← Eightfoldai Interview Insights
I knew the stack-based approach going in but fumbled explaining why it works.
Use a stack to track indices of unmatched opening parentheses, and a set to mark indices of parentheses to remove. After one pass, remove all marked characters to produce a valid string.
Pro tip: Clarify that multiple valid answers exist and that your solution returns any one; mention that the algorithm runs in O(n) time and O(n) space, which is optimal.
Restate the problem: remove the minimum number of parentheses to make the string valid. Confirm that only parentheses matter and that any valid result is acceptable.
Use a stack to store indices of unmatched opening parentheses and a set to record indices of parentheses to remove.
Iterate through the string: push index for '(', pop for ')' if stack is non-empty, otherwise mark that ')' index for removal.
After the pass, all indices remaining in the stack are unmatched '('; add them to the removal set.
Construct the result string by including only characters whose indices are not in the removal set. Return the result.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Much easier once the main solution is done, basically just return the sum of unmatched opens and closes.
Acknowledge the change in requirements and explain that the core algorithm remains the same, but the return value changes from the modified string to an integer count. Modify the existing solution to track the number of removals instead of building the result string, ensuring the count is accurate and the solution remains efficient.
Pro tip: Show that you understand the trade-offs: returning a count instead of the string can save memory and time, but you must ensure the count is computed correctly without unnecessary string operations. Also, mention that this change might allow for further optimizations, such as early termination or using a counter instead of a stack.
Confirm that the interviewer wants only the minimum number of removals, not the resulting string. Ask if the count should be the total removals or the minimum removals to make the string valid.
Recall the approach used to find the minimum removals, such as using a stack to track unmatched parentheses. Identify where the count can be incremented instead of modifying the string.
Replace string manipulation with a counter variable. For example, in the stack approach, increment a counter for each unmatched closing parenthesis and add the stack size at the end for unmatched opening parentheses.
State that the time complexity remains O(n) and space complexity can be reduced to O(1) if using a counter instead of a stack, or O(n) if a stack is still used.
Walk through a few examples to verify the count, such as '()())' where removals = 1, and ')((' where removals = 3.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the problem context: typically, we want the lexicographically smallest sequence after removing the minimum number of elements to make it valid (e.g., non-decreasing). Then, explain that we can modify the standard dynamic programming approach to track the lexicographically smallest result among those with minimum removals, or use a greedy algorithm with a stack that prioritizes smaller characters while maintaining the minimum removal count.
Pro tip: Mention that lexicographic order is determined by the first differing character, so we should prioritize making earlier characters as small as possible, even if it means later characters are larger. Also, note that if the problem allows multiple valid answers, we need to define a tie-breaking rule, and lexicographically smallest is a common choice.
Confirm what 'minimum removals' means and what makes a sequence valid (e.g., non-decreasing). Ask if the input can contain duplicates and what the expected output format is (string, array, etc.).
For example, for making a sequence non-decreasing, the minimum removals equals the length minus the longest non-decreasing subsequence (LNDS). Alternatively, a greedy stack approach can compute the minimum removals directly.
If using DP, store not just the length but also the lexicographically smallest subsequence for each state. If using a greedy stack, when a removal is possible, prefer removing a larger previous character to allow a smaller current character to take its place, ensuring lexicographic minimality.
Explain why the adapted algorithm yields the lexicographically smallest among all optimal solutions. Discuss how to compare sequences efficiently (e.g., using string comparison or custom comparators).
State the time and space complexity of your approach. Mention if there's a trade-off between simplicity and optimality, and whether a simpler approach (like generating all optimal solutions and picking the smallest) is feasible.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I was using a stack and a separate boolean array to mark deletions.
Acknowledge the current space complexity, then propose a concrete optimization such as in-place modification, two-pointer technique, or using a fixed-size array. Explain the trade-offs (e.g., time vs. space) and confirm the new complexity.
Pro tip: Always clarify the constraints and whether input modification is allowed; this shows you consider practical implications and can lead to a more suitable solution.
Briefly summarize the problem and your initial approach, highlighting the space complexity and why it uses extra space.
Analyze if the extra space can be eliminated by reusing input, using pointers, or leveraging properties of the data.
Describe a specific technique (e.g., in-place reversal, two-pointer, bit manipulation) that reduces space, and outline the steps.
Discuss the impact on time complexity, code readability, and any assumptions (e.g., mutable input).
State the new space complexity (e.g., O(1)) and verify it handles edge cases correctly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.