The prefix sum approach came to me pretty fast, binary search on top of that for the sampling step.
Start by clarifying the requirements and constraints, then propose a solution using prefix sums and binary search for O(log n) time per pick with O(n) extra space. For the follow-up, explain how to mutate the input array in-place to achieve O(1) extra space, likely using a linear scan with cumulative weights and a random target.
Pro tip: Discuss the trade-offs between time and space, and mention that mutating the input is acceptable only if the problem allows it; otherwise, a copy is needed. Also, consider edge cases like zero weights or empty lists.
Ask about input size, frequency of picks, whether the input can be mutated, and if weights can be zero. This shows attention to detail and helps tailor the solution.
Describe using prefix sums of weights and binary search to pick an index in O(log n) time. Explain how to generate a random number between 0 and total weight, then find the first prefix sum greater than that number.
Explain that by mutating the input array, you can compute cumulative sums in-place and then perform a linear scan to find the index, achieving O(n) time per pick but O(1) extra space. Alternatively, discuss other in-place techniques if applicable.
Compare time and space complexities of both approaches. Mention handling of zero weights, empty input, and the impact of mutating the input on the caller.
Reiterate the chosen solution based on constraints, and offer to code or discuss further optimizations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The O(1) space constraint is the whole point here.
Clarify that the expression is a valid string with no parentheses and integer division truncates toward zero. Then propose a single-pass left-to-right algorithm that maintains a running result and a current term, applying multiplication/division immediately and deferring addition/subtraction. Emphasize O(1) space by using only a few integer variables and no stack.
Pro tip: Explicitly discuss how you handle integer division truncation (e.g., in C++/Java, -3/2 = -1) and mention that you avoid overflow by using appropriate data types or by checking constraints. This shows attention to edge cases and language-specific behavior.
Confirm that the expression contains only non-negative integers, operators +, -, *, /, no parentheses, and that division is integer division truncating toward zero. Ask about input size and overflow concerns.
Maintain a running total and a current term. Parse numbers and operators left-to-right; for * and /, update the current term immediately; for + and -, add the current term to the total and start a new term with the appropriate sign.
Ensure division truncates toward zero as specified. Consider negative numbers, leading/trailing spaces, and potential overflow. Use long long if needed.
State that the algorithm runs in O(n) time and O(1) extra space, as it uses only a few variables. Contrast with a stack-based approach that would use O(n) space.
Walk through a few examples like '3+2*2' and ' 3/2 ' to verify correctness, especially operator precedence and division behavior.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use binary search twice: once to find the leftmost occurrence (by continuing search on the left half when target is found) and once to find the rightmost occurrence (by continuing on the right half). This achieves O(log n) time and O(1) space. Alternatively, a single binary search can find any occurrence, then expand linearly, but that risks O(n) worst-case.
Pro tip: Clarify edge cases upfront (empty array, target absent, all elements equal) and mention that you'd use two separate binary searches to guarantee O(log n) even when the array has many duplicates. Also, discuss how to avoid infinite loops by carefully updating boundaries.
Confirm the array is sorted, may contain duplicates, and that O(log n) is required. Ask about empty input, target not present, and whether the array can be modified.
Outline a helper function for binary search that finds the first or last occurrence by adjusting the search space based on whether we want leftmost or rightmost.
Perform binary search; when target is found, record the index and continue searching in the left half to find an earlier occurrence.
Similarly, when target is found, record the index and continue searching in the right half to find a later occurrence.
If either search fails to find the target, return [-1, -1]. Otherwise, return the two indices.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem and edge cases, then propose an O(n) solution using a stack or dynamic programming. Explain the algorithm step-by-step, analyze time and space complexity, and optionally discuss alternative approaches like two-pass scanning.
Pro tip: Mention that you can solve it in O(1) space with two passes, but the stack approach is simpler to implement and explain. This shows you understand trade-offs and can adapt to constraints.
Confirm that the substring must be contiguous and well-formed, and discuss edge cases like empty string or no valid substring.
Select a method such as stack-based, dynamic programming, or two-pass scanning. Briefly justify your choice based on simplicity and efficiency.
Explain the chosen algorithm in detail, using a small example to illustrate how it works step by step.
State the time and space complexity of your solution, and compare with alternatives if relevant.
Discuss how your solution handles edge cases and mentally test with examples like '(()' or ')()())'.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the problem and constraints, then propose a two-pointer approach using two dummy lists to partition nodes while preserving relative order. Walk through an example, analyze time and space complexity, and discuss edge cases and potential optimizations.
Pro tip: Emphasize that this is a stable partition, and mention that using dummy nodes simplifies edge cases. Also, note that the solution can be done in-place with O(1) extra space by rearranging pointers.
Ask if the partition should be stable (maintain relative order) and if we can modify the list in-place. Confirm that all nodes less than x come before nodes >= x.
Suggest using two dummy nodes to build two separate lists: one for nodes < x and one for nodes >= x. Then concatenate them.
Choose a sample list (e.g., 3->5->8->5->10->2->1 with x=5) and show step-by-step how nodes are distributed and linked.
State that time complexity is O(n) since we traverse the list once, and space complexity is O(1) extra space (excluding the output list) because we only use pointers.
Mention edge cases: empty list, all nodes < x, all nodes >= x, x not present. Also note that the solution is stable and can be done in-place.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Expand-around-center is my go-to for palindrome problems.
Start by clarifying the problem: count all palindromic substrings, including duplicates at different positions. Then present an efficient solution, such as expanding around each center (O(n^2) time, O(1) space), and discuss trade-offs with other approaches like DP or Manacher's algorithm.
Pro tip: Mention that you would first confirm whether the count includes single-character palindromes and overlapping substrings, as this affects the implementation. Also, briefly note that Manacher's algorithm can solve it in O(n) if optimal performance is required, showing depth beyond the typical O(n^2) solution.
Ask if single characters count and if substrings are counted by occurrence (including duplicates). Confirm input constraints (e.g., length, character set) to guide algorithm choice.
Mention that checking all O(n^2) substrings and verifying each palindrome takes O(n^3) time, which is inefficient. This sets the stage for optimization.
Explain that every palindrome has a center (a character or between two characters). Expand around each of the 2n-1 centers to count all palindromes in O(n^2) time and O(1) space.
If asked for optimal time, describe Manacher's algorithm which finds all palindromic substrings in O(n) time, though it's more complex to implement.
State time and space complexity clearly. Discuss edge cases: empty string, single character, all same characters, and strings with no palindromes longer than 1.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.