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Classic DP, I knew it the second they described it.
Recognize this as the classic House Robber dynamic programming problem. Explain that you can solve it in O(n) time and O(1) space by keeping track of the maximum loot up to the previous two houses. Walk through the recurrence relation and provide a clear example to illustrate.
Pro tip: Mention that this problem tests your ability to identify optimal substructure and overlapping subproblems, which are core to DP and also relevant to ML (e.g., sequence modeling). Also, discuss edge cases like empty input or single house to show thoroughness.
Confirm that houses are in a line, each has a non-negative amount, and you cannot rob adjacent houses. Ask if the input can be empty or contain one house.
Let dp[i] be the maximum amount you can rob from the first i houses. The recurrence is dp[i] = max(dp[i-1], dp[i-2] + nums[i]).
Since dp[i] only depends on the previous two values, use two variables to achieve O(1) space instead of an array.
Use a small example like [2,7,9,3,1] to demonstrate how the recurrence works and verify the result (12).
State time complexity O(n) and space O(1). Handle edge cases: empty array returns 0, single house returns its value.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.