3387 - Maximize Amount After Two Days of Conversions.

Medium

You are given a string initialCurrency, and you start with 1.0 of initialCurrency.

You are also given four arrays with currency pairs (strings) and rates (real numbers):

• <code>pairs1i = startCurrency_i, targetCurrency_i</code> denotes that you can convert from <code>startCurrency_i</code> to <code>targetCurrency_i</code> at a rate of rates1[i] on day 1.

• <code>pairs2i = startCurrency_i, targetCurrency_i</code> denotes that you can convert from <code>startCurrency_i</code> to <code>targetCurrency_i</code> at a rate of rates2[i] on day 2.

• Also, each targetCurrency can be converted back to its corresponding startCurrency at a rate of 1 / rate.

You can perform any number of conversions, including zero , using rates1 on day 1, followed by any number of additional conversions, including zero , using rates2 on day 2.

Return the maximum amount of initialCurrency you can have after performing any number of conversions on both days in order.

Note: Conversion rates are valid, and there will be no contradictions in the rates for either day. The rates for the days are independent of each other.

Example 1:

Input: initialCurrency = "EUR", pairs1 = \[\["EUR","USD"],"USD","JPY"], rates1 = 2.0,3.0, pairs2 = \[\["JPY","USD"],"USD","CHF","CHF","EUR"], rates2 = 4.0,5.0,6.0

Output: 720.00000

Explanation:

To get the maximum amount of EUR , starting with 1.0 EUR:

• On Day 1:

• On Day 2:

Example 2:

Input: initialCurrency = "NGN", pairs1 = \[\["NGN","EUR"]], rates1 = 9.0, pairs2 = \[\["NGN","EUR"]], rates2 = 6.0

Output: 1.50000

Explanation:

Converting NGN to EUR on day 1 and EUR to NGN using the inverse rate on day 2 gives the maximum amount.

Example 3:

Input: initialCurrency = "USD", pairs1 = \[\["USD","EUR"]], rates1 = 1.0, pairs2 = \[\["EUR","JPY"]], rates2 = 10.0

Output: 1.00000

Explanation:

In this example, there is no need to make any conversions on either day.

Constraints:

• 1 <= initialCurrency.length <= 3

• initialCurrency consists only of uppercase English letters.

• 1 <= n == pairs1.length <= 10

• 1 <= m == pairs2.length <= 10

• <code>pairs1i == startCurrency_i, targetCurrency_i</code>

• <code>pairs2i == startCurrency_i, targetCurrency_i</code>

• <code>1 <= startCurrency_i.length, targetCurrency_i.length <= 3</code>

• <code>startCurrency_i</code> and <code>targetCurrency_i</code> consist only of uppercase English letters.

• rates1.length == n

• rates2.length == m

• 1.0 <= rates1[i], rates2[i] <= 10.0

• The input is generated such that there are no contradictions or cycles in the conversion graphs for either day.