Detect Currency Arbitrage After a Cycle Fee

You are given a matrix of positive currency exchange rates, where rates[i][j] units of currency j are received for one unit of currency i. Determine whether any exchange sequence of between 1 and n steps starts and ends at the same currency and multiplies the starting amount by more than 1.0001. The threshold represents a fee equal to 0.01 percent of the starting amount charged once for the completed sequence.

Function Contract

Implement has_arbitrage(rates) -> bool.

Constraints

• 1 <= number of currencies n <= 50.
• The matrix is square and every rate is a positive finite number.
• Currencies may repeat, but the candidate sequence contains at most n exchanges.
• Comparisons should tolerate only ordinary floating-point roundoff, not erase the stated 1.0001 threshold.

Examples

rates = [[1.0, 0.5], [2.0, 1.0]]
output = false

rates = [[1.0, 2.0], [0.51, 1.0]]
output = true