Currency Exchange / Maximize After Two Days of Conversions

Starting from 1.0 unit of a given currency, maximize the final amount by applying Day 1 exchange rates first, then Day 2 rates, with self-to-self conversion always allowed at 1.0. Each day's pairs form a directed weighted graph; a DFS from the start currency finds the best reachable amount per day, then chains the Day 1 target into Day 2. Equivalent to LeetCode 3411. Maximize Amount After Two Days of Conversions Problem Overview You are given a string called initialCurrency. You begin with 1.0 unit of this currency. You also receive four arrays (lists) that define possible currency trades and their exchange rates for two different days: Day 1: pairs1[i] shows a trade from startCurrency to targetCurrency. The exchange rate for this trade is rates1[i]. Day 2: pairs2[i] shows a trade from startCurrency to targetCurrency. The exchange rate for this trade is rates2[i]. Note: You can always convert a currency to itself at a rate of 1.0. Goal: Find the maximum amount of initialCurrency you can end up with. You must perform trades using Day 1 rates first, followed by trades using Day 2 rates. Sample Cases 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: You can get 720.0 EUR by following this path: Start with 1.0 EUR. Day 1: Convert EUR → USD (rate 2.0), then USD → JPY (rate 3.0). You now have 6.0 JPY. Day 2: Convert JPY → USD (rate 4.0), then USD → CHF (rate 5.0), and finally CHF → EUR (rate 6.0). The total is 1.0 * 2.0 * 3.0 * 4.0 * 5.0 * 6.0 = 720.0. Example 2 Input: initialCurrency = "NGN" pairs1 = [["NGN","EUR"]], rates1 = [9.0] pairs2 = [["NGN","EUR"]], rates2 = [6.0] Output: 1.50000 Explanation: Trade NGN for EUR on Day 1 (Rate 9.0). Then, trade EUR back to NGN on Day 2. This results in a value of 1.5. Example 3 Input: initialCurrency = "USD" pairs1 = [["USD","EUR"]], rates1 = [1.0] pairs2 = [["EUR","JPY"]], rates2 = [10.0] Output: 1.00000 Explanation: There is no valid path to convert the money back to USD. Therefore, the maximum amount remains 1.0. Input Limits The length of initialCurrency is between 1 and 3. initialCurrency uses only uppercase English letters. The number of pairs for Day 1 (n) and Day 2 (m) is between 1 and 10. Currency names in the pairs use only uppercase English letters and have a length between 1 and 3. The size of the rates arrays matches the size of the pairs arrays. All rates are between 1.0 and 10.0. The input contains no contradictions or circular dependencies within a single day's graph.