My first instinct was brute force: enumerate all substrings, count character frequencies, check if at most one character has an odd count.
Clarify the problem: for each string, count substrings whose characters can be rearranged into a palindrome. A substring can form a palindrome if at most one character has an odd frequency. Use a bitmask to represent parity of character counts and count pairs of equal masks (or masks differing by one bit) for each string.
Pro tip: Mention that the bitmask approach works because the alphabet is small (e.g., 26 lowercase letters), and precomputing prefix masks allows O(n) per string. Also, discuss handling uppercase or other characters if the problem allows.
Confirm the definition: substrings that can be rearranged into a palindrome. Ask about character set (e.g., lowercase English letters) and input size to determine optimal approach.
A string can be rearranged into a palindrome if at most one character has an odd count. For a substring, this means the parity mask (bitmask of odd counts) has at most one bit set.
Compute prefix parity masks for each position. The parity of a substring from i to j is the XOR of prefix masks at i-1 and j. Count pairs of prefix masks that are equal or differ by exactly one bit.
For each string, iterate through prefix masks, maintaining a frequency map of masks seen so far. For each current mask, add frequencies of the same mask and masks with one bit flipped (for each character).
Time complexity: O(n * alphabet size) per string, which is O(26n) for lowercase. Space: O(2^alphabet) for the frequency map, but only O(n) distinct masks. Handle empty strings and single-character substrings.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.