Palindromic Substrings
Count all palindromic substrings, including duplicates by position.
Why does this pattern fit?
Restate the exact job
Count all palindromic substrings, including duplicates by position.
Each successful center expansion corresponds to one distinct substring occurrence.
O(n²) time · O(1) space
Counting only maximal palindromes misses their palindromic interiors.
How to solve Palindromic Substrings
The goal is to solve this problem from the pattern, not to memorize a finished answer. Use this as a check after your own attempt.
What the question asks
Count all palindromic substrings, including duplicates by position.
Why Dynamic programming fits
Each successful center expansion corresponds to one distinct substring occurrence.
State to maintain
A count and expansion pointers for odd/even centers.
Transition
Expand each center and increment on every matching boundary pair.
Time and space
O(n²) time · O(1) space
Counterexample to the tempting mistake
Counting only maximal palindromes misses their palindromic interiors.
Prove it again tomorrow
Close this page. Rebuild the state and transition from memory, write a test that exposes the mistake above, then solve a fresh input without looking back. A same-day reread is practice, not proof of retention.