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question:You are tasked with writing a function called `enhanced_bubble_sort` which sorts a list of integers using a modified version of the bubble sort algorithm. This enhanced version should include: 1. Early termination if the array becomes sorted before completing all passes. 2. A simulation mode that prints out the array after every pass, showing the progress of the sorting algorithm. Function Signature: ```python def enhanced_bubble_sort(arr: List[int], simulation: bool = False) -> List[int]: pass ``` # Input * `arr`: A list of integers (1 ≤ len(arr) ≤ 1000, -1000 ≤ arr[i] ≤ 1000). * `simulation`: A boolean flag indicating whether to print the array after each pass. # Output * The function should return the sorted list of integers in ascending order. # Constraints * Optimize to terminate early if no swaps are needed in a pass. * Ensure the function can handle edge cases such as an empty list or a list already in sorted order efficiently. # Example ```python assert enhanced_bubble_sort([64, 34, 25, 12, 22, 11, 90], True) == [11, 12, 22, 25, 34, 64, 90] ``` Expected output with `simulation=True`: ``` Pass 0: [34, 25, 12, 22, 11, 64, 90] Pass 1: [25, 12, 22, 11, 34, 64, 90] Pass 2: [12, 22, 11, 25, 34, 64, 90] Pass 3: [12, 11, 22, 25, 34, 64, 90] Pass 4: [11, 12, 22, 25, 34, 64, 90] ``` # Notes * If `simulation` is `True`, print the array with format `Pass X: <array>` after each pass where `X` is the pass number starting from 0. * Ensure the function works for all edge cases and optimizes performance by terminating early if the array becomes sorted.

answer:from typing import List def enhanced_bubble_sort(arr: List[int], simulation: bool = False) -> List[int]: n = len(arr) for pass_num in range(n): swapped = False for i in range(n - 1 - pass_num): if arr[i] > arr[i + 1]: arr[i], arr[i + 1] = arr[i + 1], arr[i] swapped = True if simulation: print(f"Pass {pass_num}: {arr}") if not swapped: break return arr

question:# Problem: You're given two integers, `low` and `high`, which define a range `[low, high]` (inclusive). Write a function `sum_dig_pow(low: int, high: int) -> List[int]` to find all numbers in this range such that the number is equal to the sum of its digits raised to consecutive powers from left to right. # Input: * `low` (an integer where 1 <= low <= high <= 10000) - Start of the range (inclusive). * `high` (an integer where low <= high <= 10000) - End of the range (inclusive). # Output: * A list of integers that meet the specified property within the range. # Constraints: * The function should return a list of such numbers or an empty list if there are no such numbers. * Ensure the solution is optimized to handle the maximum constraint efficiently. # Example 1: ```plaintext Input: low = 1, high = 10 Output: [1, 2, 3, 4, 5, 6, 7, 8, 9] ``` # Example 2: ```plaintext Input: low = 50, high = 150 Output: [89, 135] ``` # Example 3: ```plaintext Input: low = 90, high = 100 Output: [] ``` # Explanation: 1. For the number 89: - 8^1 + 9^2 = 8 + 81 = 89, hence valid. 2. For the number 135: - 1^1 + 3^2 + 5^3 = 1 + 9 + 125 = 135, hence valid. Your task is to implement the `sum_dig_pow` function to achieve the desired functionality.

answer:from typing import List def sum_dig_pow(low: int, high: int) -> List[int]: Finds all numbers in the range [low, high] such that the number is equal to the sum of its digits raised to consecutive powers from left to right. def is_valid_number(num: int) -> bool: str_num = str(num) sum_dig_pow = sum(int(str_num[i]) ** (i + 1) for i in range(len(str_num))) return sum_dig_pow == num return [num for num in range(low, high + 1) if is_valid_number(num)]

question:# Graph Traversal Challenge You are tasked with implementing two fundamental graph traversal algorithms: Depth-First Search (DFS) and Breadth-First Search (BFS). Given a graph represented as an adjacency list and a starting node, your task is to implement both traversals and return the list of nodes in the order they were visited. # Input - A graph represented as a dictionary where keys are nodes, and values are lists of connected nodes. - A starting node which is guaranteed to be a key in the graph. # Output - Two lists: One containing the order of nodes visited by DFS, and the other containing the order visited by BFS. # Constraints - The graph does not contain self-loops or multiple edges between the same nodes. - All node values are unique integers. - The graph may be disconnected. - The graph contains at most 1000 nodes and 10000 edges. # Performance Requirements - Must handle the upper limits of the constraints efficiently. - DFS iteration and recursion should both handle deep graph structures without performance degradation. # Example ```python graph = { 0: [1, 2], 1: [2], 2: [0, 3], 3: [3] } start_node = 2 dfs_order = dfs_traverse(graph, start_node) bfs_order = bfs_traverse(graph, start_node) print("DFS Order:", dfs_order) print("BFS Order:", bfs_order) ``` # Expected Output ``` DFS Order: [2, 0, 1, 3] BFS Order: [2, 0, 3, 1] ``` # Task Implement the following functions: ```python def dfs_traverse(graph, start): Return the list of nodes in the order they are visited by depth-first search. pass def bfs_traverse(graph, start): Return the list of nodes in the order they are visited by breadth-first search. pass ```

answer:def dfs_traverse(graph, start): Return the list of nodes in the order they are visited by depth-first search. visited = [] def dfs(node): if node not in visited: visited.append(node) for neighbor in graph.get(node, []): dfs(neighbor) dfs(start) return visited def bfs_traverse(graph, start): Return the list of nodes in the order they are visited by breadth-first search. visited = [] queue = [start] while queue: node = queue.pop(0) if node not in visited: visited.append(node) queue.extend(neighbor for neighbor in graph.get(node, []) if neighbor not in visited) return visited

question:# Coding Challenge You are tasked with implementing a function to match strings against given patterns with support for special characters. This function should adopt a dynamic programming approach to ensure efficient and comprehensive matching. Function Signature ```python def is_match(s: str, p: str) -> bool: Determine if the given input string matches the pattern string with special characters '.' and '*'. Args: s : str : Input string. p : str : Pattern string containing '.' and '*'. Returns: bool : True if 's' matches pattern 'p', otherwise False. ``` Input - `s` (string): The input string, containing only lowercase alphabets. - `p` (string): The pattern string, which may contain lowercase alphabets, '.' and/or '*'. Output - Returns `True` if the input string `s` matches the full pattern `p`, otherwise returns `False`. Examples ```python print(is_match("aa", "a")) # Expected Output: False print(is_match("aa", "aa")) # Expected Output: True print(is_match("aaa", "aa")) # Expected Output: False print(is_match("aa", "a*")) # Expected Output: True print(is_match("aa", ".*")) # Expected Output: True print(is_match("ab", ".*")) # Expected Output: True print(is_match("aab", "c*a*b")) # Expected Output: True ``` Constraints - Both `s` and `p` will contain at most 1000 characters. - Characters in both strings will be lowercase letters or special characters (in `p` only). Evaluation Criteria - Correctness and completeness of the implementation. - Efficient handling of edge cases and performance concerns. - Clarity and readability of the code. Develop an efficient and accurate solution that demonstrates your understanding of dynamic programming and its application in regular expression matching.

answer:def is_match(s: str, p: str) -> bool: Determine if the given input string matches the pattern string with special characters '.' and '*'. Args: s : str : Input string. p : str : Pattern string containing '.' and '*'. Returns: bool : True if 's' matches pattern 'p', otherwise False. # dp[i][j] will be True if the first i characters in s match the first j characters in p dp = [[False] * (len(p) + 1) for _ in range(len(s) + 1)] # Base case: both s and p are empty dp[0][0] = True # Handle patterns with '*' at the beginning for j in range(1, len(p) + 1): if p[j - 1] == '*': dp[0][j] = dp[0][j - 2] # Populate the dp table for i in range(1, len(s) + 1): for j in range(1, len(p) + 1): if p[j - 1] == s[i - 1] or p[j - 1] == '.': dp[i][j] = dp[i - 1][j - 1] elif p[j - 1] == '*': dp[i][j] = dp[i][j - 2] or (dp[i - 1][j] and (s[i - 1] == p[j - 2] or p[j - 2] == '.')) return dp[len(s)][len(p)]