LeetCode 516 Longest Palindromic Subsequence - Key Observation

Focus on the endpoints of your current range $[i, j]$. If $s[i] = s[j]$: both characters can be endpoints of a palindrome. The remaining problem is finding the LPS in $s[i+1..j-1]$, then adding $2$ for these matching endpoints.

If $s[i] \neq s[j]$: at least one endpoint must be excluded. Either skip $s[i]$ (solve $s[i+1..j]$) or skip $s[j]$ (solve $s[i..j-1]$). Take the maximum. This gives us a clean two-case recurrence with no need to try all split points.