关于尾递归的使用详解
这几天看到几篇关于尾递归的文章，之前对尾递归没有多大概念，所以回头研究了一下尾递归。
尾递归的概念
尾递归（Tail Recursion）的概念是递归概念的一个子集。对于普通的递归，由于必须要记住递归的调用堆栈，由此产生的耗用是难以估量的。比如下文中php小节第一个例子使用php写一个阶乘函数，就是由于递归造成了栈溢出的错误。尾递归出现的目的就是消除递归栈耗损这个缺憾的。
从代码层面看，尾递归其实一句话就可以说清楚了：
函数的最后一个操作是递归调用
比如"菲波纳锲"数列的php的递归实现：
复制代码 代码如下:
fibonacci.php
function fibonacci($n) {
if ($n return $n;
}
return fibonacci($n - 1) + fibonacci($n - 2);
}
var_dump(fibonacci(30));
这是递归函数，但不是尾递归，因为fibonacci的最后一个操作是加法操作。
转化为尾递归：
复制代码 代码如下:
function fibonacci2($n, $acc1, $acc2) {
if ($n == 0) {
return $acc1;
}
return fibonacci2($n-1, $acc2, $acc1 + $acc2);
}
fibonacci2就是一个尾递归，它增加两个累加器acc1和acc2，并给出初始的值。记住：递归转化为尾递归的思想一定是增加累加器，减少递归外操作。
尾递归在不同语言上的应用也是不同的。最常使用的就是函数式编程Erlang，几乎是所有出现递归的函数全部都修改成为尾递归。下面说一下尾递归在几个不同的语言上的表现和应用。
php中的尾递归
我们做个实验
普通递归：
复制代码 代码如下:
function factorial($n)
{
if($n == 0) {
return 1;
}
return factorial($n-1) * $n;
}
var_dump(factorial(100000000));
尾递归：
复制代码 代码如下:
function factorial($n, $acc)
{
if($n == 0) {
return $acc;
}
return factorial($n-1, $acc * $n);
}
var_dump(factorial(100000000, 1));
实验结果：
事实证明，
尾递归在php中是没有任何优化效果的!
C中的尾递归
在C中的尾递归优化是gcc编译器做的。在gcc编译的时候加上-O2会对尾递归进行优化
我们可以直接看生成的汇编代码：
(使用gdb， gcc –O2 factorial.c –o factorial; disass factorial)
未加-O2生成的汇编：
加了O2优化的汇编：
不要头大，我也是初看汇编，但是这份代码非常简单，去网上稍微搜搜命令，大致就能理解：
复制代码 代码如下:
function factoral(n, sum) {
while(n != 0){
sum = n * sum
n = n-1
}
return sum
}
gcc做的确实是智能优化。
如果你还有兴趣，你可以使用-O3对尾递归进行优化，并查看其中的汇编指令
-O3的优化是直接将循环展开
总结
一般的线性递归修改成为尾递归最大的优势在于减少了递归调用栈的开销。从php那个例子就明显看出来递归开销对程序的影响。但是并不是所有语言都支持尾递归的，即使支持尾递归的语言也一般是在编译阶段对尾递归进行优化，比如上例中的C语言对尾递归的优化。在使用尾递归对代码进行优化的时候，必须先了解这门语言对尾递归的支持。
Hot AI Tools
Undresser.AI Undress
AI-powered app for creating realistic nude photos
AI Clothes Remover
Online AI tool for removing clothes from photos.
Undress AI Tool
Undress images for free
Clothoff.io
AI clothes remover
Video Face Swap
Swap faces in any video effortlessly with our completely free AI face swap tool!
Hot Article
Hot Tools
Notepad++7.3.1
Easy-to-use and free code editor
SublimeText3 Chinese version
Chinese version, very easy to use
Zend Studio 13.0.1
Powerful PHP integrated development environment
Dreamweaver CS6
Visual web development tools
SublimeText3 Mac version
God-level code editing software (SublimeText3)
Hot Topics
1655
14
1414
52
1307
25
1253
29
1228
24
Recursive implementation of C++ functions: Is there a limit to recursion depth?
Apr 23, 2024 am 09:30 AM
The recursion depth of C++ functions is limited, and exceeding this limit will result in a stack overflow error. The limit value varies between systems and compilers, but is usually between 1,000 and 10,000. Solutions include: 1. Tail recursion optimization; 2. Tail call; 3. Iterative implementation.
BTCC tutorial: How to bind and use MetaMask wallet on BTCC exchange?
Apr 26, 2024 am 09:40 AM
MetaMask (also called Little Fox Wallet in Chinese) is a free and well-received encryption wallet software. Currently, BTCC supports binding to the MetaMask wallet. After binding, you can use the MetaMask wallet to quickly log in, store value, buy coins, etc., and you can also get 20 USDT trial bonus for the first time binding. In the BTCCMetaMask wallet tutorial, we will introduce in detail how to register and use MetaMask, and how to bind and use the Little Fox wallet in BTCC. What is MetaMask wallet? With over 30 million users, MetaMask Little Fox Wallet is one of the most popular cryptocurrency wallets today. It is free to use and can be installed on the network as an extension
How to use NetEase Mailbox Master
Mar 27, 2024 pm 05:32 PM
NetEase Mailbox, as an email address widely used by Chinese netizens, has always won the trust of users with its stable and efficient services. NetEase Mailbox Master is an email software specially created for mobile phone users. It greatly simplifies the process of sending and receiving emails and makes our email processing more convenient. So how to use NetEase Mailbox Master, and what specific functions it has. Below, the editor of this site will give you a detailed introduction, hoping to help you! First, you can search and download the NetEase Mailbox Master app in the mobile app store. Search for "NetEase Mailbox Master" in App Store or Baidu Mobile Assistant, and then follow the prompts to install it. After the download and installation is completed, we open the NetEase email account and log in. The login interface is as shown below
How to use Baidu Netdisk app
Mar 27, 2024 pm 06:46 PM
Cloud storage has become an indispensable part of our daily life and work nowadays. As one of the leading cloud storage services in China, Baidu Netdisk has won the favor of a large number of users with its powerful storage functions, efficient transmission speed and convenient operation experience. And whether you want to back up important files, share information, watch videos online, or listen to music, Baidu Cloud Disk can meet your needs. However, many users may not understand the specific use method of Baidu Netdisk app, so this tutorial will introduce in detail how to use Baidu Netdisk app. Users who are still confused can follow this article to learn more. ! How to use Baidu Cloud Network Disk: 1. Installation First, when downloading and installing Baidu Cloud software, please select the custom installation option.
Do C++ lambda expressions support recursion?
Apr 17, 2024 pm 09:06 PM
Yes, C++ Lambda expressions can support recursion by using std::function: Use std::function to capture a reference to a Lambda expression. With a captured reference, a Lambda expression can call itself recursively.
Recursive implementation of C++ functions: Comparative analysis of recursive and non-recursive algorithms?
Apr 22, 2024 pm 03:18 PM
The recursive algorithm solves structured problems through function self-calling. The advantage is that it is simple and easy to understand, but the disadvantage is that it is less efficient and may cause stack overflow. The non-recursive algorithm avoids recursion by explicitly managing the stack data structure. The advantage is that it is more efficient and avoids the stack. Overflow, the disadvantage is that the code may be more complex. The choice of recursive or non-recursive depends on the problem and the specific constraints of the implementation.
How to use Xiaomi Auto app
Apr 01, 2024 pm 09:19 PM
Xiaomi car software provides remote car control functions, allowing users to remotely control the vehicle through mobile phones or computers, such as opening and closing the vehicle's doors and windows, starting the engine, controlling the vehicle's air conditioner and audio, etc. The following is the use and content of this software, let's learn about it together . Comprehensive list of Xiaomi Auto app functions and usage methods 1. The Xiaomi Auto app was launched on the Apple AppStore on March 25, and can now be downloaded from the app store on Android phones; Car purchase: Learn about the core highlights and technical parameters of Xiaomi Auto, and make an appointment for a test drive. Configure and order your Xiaomi car, and support online processing of car pickup to-do items. 3. Community: Understand Xiaomi Auto brand information, exchange car experience, and share wonderful car life; 4. Car control: The mobile phone is the remote control, remote control, real-time security, easy
How to use spaces correctly in Go
Mar 29, 2024 pm 03:42 PM
Go language is a simple, efficient, and highly concurrency programming language. It is an open source language developed by Google. In the Go language, the use of spaces is very important, it can improve the readability and maintainability of the code. This article will introduce how to use spaces correctly in Go language and provide specific code examples. Why you need to use spaces correctly In the programming process, the use of spaces is very important for the readability and beauty of the code. Appropriate use of spaces can make code clearer and easier to read, thus reducing
