Start by clarifying the problem and edge cases, then explain the dynamic programming recurrence where dp[i] = max(dp[i-1], dp[i-2] + arr[i]). Optimize space to O(1) by keeping only the last two DP values, and analyze time and space complexity.
Pro tip: Mention that this is the 'House Robber' problem and that the same DP pattern extends to circular arrays or trees, showing you recognize common patterns and can adapt them.
Confirm that the subset can be empty, elements are non-negative, and 'adjacent' means consecutive indices. Ask about input size and whether the array can be modified.
Let dp[i] be the maximum sum using the first i elements. Derive the recurrence: dp[i] = max(dp[i-1], dp[i-2] + arr[i]).
Set dp[0] = 0 and dp[1] = arr[0] (or handle empty array). Explain why these are correct.
Observe that only the last two DP values are needed, so use two variables prev2 and prev1 to achieve O(1) space.
State O(n) time and O(1) space. Walk through a small example (e.g., [2,7,9,3,1]) to verify correctness and edge cases.
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