Find out which combinations of numbers in a set add up to a given total

Question

I\'ve been tasked with helping some accountants solve a common problem they have - given a list of transactions and a total deposit, which transactions are part of the depos

Answer 1

If I understand your problem correctly, you have a set of transactions, and you merely wish to know which of them could have been included in a given total. So if there are 4 possible transactions, then there are 2^4 = 16 possible sets to inspect. This problem is, for 100 possible transactions, the search space has 2^100 = 1267650600228229401496703205376 possible combinations to search over. For 1000 potential transactions in the mix, it grows to a total of

10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376

sets that you must test. Brute force will hardly be a viable solution on these problems.

Instead, use a solver that can handle knapsack problems. But even then, I'm not sure that you can generate a complete enumeration of all possible solutions without some variation of brute force.