Currency Arbitrage Detection

hard

CodingOld question · last reported Aug 2025

Requirements

Implement has_arbitrage(rates: list[list[float]]) -> bool.
Input consists of an $n \times n$ matrix in which rates[i][j] gives the number of units of currency j obtained by converting 1 unit of currency i. Every diagonal value is 1.
Completing an exchange loop charges a fee equal to 0.01% of the amount originally placed into the loop.
Decide whether there is an arbitrage opportunity: an exchange path that begins and finishes in the same currency and leaves you with an amount strictly greater than the starting amount once the fee has been deducted.
Return True when such an opportunity is present; otherwise return False.

n = 2, rates [[1, 0.25], [4.0, 1]] → False.

The two conversions multiply the starting amount by $0.25 \times 4.0 = 1$ , and applying the 0.01% fee makes the final amount smaller than what you began with.

hard

CodingOld question · last reported Aug 2025

Implement has_arbitrage(rates: list[list[float]]) -> bool.
Input consists of an $n \times n$ matrix in which rates[i][j] gives the number of units of currency j obtained by converting 1 unit of currency i. Every diagonal value is 1.
Completing an exchange loop charges a fee equal to 0.01% of the amount originally placed into the loop.
Decide whether there is an arbitrage opportunity: an exchange path that begins and finishes in the same currency and leaves you with an amount strictly greater than the starting amount once the fee has been deducted.
Return True when such an opportunity is present; otherwise return False.

n = 2, rates [[1, 0.25], [4.0, 1]] → False.

The two conversions multiply the starting amount by $0.25 \times 4.0 = 1$ , and applying the 0.01% fee makes the final amount smaller than what you began with.