Started with the obvious O(n^3) brute force and they let me run with it for maybe 90 seconds before asking if I could do better.
Start by clarifying the problem and discussing a brute-force O(n^3) or O(n^2) approach to establish correctness. Then, derive an efficient O(n) or O(n log n) solution by counting each character's contribution to substrings where it appears exactly once, using techniques like last occurrence tracking and combinatorial counting. Finally, analyze time and space complexity and test with edge cases.
Pro tip: Demonstrate strong problem-solving by first explaining the brute-force method, then systematically optimizing it. This shows you can think through trade-offs and communicate clearly, which is highly valued at Meta.
Restate the problem in your own words and confirm assumptions: input string, character set, and expected output. Discuss edge cases like empty string or repeated characters.
Propose a straightforward solution: iterate over all substrings, count characters with frequency 1, and sum. Analyze its O(n^3) or O(n^2) time complexity to establish a baseline.
Shift perspective: instead of iterating substrings, count for each character the number of substrings where it appears exactly once. Use last and second-last occurrence positions to compute valid left and right boundaries.
For each character at index i, let prev1 be the previous occurrence and prev2 the one before that. Then the number of substrings where this character is unique is (i - prev1) * (next1 - i) minus contributions where it appears with another occurrence? Actually, the standard formula is (i - prev1) * (next1 - i) - (i - prev1) * (next1 - prev2)? Need to be precise: The number of substrings where s[i] appears exactly once is (i - prev1) * (next1 - i) - (i - prev1) * (next1 - next2)? Wait, the correct formula is: For each occurrence at i, let L1 = prev occurrence, L2 = prev of L1, R1 = next occurrence, R2 = next of R1. Then substrings where s[i] is unique are those that include i but no other occurrence of s[i]. The left boundary can be from L1+1 to i, and right boundary from i to R1-1. So count = (i - L1) * (R1 - i). However, this counts substrings where s[i] is the only occurrence? Actually, if there is another occurrence within the substring, it would be counted multiple times? No, because we are counting for each character occurrence, but we want substrings where the character appears exactly once. So for a given character, a substring has exactly one occurrence if it includes exactly one occurrence of that character. So for each occurrence i, the substrings where this occurrence is the only one are those that start after the previous occurrence (L1) and end before the next occurrence (R1). So count = (i - L1) * (R1 - i). Summing over all occurrences gives the total number of substrings where the character appears exactly once. But wait, that counts substrings where the character appears exactly once, but we need to sum over all characters the count of characters that appear exactly once in the substring. That is different: For a given substring, we count how many characters have frequency exactly 1. So the total sum is sum over substrings of (number of characters with frequency 1). This is equivalent to sum over characters of (number of substrings where that character appears exactly once). So indeed, we can sum over characters the number of substrings where that character appears exactly once. And for a fixed character, the number of substrings where it appears exactly once is sum over its occurrences of (i - L1) * (R1 - i). So the algorithm is: For each character, find all its occurrences, and for each occurrence, compute (i - prev) * (next - i) where prev is previous occurrence (or -1) and next is next occurrence (or n). Sum these over all occurrences and all characters. This is O(n) time and O(n) space if we precompute next and prev for each index. So the efficient solution is O(n).
State time and space complexity (O(n) time, O(n) space). Walk through a small example to verify correctness, and discuss potential pitfalls like integer overflow or handling of Unicode characters.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
They asked this almost as a follow-up cooldown question.
First, clarify that the character-contribution approach (e.g., counting contributions per character) is a generalization of the sliding window technique used in the classic 'longest substring with all unique characters' problem. Then, systematically enumerate edge cases such as empty strings, repeated characters, and non-ASCII input, and discuss correctness concerns like off-by-one errors and handling of invalid inputs. Finally, relate it back to the classic problem by showing how the same sliding window logic applies, but with additional constraints or modifications.
Pro tip: Demonstrate awareness of production concerns by mentioning that while the character-contribution approach is elegant, it may not scale well for very large alphabets or streaming data, and suggest alternative data structures like bitmasks for ASCII or hash maps for Unicode.
Clearly state what the character-contribution approach entails and how it extends the sliding window technique from the classic problem. Mention that it involves tracking the contribution of each character to the current window's validity.
List edge cases such as empty string, single character, all identical characters, all unique characters, strings with spaces or special characters, and Unicode characters. Also consider cases where the window size is zero or larger than the string length.
Address potential pitfalls: off-by-one errors in window boundaries, incorrect handling of character counts when shrinking the window, and ensuring that the window always contains unique characters. Mention the importance of invariants and loop termination.
Explain how the classic 'longest substring with all unique characters' problem is a special case where the contribution of each character is simply its presence. Show how the same sliding window framework applies, but with different contribution rules.
Discuss time and space complexity, and trade-offs between using a fixed-size array (for ASCII) versus a hash map (for Unicode). Mention optimizations like using a bitmask for ASCII or early termination.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.