## Problem You are given every transaction on one bank account during the calendar year 2020. The starting balance is zero. `amounts[i]` and `dates[i]` describe one transaction: - A negative amount is a card payment. - Zero or a positive amount is an incoming transfer. - A date is formatted `YYYY-MM-DD` and is always in 2020. The card has a fee of `5` charged at the end of each month. The fee is waived for a month only when that month contains at least three card payments and the total absolute value of those card payments is at least `100`. Return the final balance after all transactions and all twelve monthly fee decisions. ### Function Contract Implement `yearEndBalance(amounts, dates)` and return an integer. ### Constraints & Assumptions - `0 <= len(amounts) = len(dates) <= 200,000`. - `-10^9 <= amounts[i] <= 10^9`. - Dates are valid 2020 dates and transactions may be supplied in any order. - A zero amount is an incoming transfer, not a card payment. - The total cost of card payments is the sum of `-amount` for negative transactions only. - Every month with no qualifying card activity pays the fee, including months with no transactions. - The final result fits in a signed 64-bit integer. ### Clarifying Questions to Ask - Is the waiver threshold inclusive? Yes: at least three payments totaling at least `100`. - Are refunds represented by positive amounts and excluded from card-payment totals? Yes. - Does transaction order within a month matter? No. - Are there always twelve fee decisions? Yes. ```hint Aggregate only what the waiver needs For each month, retain a card-payment count and the sum of absolute negative amounts; the account balance itself is simply the sum of all transactions. ``` ### Examples - `amounts = [100, 100, 100, -10]` and December dates returns `230`: transaction sum `290` minus twelve fees. - `amounts = [180, -50, -25, -25]` with all transactions in January returns `25`: January qualifies, so only eleven fees are charged. - `amounts = [1, -1, 0, -105, 1]` with two April card payments returns `-164`: April reaches total cost `106` but has only two payments, so it does not qualify. ### Evaluation Focus - Counts only negative transactions as card payments and includes all amounts in the balance. - Evaluates count and cost thresholds per calendar month. - Charges months with no transactions. - Runs in `O(n)` time with `O(12)` auxiliary state. ### Extensions to Discuss 1. How would varying monthly fees and waiver policies be represented safely? 2. What changes for a streaming ledger that can receive corrections? 3. How would multi-currency transactions affect the monthly threshold calculation?