Palindromic Substrings
The problem
Count all nonempty contiguous palindromic substrings. Substrings at different positions count separately even when their text is identical.
Example
"aaa" → 6: three length-1, two length-2, and one length-3 substring
Need a hint?
Every successful center expansion discovers one palindrome.
Write pseudocode, trace the example, or note an edge case. This scratchpad does not run code.
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Read the solution approach
Try every character as an odd center and every neighboring gap as an even center. While the endpoints match, increment the count and expand both ways. Each substring has one unique center, so nothing is counted twice.
Complexity
O(n²) time and O(1) space.
Before moving on, explain why the algorithm is correct and trace a boundary case without looking at the approach.