I went straight to coding without asking whether skipping costs a turn or not, and that bit me.
Clarify the problem constraints and define the state as the maximum profit achievable from each index. Use dynamic programming with memoization or bottom-up, computing dp[i] = max(profit[i] + dp[i + jump_length[i] + 1], dp[i+1]) with careful handling of out-of-bounds. Discuss time and space complexity, and consider optimizations like iterative DP or greedy if applicable.
Pro tip: Start by walking through a small example to confirm understanding and edge cases (e.g., jumps that overshoot the array). Then, explicitly state the recurrence relation before coding, and mention that you'd test with negative profits and varying jump lengths.
Ask about constraints: array size, profit values (can be negative?), jump lengths (can be zero?), and whether you must start at index 0. Confirm that you can choose to take or skip each index, and that taking an index forces a jump.
Let dp[i] be the maximum profit from index i to the end. Then dp[i] = max(dp[i+1] (skip), profit[i] + dp[i + jump_length[i] + 1] (take, if within bounds)). Base case: dp[n] = 0.
Decide between top-down memoization (recursive) or bottom-up iteration. For bottom-up, iterate from the end to the start. Mention that top-down is easier to reason about but may have recursion overhead.
Time complexity is O(n) since each index is computed once. Space complexity is O(n) for the DP array, but can be optimized to O(1) if we only need the next few values? Actually, due to jumps, we might need to store all, but discuss.
Walk through examples: empty array, single element, jumps that overshoot, negative profits, and large jumps. Verify that the recurrence handles out-of-bounds correctly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.