Detect currency arbitrage with costs

Q: Detect currency arbitrage with costs

This question evaluates a candidate's competency in algorithmic problem modeling, graph-based cycle detection, and numerical reasoning about exchange rates and transaction costs.

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Question

You are given a K×K matrix R of currency exchange rates where R[i][j] is the amount of currency j obtainable for one unit of currency i, and R[i][i] = 1 for all i. A closed cycle of exchanges incurs a transaction cost of 0.01% of the initial amount (applied once per completed cycle). Determine whether there exists any cycle of exchanges that yields a strictly higher final amount than the initial after accounting for this cost. Return true if such an arbitrage opportunity exists, otherwise return false.

Detect currency arbitrage with costs

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