Optimal Account Balancing (LeetCode 465)

The Futureforce university-recruiting prompt is the unchanged LeetCode 465 problem: consolidate a set of person-to-person transactions and return the minimum number of additional transfers required to settle every net balance. Requirements Input: a list of transactions, where each transaction is [from, to, amount] and means from transferred amount to to. Compute each person's net balance after all original transactions. Return the minimum number of additional transactions needed to make every net balance zero. Examples Input: [[0, 1, 10], [2, 0, 5]] Output: 2 Notes The prompt is the unchanged LeetCode 465 problem. Person identifiers do not need to be contiguous, and people with a zero net balance do not need to participate in settlement. Collapse the transaction graph into a list of non-zero net balances. In the exact search, take the first unsettled balance and pair it only with later balances of the opposite sign; apply that transfer in place, recurse, then backtrack. Skip counterparties with duplicate balance values at the same recursion depth, and stop trying alternatives after an exact cancellation. The search is exponential in the number of non-zero balances, while the balance reduction is linear in the number of input transactions. Preparation Re-solve the canonical problem from a blank editor and write the net-balance reduction before working on the minimum-transfer search. Test the implementation on already-balanced participants, repeated participants, and cases where several different settlement orders are possible.