Blockchain Transaction Fee Optimization

Problem Suppose you are dealing with a blockchain mining problem. You are given the block_size of a block and several transactions, each transaction having a unique id, size, and fee. Each transaction requires size space in the block and generates fee revenue. Your task is to maximize the revenue within the given block_size. Additionally, some transactions may have parent transactions that must be processed before they can be included (e.g., transaction4 may require transaction1, transaction2, transaction3 to be mined first). If any of these parent transactions are not yet mined, transaction4 cannot be included. Once the parent transactions have been mined, transaction4 can be mined instantly. Requirements: Implement a function to calculate the maximum revenue given the block size. Consider the impact of parent transaction relationships, ensuring these dependencies are managed appropriately during the calculation. Input: block_size: An integer representing the size of the block. transactions: A list of transactions, where each transaction is a dictionary containing id, size, fee, and optional parents (indicating a list of parent transaction IDs). Output: An integer representing the total revenue when maximizing. Example: block_size = 10 transactions = [ {'id': 'tx1', 'size': 3, 'fee': 5}, {'id': 'tx2', 'size': 4, 'fee': 6, 'parents': ['tx1']}, {'id': 'tx3', 'size': 2, 'fee': 3} ] # Example Output: 9 Notes: Ensure that parent transactions are handled before choosing a transaction. You may assume all transaction data is valid and that the transaction parent-child relationships will not create cyclic dependencies. Example Input 10 [{'id': 'tx1', 'size': 3, 'fee': 5, 'parents': []}, {'id': 'tx2', 'size': 4, 'fee': 6, 'parents': ['tx1']}, {'id': 'tx3', 'size': 2, 'fee': 3, 'parents': []}]