question:# Question: Implement a Custom Sorting Algorithm You are provided with two sorting algorithms: Quick Sort and Merge Sort. Your task is to implement a similar yet distinct custom sorting algorithm called "Custom Sort" that sorts a list of integers. Once implemented, benchmark its performance against the provided Quick Sort and Merge Sort algorithms using the included `benchmark_custom_sort` function. **Function Signature**: ```python def custom_sort(arr: List[int]) -> List[int]: pass ``` # Objectives: 1. Implement the `custom_sort` function to sort a list of integers. 2. Benchmark the performance of your custom sorting algorithm against Quick Sort and Merge Sort using the `benchmark_custom_sort` function. # Constraints: * The input list (`arr`) will contain integers ranging from -10^6 to 10^6. * The length of the input list will be between 1 and 10^5. * Your implementation should efficiently handle typical input sizes within the given constraints. # Example: ```python >>> custom_sort([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5]) [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9] >>> custom_sort([12, 4, 78, 34, 23, 56, 89]) [4, 12, 23, 34, 56, 78, 89] >>> custom_sort([5, 2, 9, 1, 5, 6]) [1, 2, 5, 5, 6, 9] ``` # Guidelines: 1. Your custom sorting algorithm should not simply be a replication of Quick Sort or Merge Sort. 2. You should ensure your implementation is optimal for typical input sizes under the given constraints. 3. Use the following `benchmark_custom_sort` function to compare the performance of your implementation against Quick Sort and Merge Sort: ```python import timeit from typing import List def quick_sort(arr: List[int]) -> List[int]: if len(arr) <= 1: return arr pivot = arr[len(arr) // 2] left = [x for x in arr if x < pivot] middle = [x for x in arr if x == pivot] right = [x for x in arr if x > pivot] return quick_sort(left) + middle + quick_sort(right) def merge_sort(arr: List[int]) -> List[int]: if len(arr) <= 1: return arr mid = len(arr) // 2 left = merge_sort(arr[:mid]) right = merge_sort(arr[mid:]) return merge(left, right) def merge(left: List[int], right: List[int]) -> List[int]: result = [] left_index, right_index = 0, 0 while left_index < len(left) and right_index < len(right): if left[left_index] < right[right_index]: result.append(left[left_index]) left_index += 1 else: result.append(right[right_index]) right_index += 1 result.extend(left[left_index:]) result.extend(right[right_index:]) return result def benchmark_custom_sort() -> None: Benchmark code for comparing 3 functions, including a custom implementation. def do_benchmark(arr: List[int]) -> None: setup = "import __main__ as z" print(f"Benchmark when arr = {arr[:10]} (truncated for display):") print(f"{quick_sort(arr)[:10]} (truncated for display)") timing = timeit.timeit(f"z.quick_sort({arr[:10]})", setup=setup, number=10) print(f"Quick Sort runs in {timing} seconds") print(f"{merge_sort(arr)[:10]} (truncated for display)") timing = timeit.timeit(f"z.merge_sort({arr[:10]})", setup=setup, number=10) print(f"Merge Sort runs in {timing} seconds") print(f"{custom_sort(arr)[:10]} (truncated for display)") timing = timeit.timeit(f"z.custom_sort({arr[:10]})", setup=setup, number=10) print(f"Custom Sort runs in {timing} seconds") for arr in ([3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5], [12, 4, 78, 34, 23, 56, 89], [5, 2, 9, 1, 5, 6]): do_benchmark(arr) print() # Example implementations of quick_sort and merge_sort for the benchmark function. def quick_sort(arr: List[int]) -> List[int]: if len(arr) <= 1: return arr pivot = arr[len(arr) // 2] left = [x for x in arr if x < pivot] middle = [x for x in arr if x == pivot] right = [x for x in arr if x > pivot] return quick_sort(left) + middle + quick_sort(right) def merge_sort(arr: List[int]) -> List[int]: if len(arr) <= 1: return arr mid = len(arr) // 2 left = merge_sort(arr[:mid]) right = merge_sort(arr[mid:]) return merge(left, right) def merge(left: List[int], right: List[int]) -> List[int]: result = [] left_index, right_index = 0, 0 while left_index < len(left) and right_index < len(right): if left[left_index] < right[right_index]: result.append(left[left_index]) left_index += 1 else: result.append(right[right_index]) right_index += 1 result.extend(left[left_index:]) result.extend(right[right_index:]) return result ```

question:# Question: Anagram Finder in a Text File Write a program that reads a text file and identifies all sets of anagrams present in the file. An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once. **Task Requirements:** 1. Implement a function `find_anagrams(file_path: str) -> List[List[str]]`: - **Description**: This function should read a text file where each line contains a single word. It should identify and return all sets of anagrams contained within the file. - **Input**: A string `file_path` which is the path to the text file containing words. - **Output**: A list of lists, where each sublist contains words that are anagrams of each other. # Constraints - The words in the file are made up of lowercase English letters only. - The file can be large, so the implementation should be efficient both in terms of time and space complexity. # Example Let's assume the contents of `words.txt` are: ``` listen silent enlist rat tar art cat tac act dog god ``` ```python # Example of find_anagrams function # Assuming the file 'words.txt' contains the words above assert find_anagrams('words.txt') == [['listen', 'silent', 'enlist'], ['rat', 'tar', 'art'], ['cat', 'tac', 'act'], ['dog', 'god']] ``` # Implementation Details - Ensure your solution can handle files with a large number of words efficiently. - Think about how you can use data structures to group words that are anagrams. - Remember to close the file properly after reading its contents. # Performance Requirements - Aim for O(n * m) time complexity, where n is the number of words in the file and m is the average length of the words. # Additional Notes - You can assume that the input file exists and is accessible for reading. - You can use standard Python libraries and data structures to aid with your implementation.

question:# Network Packet Validity Checker You are tasked with implementing a utility to verify the validity of network packets based on a list of specified rules. # Objective: Write a function `validate_packets(packets: List[Dict[str, Any]], rules: Dict[str, List[Union[int, str]]]) -> List[int]` that takes a list of packet dictionaries and a dictionary of rules and returns a list of indices of the packets that are valid. # Requirements: 1. A packet is represented as a dictionary with keys corresponding to field names and values corresponding to field values. 2. The rules dictionary has field names as keys and a list of acceptable values or ranges as values. A range is specified as a list `[min, max]`. 3. A packet is valid only if it meets all the specified rules. 4. The function should ignore fields not specified in the rules and treat packets missing required fields as invalid. # Constraints: 1. `1 <= len(packets) <= 10^4` - The list can contain up to 10,000 packets. 2. Each packet dictionary can have up to 100 fields. 3. Each field name and value can be of string type and/or numerical type, but rules should be applied strictly based on their types. # Example: ```python >>> packets = [ ... {"src": "192.168.1.1", "dst": "192.168.2.1", "size": 150}, ... {"src": "192.168.1.2", "dst": "192.168.2.2", "size": 50}, ... {"src": "192.168.1.1", "dst": "192.168.2.1", "size": 2000} ... ] >>> rules = { ... "src": ["192.168.1.1", "192.168.1.2"], ... "dst": ["192.168.2.1", "192.168.2.3"], ... "size": [0, 1000] ... } >>> validate_packets(packets, rules) [0, 1] ``` # Hints: - Utilize Python's `in` keyword for checking membership in lists. - Carefully handle both ranges and explicit values during validation. - Ensure that the function skips unnecessary checks for fields not in the rules, improving efficiency.

question:# Coding Assessment Question Context: You are required to implement an algorithm that sorts a list of strings based on their lengths. In case of a tie where two strings have the same length, the strings should maintain their relative order from the original list. This sorting approach is a stable sort. Task: Implement the function `stable_length_sort(strings: List[str]) -> List[str]` which: 1. Accepts a list of strings. 2. Returns a new list of strings sorted by their length in ascending order. Input: - `strings`: A list of strings where each string is non-empty and the list can have up to `1000` strings. Output: - A list of strings sorted by their length in ascending order and maintaining relative order for strings with the same length. Constraints: 1. `1 <= len(strings) <= 1000` (There will always be at least one string). 2. Each string will have a length between `1` and `100`. Example: ```python strings = ["word", "longest", "a", "verylongword", "mid"] assert stable_length_sort(strings) == ["a", "mid", "word", "longest", "verylongword"] ``` Note: - The sorting algorithm should be stable, maintaining the relative order of strings with the same length from the original list. You may use the following function skeleton: ```python def stable_length_sort(strings: List[str]) -> List[str]: pass ```