My first instinct was DP since it's basically a knapsack variant, but the interviewer steered me toward a greedy approach instead, sorting by fee-to-size ratio.
Recognize this as a 0/1 knapsack problem where transaction size is weight and fee is value, with block size as capacity. Present a dynamic programming solution that maximizes total fee, then discuss time/space complexity and potential optimizations for large transaction pools.
Pro tip: Mention that in real blockchain systems, transaction selection often uses a greedy approach based on fee rate (fee per byte) for simplicity and speed, but DP guarantees optimality for small block sizes like 100. This shows awareness of practical trade-offs.
Confirm that each transaction can be included at most once (0/1 knapsack), and that the goal is to maximize total fee without exceeding the block size limit.
Let dp[i][s] be the maximum fee using the first i transactions with total size exactly s (or at most s). Recurrence: dp[i][s] = max(dp[i-1][s], dp[i-1][s - size_i] + fee_i) if size_i <= s.
Use a 1D DP array of size block_limit+1, iterating transactions and updating from high to low size to avoid reusing items. Time O(n * block_size), space O(block_size).
If needed, backtrack through the DP table to identify which transactions were chosen, or maintain a parent pointer during computation.
Compare DP with greedy by fee rate, noting that greedy is faster but not always optimal; for block size 100, DP is efficient. Also mention potential integer overflow and use of 64-bit integers for fees.
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Acknowledge that the parent-child dependency introduces a precedence constraint, so the selection problem becomes a constrained optimization. Propose modeling transactions as a DAG and using a modified greedy algorithm that respects dependencies, such as selecting transactions in topological order or using a priority queue that only considers transactions whose parents are already selected.
Pro tip: Mention that in practice, you might need to handle cycles or missing parents gracefully, and consider the trade-off between optimality and computational complexity—sometimes a simple heuristic like 'include all ancestors' is sufficient for real-world blockchains.
Represent transactions as nodes and parent-child relationships as directed edges. This clarifies that a child can only be selected if all its ancestors are selected.
Modify your existing selection approach (e.g., greedy by fee) to only consider transactions whose parents are already included. Use a priority queue of 'available' transactions (those with no unselected parents).
Ensure that when you select a transaction, you also add its children to the available set. If a parent is not selected, its children remain unavailable.
Discuss whether to maximize total fee, minimize block size, or other objectives. Note that the dependency constraint may reduce the achievable optimal value compared to unconstrained selection.
Mention handling of cycles (invalid), missing parents (ignore or treat as invalid), and performance implications for large DAGs. Suggest possible optimizations like precomputing ancestor sets.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.