Longest Palindromic Substring
Signals to notice
Brute force first
Check every substring for palindrome. Each substring is independently verified. It is a fair place to begin because it matches the surface of the question, yet it does not capture the deeper structure that makes the problem simpler.
The key insight
Expand around center: for each position, expand outward while characters match. Try both odd-length (single center) and even-length (double center). Track the longest. Instead of recomputing the world every time, you preserve just enough context to let the next decision become obvious.
What must stay true
Every palindrome has a center (single character for odd length, pair for even). Expanding from the center outward checks the palindrome condition naturally — stop when characters don't match. When you keep that truth intact, each local choice supports the larger solution instead of fighting it.
Easy way to go wrong
Only checking odd-length palindromes — 'abba' is even-length and has no single center. You must try both odd and even centers at each position. When the code becomes mechanical before the idea is clear, small edge cases start breaking the whole story.