I started with brute force and the interviewer let me finish before asking if I could do better.
Break down the condition: product even means at least one element is even; difference odd means i and j have opposite parity. Count pairs by categorizing indices by parity and value parity, then use combinatorial formulas to count valid pairs without iterating over all pairs.
Pro tip: Emphasize that the formula is O(n) and explain how you derived it, showing systematic problem-solving. Also, mention that you can extend the approach to similar constraints.
Product even means not both odd. Difference odd means indices have opposite parity (one even, one odd).
Split indices into even and odd positions. For each group, count how many elements are even and odd.
For each pair of opposite index parities, count combinations where at least one element is even. Use total pairs minus pairs where both are odd.
Let E_even, O_even be counts of even/odd values at even indices; E_odd, O_odd at odd indices. Valid pairs = (E_even+O_even)*(E_odd+O_odd) - O_even*O_odd.
Test with small arrays to ensure formula matches brute force. Discuss time complexity O(n) and space O(1).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Four counters: even-indexed positions, odd-indexed positions, odd values at even indices, odd values at odd indices.
First, clarify the problem and identify the state variables needed to capture all necessary information as you traverse the data once. Then, derive the update rules for these variables and express the final answer as a function of them, ensuring the formula is correct and efficient.
Pro tip: Always define your variables with clear, descriptive names and explain why each is necessary; this shows you understand the problem deeply and can communicate complex ideas simply.
Restate the problem in your own words and confirm any assumptions or constraints with the interviewer. This ensures you're solving the right problem and sets a collaborative tone.
Determine what information must be remembered at each step to compute the final result without revisiting past data. List the variables and their meanings.
Specify how each variable changes as you process each element. Ensure the updates are correct and maintain the invariant that the variables capture the required state.
Express the answer in terms of the tracked variables after the single pass. Verify the formula with a simple example or edge case.
State the time and space complexity of your approach, emphasizing the single pass and constant extra space if applicable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
O(n) time, O(1) space, said it fast and moved on.
First, restate the problem and clarify assumptions (e.g., input size, data types, constraints). Then, walk through your solution step-by-step, deriving time and space complexity for each part and the overall algorithm. Finally, systematically enumerate edge cases, explaining why each is important and how you would test it.
Pro tip: Always relate complexity to the specific operations in your code (e.g., 'This loop runs n times, and inside we do a hash lookup which is O(1) average') and mention trade-offs (e.g., using extra space to reduce time). For edge cases, prioritize those that could cause crashes or incorrect results, and mention how you'd test them (unit tests, boundary values).
Ask clarifying questions to understand input constraints, expected output, and any special conditions. This ensures your complexity analysis and edge cases are relevant.
Walk through your algorithm, identifying the time and space complexity of each step. Sum them up, ignoring lower-order terms, and state the overall Big-O.
Differentiate between auxiliary space and total space, and mention if your algorithm is in-place or uses extra data structures. Consider recursion stack space if applicable.
List edge cases such as empty input, single element, large input, duplicates, negative numbers, overflow, and invalid inputs. Explain how each could affect your solution.
Describe how you would test these edge cases (e.g., unit tests, boundary values, stress testing) and what expected outcomes are.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the original problem and the parity constraints involved. Then, systematically analyze how flipping each parity condition affects the algorithm's logic, data structures, and edge cases, and discuss the trade-offs of any necessary modifications.
Pro tip: Demonstrate that you understand the underlying invariant: parity constraints often determine whether you can use two pointers, sliding window, or prefix sums. Mention that flipping parity may require rehashing or reindexing, and always test with small examples to validate the new approach.
Briefly explain the original problem and the role of the parity constraints (product even, j-i odd). This ensures you and the interviewer are aligned.
Analyze separately how changing the product parity and changing the index difference parity affect the solution. Consider how each constraint influences the choice of algorithm and data structures.
For each change, outline a revised algorithm. For example, if product must be odd, all elements must be odd; if j-i must be even, indices must have the same parity. Discuss how to adapt two-pointer, sliding window, or prefix sum techniques accordingly.
Discuss time and space complexity changes, and any new edge cases (e.g., empty arrays, all even/odd elements). Highlight which approach is more efficient and why.
Concisely summarize the key differences and reaffirm your systematic reasoning. Mention that you would validate with test cases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the problem and constraints: what operation is required (e.g., find median, detect duplicates, compute running statistics)? Then, explain how streaming changes the solution: you cannot index into the past, so you must maintain state incrementally, often using data structures like heaps, hash maps, or balanced trees. Finally, discuss trade-offs between time, space, and accuracy (if approximate methods are acceptable).
Pro tip: Emphasize that streaming problems often require online algorithms and that you should proactively discuss memory constraints and potential need for approximation, showing you think beyond the basic algorithm.
Ask what operation is needed on the stream (e.g., find median, detect cycle, compute frequency) and what are the constraints on memory, latency, and accuracy.
Explain why the original approach fails: no random access, cannot store all elements, and must process each element in order with limited state.
Propose a data structure that supports incremental updates, such as two heaps for median, a hash map with counters for frequency, or a balanced BST for order statistics.
Discuss time per element, total time, space usage, and whether the solution is exact or approximate. Mention if approximation (e.g., reservoir sampling, count-min sketch) is acceptable.
Address handling of out-of-order indices (if allowed), late data, and how to adapt if the stream is infinite or if indices are not strictly increasing.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.