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I started by taking input from the CSV file. I created Two Structures for the data and added some essential Data Structures to store the relevant data which came useful in the later part of the code .
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To solve the problem , the very first thing after reading the data is to perform Toplogical Sort by an algorithm of your choice ( I used Kahn's Algorithm ) , so that all the transactions are ordered correctly and we can proceed further .
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A naive approach to solve this problem would be use Recursion , and consider all the possible states of taking a particular transaction or not , but this will be of O(2n, where n is the given the number of transactions) , which is impractical
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If this was a tradition 0/1 Knapsack problem , then we could have optimized it using Dynamic Programming , but here since we have to check all the visited parents , the best possible optimization would be to use DP with Bitmasking where we maintain a mask such that (we can also keep a visited array for the same) to check wether all of our parents are visited , but given the samples , there will be 25000 order of unique states , which we can't store in our array .
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Now , inorder to find the result , we will try a greedy algorithm along with the use of traditional Knapsack
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The approach goes something like , first we find the total average ratio (fees/weight) of each Transaction .
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Then we run a loop from (0.1 to Average_total_ratio) and find at which ratio , we obtain the answer under the given constraints .
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The only demerit of this approach is that we are rejecting all those cases where we could have better answers with ratio greater than avg_total_ratio .
My result :
Final maximum Fees : 5669422
Final Weight to get this Fees : 3880668