Spent a bit too long trying to think of a greedy approach before accepting it's just DP.
Define a DP state where dp[i] represents the maximum profit starting from index i. For each index, consider the two choices: take the value and jump to i + value + 1, or skip and move to i + 1, then take the maximum. Compute dp from right to left, returning dp[0].
Pro tip: Clarify that 'going past the end' means the jump lands at or beyond the array length, and mention that you can optimize space to O(1) by only keeping the next few states if the values are bounded, but O(n) is fine.
Restate the rules: start at index 0, at each index either take the value and jump forward by value+1, or skip and move to next index. Confirm that the goal is to maximize total profit before the index goes out of bounds.
Let dp[i] be the maximum profit obtainable starting from index i. The answer will be dp[0].
At index i, if i >= n, dp[i] = 0. Otherwise, dp[i] = max(arr[i] + dp[i + arr[i] + 1], dp[i + 1]).
Iterate i from n-1 down to 0, filling the dp array. Handle out-of-bounds indices by treating dp[j] = 0 for j >= n.
Time complexity O(n), space O(n). Discuss edge cases: empty array, single element, large jumps, and all elements positive.
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First, clarify the original problem and solution, then analyze how negative numbers affect the underlying assumptions. Discuss necessary modifications to the algorithm, such as changing data structures or handling edge cases, and compare trade-offs in time and space complexity.
Pro tip: Demonstrate awareness that negative numbers can break greedy approaches or sliding window techniques, and proactively mention how you would test the modified solution with mixed-sign inputs.
Briefly summarize the initial problem and your approach, highlighting key assumptions that may be invalidated by negative numbers.
Determine which parts of your solution rely on non-negativity, such as monotonicity, prefix sums, or two-pointer techniques.
Describe how to adapt the algorithm, e.g., using Kadane's algorithm for maximum subarray, dynamic programming, or a different data structure.
Compare the modified solution's time and space complexity with the original, and discuss any new edge cases.
Walk through a small example with negative numbers to confirm correctness and mention testing strategies.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.