question:# Evaluate Reverse Polish Notation Context: In computer science, Reverse Polish Notation (RPN) is a mathematical notation in which every operator follows all of its operands. It is also known as postfix notation. For instance, the expression `4 + 5` would be represented as `4 5 +` in RPN. Evaluating RPN expressions requires the use of a stack data structure to handle the operators and operands efficiently. Problem: Write a function to evaluate the value of an arithmetic expression in Reverse Polish Notation. Function Signature: ```python def eval_rpn(tokens: list[str]) -> int: ``` Input: * `tokens`: A list of strings, where each string is either an operand, represented as a number, or an operator (+, -, *, /). Output: * An integer representing the result of evaluating the expression. Constraints: * The input list will contain between 1 and 10,000 elements. * Each element in the list will be a valid operand (integer) or a valid operator. * Division between two integers should truncate toward zero (same behavior as Python's `//` operator). Examples: ```python # Example 1 eval_rpn(["2", "1", "+", "3", "*"]) # Expected Output: 9 # Explanation: ((2 + 1) * 3) = 9 # Example 2 eval_rpn(["4", "13", "5", "/", "+"]) # Expected Output: 6 # Explanation: (4 + (13 / 5)) = 6 # Example 3 eval_rpn(["10", "6", "9", "3", "+", "-11", "*", "/", "*", "17", "+", "5", "+"]) # Expected Output: 22 # Explanation: ((10 * (6 / ((9 + 3) * -11))) + 17) + 5 = 22 ``` Performance Consideration: Ensure the implementation handles large input efficiently by using an appropriate data structure and adhering to optimal algorithmic solutions. The operations should be handled in constant time. Note: Your solution must be implemented in pure Python and should not rely on external libraries. Use comments and docstrings to clarify your approach and outline the logic where necessary.

question:# Question: Optimizing Financial Transactions Context: Financial transactions are a critical aspect of modern life, spanning investments, loans, and other monetary exchanges. Efficient management and processing of these transactions are crucial for both individuals and institutions. In this exercise, you will create a system that optimizes a sequence of financial transactions to maximize the total benefit based on given constraints. Task: Design and implement a Python class `TransactionManager` to assist with the management and optimization of financial transactions. This class should include methods to add transactions, compute the net balance, and optimize the sequence of transactions based on specific criteria. Requirements: 1. **Add Transaction**: Implement a method `add_transaction(amount: float, category: str, date: str)` to add a new transaction. - `amount` represents the transaction amount (positive for deposits/credits, negative for withdrawals/debits). - `category` is a string denoting the type of transaction (e.g., "investment", "loan", "expense"). - `date` should be in the format `YYYY-MM-DD`. 2. **Net Balance**: Implement a method `net_balance(start_date: str, end_date: str) -> float` to compute the net balance of all transactions between the specified dates. - `start_date` and `end_date` should be in the format `YYYY-MM-DD`. 3. **Optimize Investments**: Implement a method `optimize_investments() -> list` to return a sequence of investment and loan transactions that maximizes returns while minimizing interest within the provided transactions. - Assume that a positive investment transaction adds to profits, while a negative transaction (loan repayment) subtracts from profits. - The transactions should be sequenced in a way to optimize the net benefit. Implementations: - Create the `TransactionManager` class and implement the required methods. - Ensure to handle edge cases, such as incorrect date formats or invalid amounts. - Provide a clear and concise user interface to interact with the transaction system. - Include appropriate unit tests to validate the functionality of each method. Constraints: - Dates will be in the Gregorian calendar and valid. - Each transaction date will be unique. - Optimize the transactions' sequence for maximum net benefit based on the provided data. Here is the starter skeleton for your implementation: ```python from datetime import datetime from typing import List, Tuple class TransactionManager: def __init__(self): self.transactions = [] def add_transaction(self, amount: float, category: str, date: str): Add a new transaction to the manager. Args: amount: The transaction amount. category: The transaction category. date: The transaction date in YYYY-MM-DD format. Example: >>> manager = TransactionManager() >>> manager.add_transaction(1000, "investment", "2023-09-01") >>> manager.add_transaction(-500, "loan", "2023-10-01") try: date_obj = datetime.strptime(date, '%Y-%m-%d') self.transactions.append((amount, category, date_obj)) except ValueError as ve: raise ValueError("Date must be in YYYY-MM-DD format") from ve def net_balance(self, start_date: str, end_date: str) -> float: Calculate net balance between two dates. Args: start_date: The start date in YYYY-MM-DD format. end_date: The end date in YYYY-MM-DD format. Returns: The net balance as a float. Example: >>> manager = TransactionManager() >>> manager.add_transaction(1000, "investment", "2023-09-01") >>> manager.add_transaction(-500, "loan", "2023-10-01") >>> manager.net_balance("2023-09-01", "2023-10-01") 500.0 try: start = datetime.strptime(start_date, '%Y-%m-%d') end = datetime.strptime(end_date, '%Y-%m-%d') if start > end: raise ValueError("Start date must be before end date") net = sum(amount for amount, _, date in self.transactions if start <= date <= end) return net except ValueError as ve: raise ValueError("Dates must be in YYYY-MM-DD format") from ve def optimize_investments(self) -> List[Tuple[float, str, datetime]]: Optimize sequence of investments and loans to maximize net benefit. Returns: A list of transactions maximizing the net benefit. Example: >>> manager = TransactionManager() >>> manager.add_transaction(1000, "investment", "2023-09-01") >>> manager.add_transaction(-500, "loan", "2023-10-01") >>> manager.optimize_investments() [(1000, 'investment', datetime.datetime(2023, 9, 1, 0, 0))] # Placeholder logic for optimization, to be implemented investments = [trans for trans in self.transactions if trans[1] == 'investment'] loans = [trans for trans in self.transactions if trans[1] == 'loan'] # Implement logic to maximize net benefit return investments # Change according to optimization logic ``` Input and Output Format: - `add_transaction` takes three parameters: float for amount, string for category, and string for date. - `net_balance` takes two string parameters for start and end dates and returns a float. - `optimize_investments` returns a list of tuples containing the transaction amount, category, and date in datetime format. Constraints: - Transaction amounts will be realistic financial values. - All methods must handle invalid inputs and edge cases gracefully. - Ensure computational efficiency while optimizing the transactions. Good luck!

question:# Count Unique Characters Problem Context: You are given a list of strings. Your task is to write a function that calculates the number of unique characters present in each string and return the result as a dictionary where the keys are the original strings and the values are the counts of their unique characters. Function Signature: ```python def count_unique_characters(strings: list) -> dict: ``` Input: * **strings (list)**: A list of strings containing only lowercase alphabets. Output: * **dict**: A dictionary where each key is a string from the input list and its value is the count of unique characters in that string. Constraints: 1. Strings will contain only lowercase alphabetic characters (a-z). 2. The list will have at least one string and at most 100 strings. 3. Each string will have a length between 1 and 100 characters (inclusive). Example: ```python >>> count_unique_characters(['apple', 'banana', 'cherry']) {'apple': 4, 'banana': 3, 'cherry': 5} >>> count_unique_characters(['abc', 'abc', 'ab', 'bcd']) {'abc': 3, 'abc': 3, 'ab': 2, 'bcd': 3} ``` Errors: 1. Raise `ValueError` with an appropriate message if the input list is empty. 2. Raise `TypeError` with an appropriate message if any of the elements in the list are not strings. Implementation Instructions: 1. Verify input constraints and raise errors accordingly. 2. Use appropriate data structures to count unique characters in each string. 3. Construct and return the dictionary with strings as keys and their unique character counts as values.

question:Problem Statement You are given a list of integers and a target sum. Your task is to write a function `find_triplet_sum` that finds if there exists a triplet (three elements) in the list whose sum equals the given target sum. If such a triplet exists, return a sorted tuple containing these three elements. If multiple such triplets exist, return any one of them. If no such triplet exists, return an empty tuple. # Input * `arr` (list of integers): The list of integers. Constraints: (0 leq text{len(arr)} leq 10^5). * `target` (integer): The target sum. # Output * A sorted tuple of three integers whose sum is equal to the target sum, or an empty tuple if no such triplet exists. # Examples ```python find_triplet_sum([1, 2, 3, 4, 5, 6], 12) # Expected output: (1, 4, 7) find_triplet_sum([12, 3, 4, 1, 6, 9], 24) # Expected output: (3, 9, 12) find_triplet_sum([-1, 0, 1, 2, -1, -4], 0) # Expected output: (-1, -1, 2) find_triplet_sum([1, 1, 1, 1], 10) # Expected output: () find_triplet_sum([], 5) # Expected output: () ``` # Constraints * Ensure the function handles cases where the list is either empty or has fewer than three elements by returning an empty tuple. # Additional Notes * The returned tuple should have digits sorted in ascending order, e.g., (1, 2, 3). * The function should aim for a time complexity better than (O(n^3)), where (n) is the length of the list.