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question:# Context You are tasked with parsing and evaluating simple mathematical expressions. These expressions will only contain integer numbers, parentheses for grouping, and the binary operators `+` (addition) and `*` (multiplication). Operator precedence follows standard mathematical rules: multiplication has higher precedence than addition, and parentheses can be used to override this precedence. You need to write a function called `evaluate_expression` that takes a string representing the expression and returns the evaluated result as an integer. # Function Implementation You need to implement the function `evaluate_expression`: ```python def evaluate_expression(expression): Evaluate a mathematical expression containing integers, parentheses, and +, * operators. Args: expression (str): The mathematical expression to evaluate. Returns: int: The result of evaluating the expression. Example: >>> evaluate_expression("(2+3)*(4+5)") 45 pass ``` * **Input Format**: - `expression`: A string containing the mathematical expression. The length of the expression will not exceed 100 characters. * **Output Format**: - An integer representing the result of the evaluated expression. * **Constraints**: - The expression will only contain digits `0-9`, parentheses `()`, and the operators `+` and `*`. - The expression will be well-formed (i.e., no unmatched parentheses and no syntax errors). # Example ```python # Given the expression "(2+3)*(4+5)" print(evaluate_expression("(2+3)*(4+5)")) # Output: 45 # Given the expression "2+3*4" print(evaluate_expression("2+3*4")) # Output: 14 # Given the expression "(1+2)*(3+4)+5" print(evaluate_expression("(1+2)*(3+4)+5")) # Output: 26 ``` # Additional Notes * Implement a parser that respects operator precedence and correctly handles parentheses. * You can assume the expression is always valid and does not contain invalid characters. * Do not use `eval` or similar built-in functions directly for evaluation.
answer:def evaluate_expression(expression): Evaluate a mathematical expression containing integers, parentheses, and +, * operators. Args: expression (str): The mathematical expression to evaluate. Returns: int: The result of evaluating the expression. def parse_expression(expression): tokens = list(expression.replace(' ', '')) return parse_addition(tokens) def parse_addition(tokens): result = parse_multiplication(tokens) while tokens and tokens[0] == '+': tokens.pop(0) result += parse_multiplication(tokens) return result def parse_multiplication(tokens): result = parse_parentheses(tokens) while tokens and tokens[0] == '*': tokens.pop(0) result *= parse_parentheses(tokens) return result def parse_parentheses(tokens): if tokens[0] == '(': tokens.pop(0) result = parse_addition(tokens) tokens.pop(0) # this should be ')' return result return parse_number(tokens) def parse_number(tokens): num = 0 while tokens and tokens[0].isdigit(): num = num * 10 + int(tokens.pop(0)) return num return parse_expression(expression)
question:# Problem Statement You are provided with an implementation of a matrix rotation function that rotates a given n x n matrix by 90 degrees clockwise. Your task is to extend this functionality to support both clockwise and counterclockwise rotations based on user input. # Requirements 1. **Rotation Direction**: Modify the function to accept an additional parameter that specifies the rotation direction ('clockwise' or 'counterclockwise'). 2. **Matrix Rotation**: Implement the logic to rotate the matrix 90 degrees either clockwise or counterclockwise based on the input. # Input/Output - **Input**: A matrix represented as a list of lists, and a string indicating the direction of rotation ('clockwise' or 'counterclockwise'). - **Output**: The rotated matrix. # Constraints 1. The matrix will always be a square matrix (n x n) where 1 <= n <= 100. 2. The matrix will contain integer values. # Function Signature ```python def rotate_matrix(matrix: list[list[int]], direction: str) -> list[list[int]]: pass ``` # Example ```python matrix = [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ] # Clockwise rotation result = rotate_matrix(matrix, 'clockwise') # Output: [ # [7, 4, 1], # [8, 5, 2], # [9, 6, 3] # ] # Counterclockwise rotation result = rotate_matrix(matrix, 'counterclockwise') # Output: [ # [3, 6, 9], # [2, 5, 8], # [1, 4, 7] # ] ``` # Implementation Details 1. For clockwise rotation: - Transpose the matrix. - Reverse each row in the transposed matrix. 2. For counterclockwise rotation: - Transpose the matrix. - Reverse each column in the transposed matrix. 3. Ensure the function handles both rotation directions based on the provided input.
answer:def rotate_matrix(matrix: list[list[int]], direction: str) -> list[list[int]]: if direction == 'clockwise': # Transpose the matrix transposed = list(map(list, zip(*matrix))) # Reverse each row in the transposed matrix rotated = [row[::-1] for row in transposed] elif direction == 'counterclockwise': # Transpose the matrix transposed = list(map(list, zip(*matrix))) # Reverse each column in the transposed matrix rotated = transposed[::-1] else: raise ValueError("Invalid direction. Use 'clockwise' or 'counterclockwise'.") return rotated
question:Array Rotation Utility In many computer science and engineering applications, rotating arrays is a common operation. Your task is to implement a class `ArrayRotator` that provides utility methods to rotate an array to the left or right by a specified number of positions. 1. **rotate_left(arr: List[int], k: int) -> List[int]**: Rotate the array `arr` to the left by `k` positions. 2. **rotate_right(arr: List[int], k: int) -> List[int]**: Rotate the array `arr` to the right by `k` positions. 3. **is_rotated_version(arr1: List[int], arr2: List[int]) -> bool**: Check if `arr2` is a rotated version of `arr1`. 4. **find_rotation_count(arr: List[int]) -> int**: Return the number of positions the array `arr` needs to be rotated to become sorted in ascending order. # Requirements: * The input `arr` will be a list of integers. * The input `k` will be a non-negative integer. * You may assume that `arr` contains at least one element. * Your implementation should handle edge cases such as an empty array gracefully. # Example: ```python class ArrayRotator: @staticmethod def rotate_left(arr: List[int], k: int) -> List[int]: # Implement this method pass @staticmethod def rotate_right(arr: List[int], k: int) -> List[int]: # Implement this method pass @staticmethod def is_rotated_version(arr1: List[int], arr2: List[int]) -> bool: # Implement this method pass @staticmethod def find_rotation_count(arr: List[int]) -> int: # Implement this method pass # Example Usage: assert ArrayRotator.rotate_left([1, 2, 3, 4, 5], 2) == [3, 4, 5, 1, 2] # Rotates left by 2 positions assert ArrayRotator.rotate_right([1, 2, 3, 4, 5], 2) == [4, 5, 1, 2, 3] # Rotates right by 2 positions assert ArrayRotator.is_rotated_version([1, 2, 3, 4, 5], [4, 5, 1, 2, 3]) == True # Checks if it's a rotated version assert ArrayRotator.find_rotation_count([4, 5, 1, 2, 3]) == 2 # Number of rotations to be sorted ``` Implement the class `ArrayRotator` with the specified methods using efficient algorithms for array manipulation and rotation.
answer:from typing import List class ArrayRotator: @staticmethod def rotate_left(arr: List[int], k: int) -> List[int]: Rotate the array arr to the left by k positions. n = len(arr) k %= n # In case k is greater than n return arr[k:] + arr[:k] @staticmethod def rotate_right(arr: List[int], k: int) -> List[int]: Rotate the array arr to the right by k positions. n = len(arr) k %= n # In case k is greater than n return arr[-k:] + arr[:-k] @staticmethod def is_rotated_version(arr1: List[int], arr2: List[int]) -> bool: Check if arr2 is a rotated version of arr1. if len(arr1) != len(arr2): return False return any(arr1[i:] + arr1[:i] == arr2 for i in range(len(arr1))) @staticmethod def find_rotation_count(arr: List[int]) -> int: Return the number of positions the array arr needs to be rotated to become sorted in ascending order. n = len(arr) for i in range(n): if arr[i:] + arr[:i] == sorted(arr): return i return 0
question:# Problem Description You are given an integer array `nums` and an integer `target`. Your task is to implement a method named `find_closest_sum(self, target: int) -> int` in the `ClosestSum` class that finds three integers in `nums` such that the sum is closest to `target`. You should return the sum of the three integers. You may assume that each input would have exactly one solution. # Requirements - The function should return the closest possible sum of any three integers in the array to the given target. - Your solution should efficiently handle both small and large arrays. # Input - `target (int)`: An integer target sum. - `nums (List[int])`: A list of integers, where the length is between 3 and 10^5. # Output - An integer representing the sum of three integers in `nums` closest to the `target`. # Constraints - The length of `nums` is between 3 and 10^5. - `-10^4 <= nums[i] <= 10^4` - `-10^5 <= target <= 10^5` # Examples Example 1: ```python nums = [-1, 2, 1, -4] target = 1 closest_sum = ClosestSum(nums) print(closest_sum.find_closest_sum(target)) # Output: 2 # Explanation: The sum that is closest to the target is 2. (-1 + 2 + 1 = 2) ``` Example 2: ```python nums = [1, 1, -1, -1, 3] target = -1 closest_sum = ClosestSum(nums) print(closest_sum.find_closest_sum(target)) # Output: -1 # Explanation: The sum that is closest to the target is -1. (1 + -1 + -1 = -1) ``` # Notes - Sort the array before processing it to leverage the sorted order in the algorithm. - You should use a combination of a loop and two-pointer technique to achieve the desired result efficiently. - Ensure your implementation handles all edge cases gracefully. ```python class ClosestSum: def __init__(self, nums: List[int]): self.nums = nums def find_closest_sum(self, target: int) -> int: nums = sorted(self.nums) closest_sum = sum(nums[:3]) for i in range(len(nums) - 2): left, right = i + 1, len(nums) - 1 while left < right: current_sum = nums[i] + nums[left] + nums[right] if abs(target - current_sum) < abs(target - closest_sum): closest_sum = current_sum if current_sum < target: left += 1 elif current_sum > target: right -= 1 else: return current_sum return closest_sum ``` This problem tests your ability to manipulate arrays, sort them, and apply a two-pointer technique efficiently to solve for the closest sum in a large list of integers.
answer:from typing import List class ClosestSum: def __init__(self, nums: List[int]): self.nums = nums def find_closest_sum(self, target: int) -> int: # Sort the array first nums = sorted(self.nums) closest_sum = sum(nums[:3]) for i in range(len(nums) - 2): left, right = i + 1, len(nums) - 1 while left < right: current_sum = nums[i] + nums[left] + nums[right] if abs(target - current_sum) < abs(target - closest_sum): closest_sum = current_sum if current_sum < target: left += 1 elif current_sum > target: right -= 1 else: return current_sum return closest_sum