Backend Development
PHP Problem
How to obtain a 10-line Yang Hui triangle through a PHP program
How to obtain a 10-line Yang Hui triangle through a PHP program
Those who have studied programming languages or algorithms are bound to come into contact with the Yang Hui Triangle (one of the outstanding research results of ancient Chinese mathematics). It itself is not profound. Today we will use PHP to write a program to output a Yang Hui triangle with 4 rows and 3 columns.
First of all, let’s understand Yang Hui Triangle.
Yang Hui's triangle is a geometric arrangement of Newton's binomial coefficients in a triangle. Each number in it is equal to the sum of the two numbers above.
We can easily find the pattern from the above picture:
The elements before and after each row are 1
There are several elements in whichever row
Starting from the third row, except for the beginning and end of each row, every other element is above The sum of two adjacent elements (the sum of the number at the same position in the previous row and the previous digit at the same position in the previous row)
After finding the pattern, we can set up the algorithm, Then set the program according to the algorithm (this article uses array double for loop nesting to implement Yang Hui's triangle. If you don't know about for loops, you can check out "PHP Loop Learning 3: How to use for loop statements to traverse arrays" )
Algorithm analysis: There is an array with row i and column j (j is less than or equal to i)
Double for loop, the first level of loop, traverses row i of the array; The second level of loop traverses column j of the array. And the column j value of the array must be less than or equal to the row i value of the array
Use the if statement in the second-level loop body to make a judgment. When
j=1or # When ##i=j, the value is$array[i][j] = 1;## and other times, - $array[i][j]
=
$array[ i-1 ][ j-1 ]$array[ i-1 ][ j ]Let’s take a look at the PHP program code that implements the function:
<?php
function yh_put($max) {
$array = [];
// 循环列数
for($i = 1; $i <= $max; $i++) {
// 循环行数
for( $j=1; $j <= $i; $j++) {
// 每行的第一个和最后一个都是1
if( $j == 1 || $j == $i ) {
echo $array[$i][$j] = 1;
} else {
// 上一行同位置的数 + 上一行同位置的前一位数之和
echo $array[$i][$j] = $array[ $i-1 ][ $j-1 ]+$array[ $i-1 ][ $j ];
}
echo " ";
}
echo "<br>";
}
unset($array);
}
yh_put(10);The output result is:
Finally, I would like to recommend a free video tutorial on PHP arrays:
PHP function array array function video explanationThe above is the detailed content of How to obtain a 10-line Yang Hui triangle through a PHP program. For more information, please follow other related articles on the PHP Chinese website!
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
AI Hentai Generator
Generate AI Hentai for free.
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
1378
52
Best practices for performance optimization in PHP programs
Jun 06, 2023 am 09:20 AM
PHP is a popular programming language that is widely used for website and web application development. However, when PHP applications become more and more complex, performance issues also manifest themselves. Therefore, performance optimization has become an important aspect in PHP development. In this article, we will introduce optimization best practices in PHP programs to help you improve the performance of your applications. 1. Choose the correct PHP version and extensions First, make sure you are using the latest PHP version. New releases usually include performance improvements and bug fixes, as well as
How to use GitHub Actions for automated packaging and deployment of PHP programs?
Jul 31, 2023 pm 02:28 PM
How to use GitHubActions for automated packaging and deployment of PHP programs? Introduction With the rise of cloud computing and DevOps, automation and continuous integration of software development have become increasingly important. GitHubActions is a powerful automation tool that can help developers achieve rapid and efficient software development and deployment. In this article, we will focus on how to use GitHubActions for automated packaging and deployment of PHP programs to improve development efficiency. 1. Assume
Best practices for routing management in PHP programs
Aug 25, 2023 pm 12:28 PM
Route management is one of the most critical parts of any web application because they determine how a URL request will be processed and responded to. PHP is a widely used web programming language and many developers use PHP to build their web applications. In this article, we will discuss the best practices for routing management in PHP programs. Using the MVC Framework Many PHP applications are developed using the MVC (Model-View-Controller) framework. In this framework,
How to package and deploy PHP programs in Ubuntu environment?
Jul 29, 2023 pm 09:42 PM
How to package and deploy PHP programs in Ubuntu environment? With the popularity of PHP development and the increase in application scenarios, we often need to package and deploy the developed PHP programs so that they can be easily deployed and run in different environments. This article will introduce how to package and deploy PHP programs in the Ubuntu environment for developers' reference and use. First, we need to install some necessary software and tools to ensure that we can package and deploy smoothly. We need to install the following packages: PHP: Make sure you have
Copy all contents of one directory to another directory in PHP
Aug 29, 2023 pm 02:41 PM
What is PHP? PHP stands for Hypertext Preprocessor and is a widely used server-side scripting language mainly used for web development. It provides developers with a powerful and flexible platform to create dynamic web pages and applications. PHP can be embedded in HTML code, allowing for seamless integration of server-side functionality with client-side elements. Its syntax is similar to C and Perl, making it relatively easy to learn and use for programmers familiar with these languages. PHP allows server-side scripts to be executed on a web server, generating dynamic content that can be delivered to the user's browser. It supports a variety of databases and is suitable for developing database-driven websites. Additionally, PHP offers a vast ecosystem of open source libraries and frameworks that facilitate rapid development and enhance code
Naive algorithm for PHP program for pattern search
Aug 22, 2023 am 10:57 AM
What is PHP? PHP (Hypertext Preprocessor) is a web development language widely used as a server-side scripting language. It allows developers to embed code in HTML files to create dynamic web pages and interact with databases. PHP is known for its simplicity, versatility, and extensive integration capabilities with popular databases. It offers a wide range of extension capabilities and has a large developer community ensuring there is abundant resources and support What are naive algorithms in PHP? TheNaivealgorithm,alsoknownastheBruteForcealgorithm,isasimplepatternsearchingalgorithmus
How to use caching strategies to reduce the memory footprint of PHP programs?
Aug 10, 2023 pm 12:53 PM
How to use caching strategies to reduce the memory footprint of PHP programs? Summary: When developing PHP programs, we often encounter the problem of excessive memory usage. In order to solve this problem, we can use caching strategies to reduce the memory footprint of PHP programs. This article will introduce how to use caching strategies to optimize PHP programs and give corresponding code examples. 1. Why you need to use caching strategy In PHP, every time a page is requested, the server will re-execute the PHP script to generate the page content. This means that each request will result in a
How to package and deploy PHP programs in a Mac environment?
Jul 31, 2023 pm 03:58 PM
How to package and deploy PHP programs in a Mac environment? In the Mac environment, we can use some tools to package and deploy our PHP programs. This article will introduce how to use Composer and Docker for packaging and deployment. Install Composer and Docker First, we need to install Composer and Docker. Composer is a dependency management tool for PHP, and Docker is a platform for creating and deploying containerized applications. Comp
