My first instinct was to just slide a window and check prefix matches, which works fine.
Clarify the problem constraints and edge cases, then propose an efficient algorithm. A good approach is to use a string matching algorithm like KMP to find all occurrences of the target in the original string, and for each occurrence at index i, the number of substrings starting at i is (n - i), where n is the length of the original string. Sum these counts to get the total.
Pro tip: Mention the trade-offs between different approaches (e.g., naive O(n*m) vs. KMP O(n+m)) and discuss how to handle overlapping occurrences. Also, consider if the target is empty or longer than the original string.
Ask clarifying questions: Are we counting distinct substrings or all substrings (including duplicates)? Should we consider overlapping occurrences? What are the constraints on string lengths and character set?
Explain a simple solution: iterate over each starting index i, check if the substring from i of length equal to target matches the target. If yes, increment count by (n - i). This is O(n*m) time.
Propose using an efficient string matching algorithm like KMP or Rabin-Karp to find all occurrences of the target in O(n+m) time. For each match at index i, add (n - i) to the count.
Consider cases: target is empty (then every substring has empty prefix, so count = n*(n+1)/2), target longer than original (count = 0), and overlapping matches (handled naturally by the algorithm).
State time and space complexity: O(n+m) time, O(m) space for KMP. Walk through a small example to verify correctness, e.g., original='aaaa', target='aa' -> matches at indices 0,1,2 -> counts: 4,3,2 -> total 9.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This tripped me up more than it should have.
Clarify the problem: given a string S and a target string T, find the minimum length substring of S that contains all characters of T (considering duplicates). Use a sliding window with two pointers and a frequency map to track character counts, expanding the right pointer until all characters are matched, then shrinking the left pointer to find the minimal window.
Pro tip: After presenting the optimal solution, mention that if the target has many distinct characters, you can optimize the 'formed' check by tracking a counter of satisfied unique characters instead of comparing full frequency maps each time.
Confirm whether the substring must contain the target as a subsequence or with exact character counts, and handle cases like empty target, target longer than source, or no valid window.
Explain that a brute-force check of all substrings is O(n^2 * m), so a sliding window with two pointers achieves O(n) time by maintaining a window that satisfies the target's character counts.
Use a frequency map for the target and a window frequency map, plus a 'formed' counter to track how many unique characters have met the required count. Maintain the invariant that the window is the smallest valid window ending at the right pointer.
Expand right pointer, update window counts and formed counter. When formed equals required unique characters, shrink left pointer while the window remains valid, updating the minimum length and start index.
State time complexity O(n + m) and space O(k) where k is unique characters in target. Walk through a small example to verify correctness, and discuss potential optimizations like early termination if minimum length equals target length.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.