PHP Program to Count Sets of 1s and 0s in a Binary Matrix Last Updated : 22 Jul, 2024 Summarize Comments Improve Suggest changes Share Like Article Like Report Given a N x M Binary Matrix, count the number of sets where a set can be formed one or more same values in a row or column. Examples: Input: [[ 1, 0, 1 ], [ 0, 1, 0 ]] Output: 8 Explanation: There are six one-element sets (three 1s and three 0s). There are two two - element sets, the first one consists of the first and the third cells of the first row. The second one consists of the first and the third cells of the second row. Input: [[ 1, 0 ], [ 1, 1 ]] Output: 6The number of non-empty subsets of x elements is 2x - 1. We traverse every row and calculate numbers of 1’s and 0’s cells. For every u zeros and v ones, total sets is 2u - 1 + 2v - 1. We then traverse all columns and compute same values and compute overall sum. We finally subtract m x n from the overall sum as single elements are considered twice. PHP <?php // PHP program to compute number of sets // in a binary matrix. // Number of columns $m = 3; // Number of rows $n = 2; // Function to calculate the number // of non empty sets of cell function countSets($a) { global $m, $n; // Stores the final answer $res = 0; // Traverses row-wise for ($i = 0; $i < $n; $i++) { $u = 0; $v = 0; for ( $j = 0; $j < $m; $j++) $a[$i][$j] ? $u++ : $v++; $res += pow(2, $u) - 1 + pow(2, $v) - 1; } // Traverses column wise for ($i = 0; $i < $m; $i++) { $u = 0;$v = 0; for ($j = 0; $j < $n; $j++) $a[$j][$i] ? $u++ : $v++; $res += pow(2, $u) - 1 + pow(2, $v) - 1; } // At the end subtract // n*m as no of single // sets have been added // twice. return $res-($n*$m); } // Driver Code $a = array(array(1, 0, 1), array(0, 1, 0)); echo countSets($a); ?> Output8Time Complexity: O(n * m) Space Complexity: O(1) as no extra space has been taken.Please refer complete article on Counting sets of 1s and 0s in a binary matrix for more details! Comment More infoAdvertise with us K kartik Follow Improve Article Tags : PHP Similar Reads PHP Tutorial PHP is a widely used, open-source server-side scripting language primarily designed for web development. It is embedded directly into HTML and generates dynamic content on web pages. It allows developers to handle database interactions, session management, and form handling tasks.PHP code is execute 9 min read Top 60+ PHP Interview Questions and Answers -2025 PHP is a popular server-side scripting language, widely known for its efficiency in web development and versatility across various platforms. PHP is extensively utilized by top companies such as Facebook, WordPress, Slack, Wikipedia, MailChimp, and many more due to its robust features and high perfo 15+ min read PHP Introduction PHP stands for Hypertext Preprocessor. It is an open-source, widely used language for web development. Developers can create dynamic and interactive websites by embedding PHP code into HTML. PHP can handle data processing, session management, form handling, and database integration. The latest versi 8 min read Version Control Systems Version Control Systems (VCS) are essential tools used in software development and collaborative projects to track and manage changes to code, documents, and other files. Whether you're working alone or as part of a team, version control helps ensure that your work is safe, organized, and easy to co 7 min read PHP Arrays Arrays are one of the most important data structures in PHP. They allow you to store multiple values in a single variable. PHP arrays can hold values of different types, such as strings, numbers, or even other arrays. Understanding how to use arrays in PHP is important for working with data efficien 5 min read PHP | Functions A function in PHP is a self-contained block of code that performs a specific task. It can accept inputs (parameters), execute a set of statements, and optionally return a value. PHP functions allow code reusability by encapsulating a block of code to perform specific tasks.Functions can accept param 8 min read Difference between HTTP GET and POST Methods HTTP (Hypertext Transfer Protocol) specifies a collection of request methods to specify what action is to be performed on a particular resource. The most commonly used HTTP request methods are GET, POST, PUT, PATCH, and DELETE. This article covers the 2 most common HTTP request methods, i.e. the GET 4 min read PHP Data Types In PHP, data types define the kind of value a variable can hold. PHP is a loosely typed language, meaning you donât need to declare the data type of a variable. It is automatically assigned based on the value. But it is important to understand data types because it is important for writing reliable, 4 min read PHP Operators In PHP, operators are special symbols used to perform operations on variables and values. Operators help you perform a variety of tasks, such as mathematical calculations, string manipulations, logical comparisons, and more. Understanding operators is essential for writing effective and efficient PH 8 min read Creating a Registration and Login System with PHP and MySQL A registration and login system is a fundamental component of many web applications and provides user authentication and security. This allows users to create an account log in with their login credentials and manage their session securely. By using PHP for server-side scripting and MYSQL for databa 12 min read Like