Looked like a classic knapsack at first and I started mentally reaching for a heap-based approach.
Recognize this as the 0/1 Knapsack problem and clearly state that it can be solved optimally with dynamic programming in O(N * capacity) time and space. Then discuss the trade-offs: for large N and capacity, DP may be infeasible, so consider greedy heuristics or approximation algorithms, and mention that in practice, block space is limited and transactions have additional constraints like dependencies.
Pro tip: Coinbase values production-ready thinking: mention that in real blockchain systems, transaction selection often uses a greedy fee-rate (fee per byte) heuristic due to time constraints, and that the optimal DP solution is a good benchmark but may not be practical for large mempools.
Restate the problem to ensure understanding: we need to select a subset of transactions to maximize total fee without exceeding block size capacity. Ask if transactions can be partially included (no, they are indivisible) and if there are any other constraints (e.g., dependencies).
Recognize this as the 0/1 Knapsack problem, where each transaction is an item with weight (size) and value (fee), and the block capacity is the knapsack capacity. State that it is NP-hard but solvable in pseudo-polynomial time with DP.
Explain the DP approach: create a table dp[i][w] representing max fee using first i transactions with capacity w. Recurrence: dp[i][w] = max(dp[i-1][w], dp[i-1][w - size_i] + fee_i) if size_i <= w. Time and space O(N * capacity).
For large N and capacity, DP may be too slow or memory-heavy. Mention greedy by fee/size ratio as a fast heuristic (not always optimal) and approximation schemes (FPTAS) if needed. Also note that in practice, block space is limited and transactions may have dependencies, making it a more complex scheduling problem.
Relate to Coinbase's domain: in blockchain, transaction selection often uses a greedy fee-rate approach due to real-time constraints. Mention that the optimal DP solution is a good benchmark but may not be used in production for large mempools.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.