Appearance
question:# Hit Probability in a Circular Field You are developing a game where a player shoots arrows at a target represented by a circle on a 2D plane. For a simulation task, you need to determine the probability of hitting the target based on multiple shooting attempts. Task Write a function `hit_probability` that calculates the probability of hitting the circular target given the results of multiple shots. Function Signature ```python def hit_probability(radius: float, shots: list[tuple[float, float]]) -> float: pass ``` Input - `radius` (float): The radius of the circular target. It should be a positive value. - `shots` (list of tuples): A list of coordinates representing the positions where the shots landed. Each tuple contains two floats representing the x and y coordinates of a shot. Output - Returns the probability (float) of hitting the target, which is the ratio of the number of shots that landed inside or on the target to the total number of shots. Constraints - Radius should be a positive number. - The list of shots can be empty or contain any number of shot coordinates. Errors - The function should raise a `ValueError` if the radius is not positive. Examples ```python hit_probability(5.0, [(0,0), (3,4), (6,8), (5,0)]) # Should return 0.75 because 3 out of 4 shots are within the radius hit_probability(3.0, [(3,3), (0,0), (-3,-3)]) # Should return 0.333 because 1 out of 3 shots are within the radius hit_probability(2.0, [(1,1), (2,2)]) # Should return 0.5 because 1 out of 2 shots are within the radius hit_probability(1.0, [(1,0.5), (1,1), (0,1)]) # Should return 1.0 because 3 out of 3 shots are within the radius hit_probability(3.0, []) # Should return 0.0 because there are no shots ``` Hints - A shot is considered within the target if the distance from the origin to the shot coordinates `(x, y)` is less than or equal to the radius, i.e., ( sqrt{x^2 + y^2} leq text{radius} ).
answer:import math def hit_probability(radius: float, shots: list[tuple[float, float]]) -> float: if radius <= 0: raise ValueError("Radius must be a positive number") if not shots: return 0.0 hits = 0 for x, y in shots: distance = math.sqrt(x**2 + y**2) if distance <= radius: hits += 1 return hits / len(shots)
question:# Problem Statement: You are given a list of integers, and your task is to reorder the list such that the first element is the maximum value, the second element is the minimum value, the third element is the second maximum, the fourth element is the second minimum, and so on. # Function Signature: ```python def reorder_list(nums: List[int]) -> List[int] ``` # Input: - `nums` (List[int]): A list of integers (1 ≤ len(nums) ≤ 10^5, -10^9 ≤ nums[i] ≤ 10^9) # Output: - (List[int]): The reordered list according to the described rules. # Constraints: - The function should operate efficiently with a maximum time complexity of O(n log n). - Consider edge cases such as an empty list, a single-element list, and when all elements are the same. # Example: ```python # Example 1: reorder_list([1, 3, 2, 5, 4]) # Returns: [5, 1, 4, 2, 3] # Example 2: reorder_list([10, -1, 2, 11, -5]) # Returns: [11, -5, 10, -1, 2] # Example 3: reorder_list([3]) # Returns: [3] # Example 4: reorder_list([]) # Returns: [] ``` # Hints: - Use sorting to efficiently arrange the elements first. - Consider using two pointers to alternately select the maximum and minimum values from the sorted list. - Ensure to handle the list in-place if possible, to minimize additional space usage. # Additional Context: The task requires careful rearrangement of the elements to ensure the alternating pattern is maintained. Efficient use of sorting and two-pointer technique can greatly simplify the implementation.
answer:from typing import List def reorder_list(nums: List[int]) -> List[int]: Reorders the list such that the first element is the maximum value, the second element is the minimum value, the third element is the second maximum, the fourth element is the second minimum, and so on. if not nums: return [] nums.sort() result = [] left, right = 0, len(nums) - 1 while left <= right: if left == right: result.append(nums[left]) else: result.append(nums[right]) result.append(nums[left]) left += 1 right -= 1 return result
question:# Problem Statement Design a function `find_common_elements(matrix)` that finds all the common elements present in each row of a given matrix. # Function Signature ```python def find_common_elements(matrix: list[list[int]]) -> list[int]: pass ``` # Input - `matrix`: A list of lists of integers where each inner list represents a row of the matrix. # Output - A list of integers that are common to all rows of the matrix. # Constraints - Each row in the `matrix` contains at least 1 element. - All elements in the matrix are integers, and their values range between `-1000` and `1000`. - The matrix has at least 1 row and at most 100 rows. - Each row has at least 1 element and at most 100 elements. # Example ```python matrix1 = [ [1, 2, 3, 4, 5], [2, 3, 5, 8, 10], [2, 3, 6, 7, 9] ] find_common_elements(matrix1) # Expected output: [2, 3] matrix2 = [ [10, 15, 20, 25], [15, 20, 35, 40, 50], [5, 15, 20, 30] ] find_common_elements(matrix2) # Expected output: [15, 20] ``` # Notes - The order of the output list does not matter. - If there are no common elements across all rows, the function should return an empty list. - Consider edge cases such as a matrix with only one row or a matrix with rows that have no common elements.
answer:def find_common_elements(matrix: list[list[int]]) -> list[int]: if not matrix: return [] # Initialize the common elements set with the first row's elements common_elements = set(matrix[0]) # Iterate through the rest of the rows and perform intersection for row in matrix[1:]: common_elements.intersection_update(row) return list(common_elements)
question:# Scenario You are tasked with developing a system to measure and evaluate the performance of software applications. One of the key metrics is the average response time of a system over a specific period. You have access to predefined functions that fetch system response times. # Task Create a function that calculates the average response time of the system over a given period by utilizing the `get_response_times(start, end)` function. # Function Signature ```python def average_response_time(start: datetime, end: datetime) -> float: pass ``` # Input and Output * **Input**: * `start`: A `datetime` object representing the start of the time period. * `end`: A `datetime` object representing the end of the time period. * **Output**: * Returns a float representing the average response time over the specified period. # Constraints * Utilize the provided `get_response_times(start, end)` function to fetch data. * Assume that the API provides data consistently and without delays. * The `start` time should be before or equal to the `end` time. * Handle edge cases such as no response times within the specified period. # Example ```python from datetime import datetime start_time = datetime(2023, 1, 1, 0, 0, 0) end_time = datetime(2023, 1, 2, 0, 0, 0) result = average_response_time(start_time, end_time) print(result) # Expected to print the average response time for the period from 2023-01-01 00:00:00 to 2023-01-02 00:00:00 ``` # Performance Requirements Ensure the function handles large data sets efficiently and processes the response times within reasonable limits. Optimize for accuracy and performance in varying system loads and durations.
answer:from datetime import datetime from typing import List def get_response_times(start: datetime, end: datetime) -> List[float]: Mock function to simulate fetching of response times. In an actual implementation, this function would fetch data from a database or monitoring system. # Sample data for demonstration: sample_data = { (datetime(2023, 1, 1, 0, 0, 0), datetime(2023, 1, 1, 23, 59, 59)): [200, 210, 190, 220], (datetime(2023, 1, 2, 0, 0, 0), datetime(2023, 1, 2, 23, 59, 59)): [230, 250, 240, 210], } return sample_data.get((start, end), []) def average_response_time(start: datetime, end: datetime) -> float: Calculate the average response time of the system over the given period. Parameters: start (datetime): The start of the time period. end (datetime): The end of the time period. Returns: float: The average response time over the specified period. response_times = get_response_times(start, end) if not response_times: # Handle the case with no data return 0.0 return sum(response_times) / len(response_times)