Maximize stock profit with one or two trades

You are given an array `prices` where `prices[i]` is the price of a given stock on day `i` (0-indexed). You want to maximize your profit by choosing when to buy and sell this stock, subject to the constraints below. You may not hold more than one share at a time (i.e., you must sell before you can buy again). Assume: - `1 <= n <= 10^5`, where `n = prices.length`. - `0 <= prices[i] <= 10^4`. ### Part A: At most one transaction You are allowed to complete **at most one** transaction (i.e., buy once and sell once). - Return the **maximum profit** you can achieve. - If no profit is possible, return `0`. **Example** - Input: `prices = [7, 1, 5, 3, 6, 4]` - Output: `5` - Explanation: Buy on day 1 (price = 1) and sell on day 4 (price = 6), profit = 6 − 1 = 5. --- ### Part B: At most two transactions Now you are allowed to complete **at most two transactions**. - Each transaction is a buy followed by a sell. - You must sell the stock before you buy again. - You cannot engage in multiple transactions at the same time. Return the **maximum total profit** you can achieve with at most two transactions. **Example** - Input: `prices = [3, 3, 5, 0, 0, 3, 1, 4]` - Output: `6` - Explanation: - Buy on day 3 (price = 0), sell on day 5 (price = 3), profit = 3. - Then buy on day 6 (price = 1), sell on day 7 (price = 4), profit = 3. - Total profit = 3 + 3 = 6. Design algorithms for both parts that run in **O(n)** time and **O(1)** or **O(n)** extra space.