answer:```python from collections import defaultdict, deque def topological_sort(graph): in_degree = defaultdict(int) for node in graph: for neighbor in graph[node]: in_degree[neighbor] += 1 queue = deque([node for node in graph if in_degree[node] == 0]) sorted_order = [] while queue: node = queue.popleft() sorted_order.append(node) for neighbor in graph[node]: in_degree[neighbor] -= 1 if in_degree[neighbor] == 0: queue.append(neighbor) if len(sorted_order) != len(graph): return Graph contains a cycle and cannot be topologically sorted return sorted_order # Example usage: graph = { 'A': ['B', 'C'], 'B': ['D', 'E'], 'C': ['F'], 'D': [], 'E': ['F'], 'F': [] } print(topological_sort(graph)) # Output: ['A', 'C', 'B', 'E', 'D', 'F'] ``` Kahn's Algorithm works by: 1. Calculating the in-degree of each node (number of edges pointing towards it). 2. Creating a queue with nodes having an in-degree of 0 (no edges pointing towards them). 3. While the queue is not empty: * Dequeue a node and add it to the sorted order. * Decrease the in-degree of its neighbors by 1. * Add neighbors with in-degree 0 to the queue. 4. If the sorted order contains all nodes, return it as the topological sorting. If not, the graph contains a cycle, and topological sorting is not possible. This implementation assumes the input graph is represented as a dictionary (adjacency list) where each key is a node and its corresponding value is a list of its neighbors.

answer:```python import sys import heapq def dijkstra(graph, start, end): # Initialize distances to infinity and previous nodes to None distances = {node: sys.maxsize for node in graph} previous = {node: None for node in graph} distances[start] = 0 # Create a priority queue with the starting node queue = [(0, start)] while queue: current_distance, current_node = heapq.heappop(queue) # If we've reached the end node, we can stop if current_node == end: break # Skip if the current distance is greater than the already known distance if current_distance > distances[current_node]: continue # Iterate over the neighbors of the current node for neighbor, weight in graph[current_node].items(): distance = current_distance + weight # If we found a shorter path to the neighbor, update its distance and add it to the queue if distance < distances[neighbor]: distances[neighbor] = distance previous[neighbor] = current_node heapq.heappush(queue, (distance, neighbor)) # Build the shortest path path = [] current_node = end while current_node is not None: path.append(current_node) current_node = previous[current_node] # Return the shortest path and its distance return path[::-1], distances[end] # Example usage: graph = { 'A': {'B': 1, 'C': 4}, 'B': {'A': 1, 'C': 2, 'D': 5}, 'C': {'A': 4, 'B': 2, 'D': 1}, 'D': {'B': 5, 'C': 1} } start_node = 'A' end_node = 'D' shortest_path, shortest_distance = dijkstra(graph, start_node, end_node) print(fThe shortest path from {start_node} to {end_node} is: {shortest_path}) print(fThe shortest distance is: {shortest_distance}) ``` This implementation of Dijkstra's algorithm uses a priority queue to efficiently find the shortest path between two nodes in a weighted graph. It returns both the shortest path and its distance. **Note:** * The graph is represented as a dictionary where each key is a node, and its corresponding value is another dictionary that maps its neighbors to their respective weights. * The algorithm assumes that all weights are non-negative. * If the graph does not contain the end node or there is no path from the start node to the end node, the algorithm will not return a valid result. You might want to add error handling to cover these cases, depending on your specific use case.

answer:Proper error checking and debugging are crucial steps in ensuring the reliability and robustness of your Python program. Here's a concise overview of how to approach error checking and the tools available for debugging: **Error Checking** 1. **Use try-except blocks**: Wrap code that may raise exceptions in `try` blocks, and catch specific exceptions with `except` blocks to handle errors gracefully. 2. **Validate inputs**: Verify the type and value of inputs to prevent errors, especially when dealing with user input or external data. 3. **Use assertions**: Use `assert` statements to verify assumptions about your code's state, helping you catch errors early in development. 4. **Log errors**: Log errors and exceptions to track issues in production, using libraries like `logging`. **Debugging Tools** 1. **Built-in `pdb` module**: Use the `pdb` module to set breakpoints, inspect variables, and step through code. 2. **Print statements**: Strategically place print statements to inspect variable values and code flow. 3. **Logging libraries**: Utilize logging libraries like `loguru` or ` structlog` for more advanced logging capabilities. 4. **IDEs and editors**: Leverage built-in debugging tools in IDEs like PyCharm, VS Code, or Spyder. 5. **Third-party libraries**: * `ipdb`: An interactive debugger with advanced features. * `py-spy`: A sampling profiler for performance optimization. * `line_profiler`: A line-by-line profiler for performance optimization. **Best Practices** 1. **Write unit tests**: Test individual components to catch errors early. 2. **Use type hinting**: Specify expected types for function arguments and return values. 3. **Code reviews**: Regularly review code with peers to catch errors and improve code quality. 4. **Monitor production logs**: Regularly inspect logs to identify and fix issues in production. **Example: Try-except block** ```python try: # Code that may raise an exception x = 1 / 0 except ZeroDivisionError: # Handle the exception print(Cannot divide by zero!) ``` Remember to balance error checking with code readability and performance. Excessive error checking can lead to convoluted code, while insufficient error checking can result in unexpected crashes.

answer:Here are a few examples of how you can perform error checking and input validation in Python: **Example 1: Validating Integer Input** ```python def validate_integer_input(prompt): while True: try: value = int(input(prompt)) if value < 0: print(Please enter a non-negative integer.) else: return value except ValueError: print(Invalid input. Please enter an integer.) age = validate_integer_input(Enter your age: ) ``` **Example 2: Validating String Input with Regular Expressions** ```python import re def validate_email_input(prompt): email_pattern = r^[a-zA-Z0-9_.+-]+@[a-zA-Z0-9-]+.[a-zA-Z0-9-.]+ while True: email = input(prompt) if re.match(email_pattern, email): return email else: print(Invalid email address. Please try again.) email = validate_email_input(Enter your email: ) ``` **Example 3: Validating Dictionary Input** ```python def validate_user_data(data): required_fields = [name, age, email] if not all(field in data for field in required_fields): raise ValueError(Missing required fields) if not isinstance(data[age], int) or data[age] < 0: raise ValueError(Invalid age) return data user_data = { name: John Doe, age: 30, email: [email protected] } try: validated_data = validate_user_data(user_data) except ValueError as e: print(fError: {e}) ``` **Example 4: Using a Validation Library** ```python from voluptuous import Schema, Invalid def validate_user_data(data): schema = Schema({ name: str, age: int, email: str }) try: return schema(data) except Invalid as e: print(fError: {e}) user_data = { name: John Doe, age: 30, email: [email protected] } validated_data = validate_user_data(user_data) ``` These examples demonstrate different approaches to input validation, including: * Using try-except blocks to catch exceptions * Using regular expressions to validate string input * Validating dictionary input using required fields and type checks * Using a validation library like Voluptuous to simplify validation logic