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question:def is_palindrome_recursive(s: str) -> bool: Checks if a given string is a palindrome using a recursive approach. Args: s (str): The string to check. Returns: bool: True if the string is a palindrome, False otherwise. >>> is_palindrome_recursive("") == True >>> is_palindrome_recursive("a") == True >>> is_palindrome_recursive("abba") == True >>> is_palindrome_recursive("abcd") == False >>> is_palindrome_recursive("racecar") == True >>> is_palindrome_recursive("hello") == False >>> is_palindrome_recursive("Aba") == False

answer:def is_palindrome_recursive(s): Checks if a given string is a palindrome using a recursive approach. Args: s (str): The string to check. Returns: bool: True if the string is a palindrome, False otherwise. # Define the base case: An empty string or a single character string is a palindrome if len(s) <= 1: return True # Check the characters at the beginning and end of the string if s[0] == s[-1]: # Call the function recursively with the substring excluding the checked characters return is_palindrome_recursive(s[1:-1]) # If the characters do not match, it's not a palindrome return False

question:def analyze_numbers(numbers: List[int]) -> Dict[int, Dict[str, Union[int, List[int]]]]: Analyzes the input list of numbers and returns a dictionary with information about the frequency and indices of each unique number. Arguments: numbers -- list of integers Returns: dict -- a dictionary where keys are the unique integers from the list, and values are dictionaries with 'frequency' and 'indices'. >>> analyze_numbers([1, 2, 2, 3, 1, 2, 4]) {1: {'frequency': 2, 'indices': [0, 4]}, 2: {'frequency': 3, 'indices': [1, 2, 5]}, 3: {'frequency': 1, 'indices': [3]}, 4: {'frequency': 1, 'indices': [6]}} >>> analyze_numbers([5, 6, 7]) {5: {'frequency': 1, 'indices': [0]}, 6: {'frequency': 1, 'indices': [1]}, 7: {'frequency': 1, 'indices': [2]}} >>> analyze_numbers([8, 8, 8, 8]) {8: {'frequency': 4, 'indices': [0, 1, 2, 3]}} >>> analyze_numbers([]) {} >>> analyze_numbers([-1, -2, -2, -3, -1, -2, -4]) {-1: {'frequency': 2, 'indices': [0, 4]}, -2: {'frequency': 3, 'indices': [1, 2, 5]}, -3: {'frequency': 1, 'indices': [3]}, -4: {'frequency': 1, 'indices': [6]}} >>> analyze_numbers([1, -1, 2, -2, 1, -2, 0]) {1: {'frequency': 2, 'indices': [0, 4]}, -1: {'frequency': 1, 'indices': [1]}, 2: {'frequency': 1, 'indices': [2]}, -2: {'frequency': 2, 'indices': [3, 5]}, 0: {'frequency': 1, 'indices': [6]}}

answer:def analyze_numbers(numbers): Analyzes the input list of numbers and returns a dictionary with information about the frequency and indices of each unique number. Arguments: numbers -- list of integers Returns: dict -- a dictionary where keys are the unique integers from the list, and values are dictionaries with 'frequency' and 'indices'. result = {} for index, number in enumerate(numbers): if number not in result: result[number] = {'frequency': 0, 'indices': []} result[number]['frequency'] += 1 result[number]['indices'].append(index) return result

question:def sort_students(student_scores): Sorts the list of student scores first by score in descending order and then by name alphabetically if scores are the same. Args: student_scores (list of tuple): A list where each tuple contains a student's name (str) and score (int). Returns: list of tuple: The sorted list of student scores. Example: >>> sort_students([('Alice', 88), ('Bob', 95), ('Charlie', 88), ('David', 95)]) [('Bob', 95), ('David', 95), ('Alice', 88), ('Charlie', 88)] >>> sort_students([]) [] >>> sort_students([('Alice', 88)]) [('Alice', 88)] >>> sort_students([('Adam', 88), ('Adam', 95), ('Adam', 78)]) [('Adam', 95), ('Adam', 88), ('Adam', 78)] >>> sort_students([('Charlie', 88), ('Alice', 88), ('Bob', 88)]) [('Alice', 88), ('Bob', 88), ('Charlie', 88)] >>> sort_students([('Zoe', 90), ('John', 45), ('Abby', 67), ('Rachel', 74)]) [('Zoe', 90), ('Rachel', 74), ('Abby', 67), ('John', 45)]

answer:def sort_students(student_scores): Sorts the list of student scores first by score in descending order and then by name alphabetically if scores are the same. Args: student_scores (list of tuple): A list where each tuple contains a student's name (str) and score (int). Returns: list of tuple: The sorted list of student scores. # Sort primarily by score in descending order and secondarily by name in ascending order return sorted(student_scores, key=lambda student: (-student[1], student[0]))

question:from typing import List def merge_sorted_arrays(arr1: List[int], arr2: List[int]) -> List[int]: Merges two sorted arrays into a single sorted array. Parameters: arr1 (list of int): First sorted array. arr2 (list of int): Second sorted array. Returns: list of int: Merged sorted array. >>> merge_sorted_arrays([1, 3, 5], [2, 4, 6]) [1, 2, 3, 4, 5, 6] >>> merge_sorted_arrays([1, 2, 2, 3], [2, 2, 4, 5]) [1, 2, 2, 2, 2, 3, 4, 5] >>> merge_sorted_arrays([], []) [] >>> merge_sorted_arrays([1, 2, 3], []) [1, 2, 3] >>> merge_sorted_arrays([], [1, 2, 3]) [1, 2, 3] >>> merge_sorted_arrays([1], [2]) [1, 2] >>> merge_sorted_arrays([2], [1]) [1, 2] >>> merge_sorted_arrays([1, 2, 3, 5], [0, 6, 7, 8, 9, 10]) [0, 1, 2, 3, 5, 6, 7, 8, 9, 10] >>> merge_sorted_arrays([0, 6, 7, 8, 9, 10], [1, 2, 3, 5]) [0, 1, 2, 3, 5, 6, 7, 8, 9, 10]

answer:def merge_sorted_arrays(arr1, arr2): Merges two sorted arrays into a single sorted array. Parameters: arr1 (list of int): First sorted array. arr2 (list of int): Second sorted array. Returns: list of int: Merged sorted array. merged_array = [] i, j = 0, 0 while i < len(arr1) and j < len(arr2): if arr1[i] < arr2[j]: merged_array.append(arr1[i]) i += 1 else: merged_array.append(arr2[j]) j += 1 # Append remaining elements from both arrays, if any while i < len(arr1): merged_array.append(arr1[i]) i += 1 while j < len(arr2): merged_array.append(arr2[j]) j += 1 return merged_array