The Complete Guide to Python Recursive Functions: Learn from the Basics

Comprehensive guide to learning Python recursive functions from scratch

Python is a very popular programming language. It has the characteristics of simplicity, readability, and recursion. It is one of the commonly used techniques in Python. Recursion refers to the process of calling itself in a function definition. Recursive functions can decompose complex problems into smaller sub-problems to solve. This article will introduce you to the basic concepts and usage scenarios of recursive functions and provide some specific code examples to help you thoroughly master the use of Python recursive functions.

1. The basic concept of recursive function

Recursive function is a technology that directly or indirectly calls itself in the function definition. It usually consists of two parts: recursive conditions and recursive operations. Recursive conditions are conditions under which a function stops calling itself, and recursive operations are operations that a function needs to perform before or after calling itself.

The basic structure of the recursive function is as follows:

def recursive_function(parameters):
    # 递归条件
    if condition:
        # 终止递归
        return base_case
    else:
        # 递归操作
        recursive_function(modified_parameters)

Among them, parameters represent the parameters passed into the recursive function, condition represents the condition for the recursion to stop, base_case represents the return value when the recursion stops, and modified_parameters represents each The parameters passed in during the recursive call.

2. Usage scenarios of recursive functions

The most common application scenario of recursive functions is to deal with problems involving tree structures and their variants, such as binary tree traversal, graph traversal, etc. In addition, recursive functions can also be used in algorithms such as divide and conquer, dynamic programming, and backtracking to solve problems.

For example, calculating the factorial of a number is a typical recursive problem. The following is an example code for a recursive function that calculates factorial:

def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)

In this example, the recursive function factorial accepts a parameter n and determines whether n is equal to 0. If it is 0, it returns 1, otherwise it returns n times factorial(n-1). In this way, a large problem is divided into small sub-problems and solved step by step through recursion.

3. Precautions for recursive functions

When writing recursive functions, you need to pay attention to the following matters:

1. Make sure that the recursive function stops calling itself to avoid infinite Recursive situations cause the program to crash.
2. In the recursive function, the parameters passed in are updated in time to ensure that the problem size is reduced with each recursive call.
3. Make sure the termination condition of the recursive function is correct, otherwise the recursion may not end normally.
4. To avoid repeated calculations, you can use techniques such as caching or pruning to improve the efficiency of recursive functions.

4. Specific code examples of recursive functions

The following are some common code examples of recursive functions for your reference:

1. Fibona Deed sequence

def fibonacci(n):
    if n <= 1:
        return n
    else:
        return fibonacci(n-1) + fibonacci(n-2)

2. Factorial

def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)

3. Tower of Hanoi

def hanoi(n, source, auxiliary, target):
    if n > 0:
        hanoi(n-1, source, target, auxiliary)
        print("Move disk", n, "from", source, "to", target)
        hanoi(n-1, auxiliary, source, target)

4. Array summation

def array_sum(arr):
    if len(arr) == 0:
        return 0
    else:
        return arr[0] + array_sum(arr[1:])

Summary:

This article introduces a comprehensive guide to Python recursive functions from the basic concepts and usage scenarios of recursive functions to specific code examples. By learning the use of recursive functions, you can better solve complex problems and improve programming efficiency. I hope this article can help you better understand and use Python recursive functions.

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