Dynamic programming (DP) optimizes the solution process by breaking down complex problems into simpler subproblems and storing their results to avoid repeated calculations. There are two main methods: 1. Top-down (memorization): recursively decompose the problem and use cache to store intermediate results; 2. Bottom-up (table): Iteratively build solutions from the basic situation. Suitable for scenarios where maximum/minimum values, optimal solutions or overlapping subproblems are required, such as Fibonacci sequences, backpacking problems, etc. In Python, it can be implemented through decorators or arrays, and attention should be paid to identifying recursive relationships, defining the benchmark situation, and optimizing the complexity of space.

Python's socket module is the basis of network programming, providing low-level network communication functions, suitable for building client and server applications. To set up a basic TCP server, you need to use socket.socket() to create objects, bind addresses and ports, call .listen() to listen for connections, and accept client connections through .accept(). To build a TCP client, you need to create a socket object and call .connect() to connect to the server, then use .sendall() to send data and .recv() to receive responses. To handle multiple clients, you can use 1. Threads: start a new thread every time you connect; 2. Asynchronous I/O: For example, the asyncio library can achieve non-blocking communication. Things to note

The core answer to Python list slicing is to master the [start:end:step] syntax and understand its behavior. 1. The basic format of list slicing is list[start:end:step], where start is the starting index (included), end is the end index (not included), and step is the step size; 2. Omit start by default start from 0, omit end by default to the end, omit step by default to 1; 3. Use my_list[:n] to get the first n items, and use my_list[-n:] to get the last n items; 4. Use step to skip elements, such as my_list[::2] to get even digits, and negative step values ??can invert the list; 5. Common misunderstandings include the end index not

Polymorphism is a core concept in Python object-oriented programming, referring to "one interface, multiple implementations", allowing for unified processing of different types of objects. 1. Polymorphism is implemented through method rewriting. Subclasses can redefine parent class methods. For example, the spoke() method of Animal class has different implementations in Dog and Cat subclasses. 2. The practical uses of polymorphism include simplifying the code structure and enhancing scalability, such as calling the draw() method uniformly in the graphical drawing program, or handling the common behavior of different characters in game development. 3. Python implementation polymorphism needs to satisfy: the parent class defines a method, and the child class overrides the method, but does not require inheritance of the same parent class. As long as the object implements the same method, this is called the "duck type". 4. Things to note include the maintenance

Python's datetime module can meet basic date and time processing requirements. 1. You can get the current date and time through datetime.now(), or you can extract .date() and .time() respectively. 2. Can manually create specific date and time objects, such as datetime(year=2025, month=12, day=25, hour=18, minute=30). 3. Use .strftime() to output strings in format. Common codes include %Y, %m, %d, %H, %M, and %S; use strptime() to parse the string into a datetime object. 4. Use timedelta for date shipping

The "Hello,World!" program is the most basic example written in Python, which is used to demonstrate the basic syntax and verify that the development environment is configured correctly. 1. It is implemented through a line of code print("Hello,World!"), and after running, the specified text will be output on the console; 2. The running steps include installing Python, writing code with a text editor, saving as a .py file, and executing the file in the terminal; 3. Common errors include missing brackets or quotes, misuse of capital Print, not saving as .py format, and running environment errors; 4. Optional tools include local text editor terminal, online editor (such as replit.com)

To generate a random string, you can use Python's random and string module combination. The specific steps are: 1. Import random and string modules; 2. Define character pools such as string.ascii_letters and string.digits; 3. Set the required length; 4. Call random.choices() to generate strings. For example, the code includes importrandom and importstring, set length=10, characters=string.ascii_letters string.digits and execute ''.join(random.c

TuplesinPythonareimmutabledatastructuresusedtostorecollectionsofitems,whereaslistsaremutable.Tuplesaredefinedwithparenthesesandcommas,supportindexing,andcannotbemodifiedaftercreation,makingthemfasterandmorememory-efficientthanlists.Usetuplesfordatain