it with the first one.
3. She keeps doing this until she has processed exactly half of the crate.
4. Then she compares her small sticky note to what's left in the original crate.
5. If they match, it's a palindrome.

Mathilda used almost zero extra space. She didn't need a huge floor. She didn't need a photocopy machine. She just used her brain (The CPU) and one tiny note (A Variable).