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Model the problem as a directed graph where each character is a node and edges represent the relative order derived from adjacent word comparisons. Then perform a topological sort to determine a valid character ordering, detecting cycles to handle invalid inputs.
Pro tip: Clarify edge cases upfront, such as duplicate words, empty strings, and cycles, and discuss how you would handle them. Mention that the solution is essentially topological sorting and that you would use Kahn's algorithm or DFS, showing awareness of time and space complexity.
Confirm assumptions: dictionary is sorted, words are non-empty, and characters are from a finite alphabet. Discuss handling of invalid inputs like cycles or duplicate words.
Iterate through adjacent word pairs, find the first differing character, and add a directed edge from the first to the second. Track all unique characters as nodes.
Perform topological sorting using DFS or BFS (Kahn's algorithm) to produce a linear ordering of characters. Detect cycles to determine if a valid ordering exists.
Address cases like a cycle (return empty string), a prefix word appearing after a longer word (invalid), and multiple valid orderings (return any).
State time complexity O(C + N) where C is total characters and N is number of unique characters, and space complexity O(N + E) for the graph.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use a divide-and-conquer strategy: split the string at characters that appear fewer than k times, then recursively find the longest valid substring in each part. Alternatively, use a sliding window with a fixed number of distinct characters, iterating over all possible distinct counts from 1 to 26.
Pro tip: Discuss the trade-offs between the divide-and-conquer and sliding window approaches, and mention that the sliding window approach can be optimized to O(26*n) time, which is effectively O(n).
Confirm that the substring must be contiguous and that every character in the substring must appear at least k times. Ask about constraints on string length and character set.
Mention that checking all substrings would be O(n^2) or O(n^3) and is inefficient for large inputs.
Explain that if a character appears fewer than k times in the whole string, it cannot be part of any valid substring, so split at that character and recurse on the parts.
For each possible number of distinct characters (1 to 26), use a sliding window to find the longest substring with exactly that many distinct characters where each appears at least k times.
Compare time and space complexity: divide-and-conquer is O(n * 26) in worst case but can be O(n log n) on average; sliding window is O(26 * n) = O(n). Discuss which is more suitable based on constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.