Compute max profit with forced trades
Overview
This question evaluates algorithmic problem-solving in the Coding & Algorithms domain, focusing on array processing and constrained optimization for maximizing stock-trading profit under a forced-trade requirement for exactly one or two buy-sell transactions; it assesses state management, edge-case handling, and arithmetic reasoning.
Given an array prices where prices[i] is the stock price on day i, solve two related tasks under a forced-trade constraint: (a) Exactly one transaction: choose one buy day and one later sell day to maximize profit; if prices never rise, return the least possible loss that results from exactly one buy and one sell. (b) Exactly two transactions: choose two non-overlapping buy-sell pairs (sell before the next buy) to maximize total profit; if necessary, include losses so that exactly two transactions are performed. Implement two functions (e.g., profitExactlyOne(prices), profitExactlyTwo(prices)) and specify assumptions (single share per transaction; no transaction costs; cannot short). Handle edge cases (empty or single-element arrays). No explicit time-complexity requirement.