Got through the basic solution fine, the recurrence isn't hard once you see it.
Start by clarifying the problem and edge cases, then explain the dynamic programming recurrence: at each house, the maximum loot is the max of skipping it (previous max) or robbing it (current value + max from two houses back). Optimize space by keeping only two variables instead of a full DP array, and walk through a small example to verify correctness.
Pro tip: Emphasize the space optimization from O(n) to O(1) by noting that only the last two states are needed, and mention that this pattern generalizes to similar problems like 'House Robber II' (circular street) or 'House Robber III' (tree structure).
Restate the problem in your own words, confirm that houses are in a line, values are non-negative, and ask about edge cases like empty array or single house.
Let dp[i] be the max loot from first i houses. Then dp[i] = max(dp[i-1], nums[i-1] + dp[i-2]), with base cases dp[0]=0, dp[1]=nums[0].
Observe that dp[i] depends only on dp[i-1] and dp[i-2], so replace the array with two variables (prev2 and prev1) and update iteratively.
Trace the algorithm on a small input like [2,7,9,3,1] to demonstrate correctness and show how the variables update.
State that time is O(n) and space is O(1). Briefly mention extensions like circular arrangement (House Robber II) or tree structure (House Robber III).
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State the time and space complexity of your solution clearly, using Big-O notation, and explain how you derived them from your code. Relate the complexities to the input size and any auxiliary data structures used, and briefly discuss trade-offs if applicable.
Pro tip: Always mention the worst-case complexity and clarify if average-case differs; also, if you optimized space at the cost of time or vice versa, explain your reasoning—this shows you consider practical constraints.
Define what N represents (e.g., number of elements, length of string) and any other relevant variables like M for a second input.
Break down your algorithm into loops, recursion, or operations, and count how many times each executes relative to N. Express the total as a Big-O term, ignoring constants and lower-order terms.
Consider all memory used: input storage (if modified), auxiliary data structures (arrays, hash maps, recursion stack), and output. Sum them and express as Big-O, again ignoring constants.
Briefly justify why the complexities are what they are, and if you made any trade-offs (e.g., using extra space to reduce time), mention them.
Conclude with a concise statement: 'The time complexity is O(...) and space complexity is O(...).'
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This is basically built into the O(1) solution already if you do it right from the start, so I had to reframe my answer a bit since I'd already done it.
Start by restating the current space complexity and the constraints, then propose a concrete optimization (e.g., in-place modification, bit manipulation, or streaming). Walk through the trade-offs (time, readability, correctness) and justify why the space savings are worth it in the context of Google-scale systems.
Pro tip: Quantify the impact: e.g., 'This reduces memory from O(n) to O(1), saving X GB for n=1B, which matters for latency and cost.' Also, mention that you'd validate with edge cases and profiling.
State the current space complexity and identify what consumes memory (e.g., auxiliary data structures, recursion stack).
Suggest a specific technique to reduce space, such as in-place algorithms, bit vectors, or reusing input.
Discuss the impact on time complexity, code complexity, and maintainability. Compare alternatives.
Explain why the optimization matters for the given constraints (e.g., large data, memory limits, cost).
Mention how you'd ensure correctness (edge cases, unit tests) and measure the actual improvement.
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This one caught me more than I'd like to admit.
Modify the dynamic programming solution to store both the maximum robbed value and the decision (rob or skip) at each house. Then backtrack from the end to reconstruct one optimal set of indices. Alternatively, maintain a parent pointer or store the chosen indices directly in the DP state.
Pro tip: Emphasize that while multiple optimal plans may exist, returning any one is sufficient; this simplifies reconstruction. Also, mention that the DP can be optimized to O(1) space for the value, but reconstruction requires O(n) space to store decisions.
Define dp[i] as the maximum value robbable from houses 0..i. Additionally, maintain a decision array (e.g., choice[i]) indicating whether house i was robbed in the optimal solution for the prefix up to i.
Iterate through houses, computing dp[i] = max(dp[i-1], dp[i-2] + nums[i]). Record which option was chosen: if dp[i-1] > dp[i-2] + nums[i], then house i is not robbed; otherwise, it is robbed.
Starting from i = n-1, if choice[i] indicates house i was robbed, add i to the result list and move to i-2; otherwise, move to i-1. Continue until i < 0.
Ensure the reconstruction handles cases where n=0 or n=1 correctly. Return the list of indices (order does not matter, but typically ascending or descending is fine).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.