Topological Sorting28 Aug 2024 | 10 min read A topological sort or topological ordering of a directed graph is a linear ordering of its vertices in which u occurs before v in the ordering for every directed edge uv from vertex u to vertex v. For example, the graph's vertices could represent jobs to be completed, and the edges could reflect requirements that one work must be completed before another. In this case, a topological ordering is just a legitimate task sequence. A topological sort is a graph traversal in which each node v is only visited after all of its dependencies have been visited. If the graph contains no directed cycles, then it is a directed acyclic graph. Any DAG has at least one topological ordering, and there exist techniques for building topological orderings in linear time for any DAG. Topological sorting has many applications, particularly in ranking issues like the feedback arc set. Even if the DAG includes disconnected components, topological sorting is possible. Java CodeNow let's write a sample java code for topological sorting. Output The above Java code gives the following output. Please Choose one of the Operations:: 1. To create a Directed Acyclic Graph (DAG) for topological sort. 2. To print the result of the topological sort. 1 Directed Acyclic Graph (DAG) created successfully. Do you want to continue (Type y or n) y Please Choose one of the Operations:: 1. To create a Directed Acyclic Graph (DAG) for topological sort. 2. To print the result of the topological sort. 2 The result after topological sort of the Directed Acyclic Graph 25 20 15 10 5 0 Do you want to continue (Type y or n) n So, in the above Java code, we have created a class named Graph that will represent a directed graph using adjacency list representation. Different member functions to perform various operations like adding a new node in the graph are also written. A function named topologicalSort() is written to perform the actual task of the topological sort of the graph. The topologicalSort() function internally calls a recursive function named topologicalSortUtil() that consists of the actual logic of the topological sorting of the graph. Once the topological sorting is performed on the graph, the graph's nodes are printed due to the topological operation. C++ CodeLet's see the C++ code, Output The above C++ code gives the following output. Directed Acyclic Graph (DAG) created successfully. The result of topological Sort is 5 4 2 3 1 0 So, in the above C++ code, we created a class named Graph that will represent a directed graph using adjacency list representation. Different member functions to perform various operations like adding a new node in the Graph are also written. Then a function named topologicalSort() is written to perform the actual task of the topological sort of the graph. The topologicalSort() function internally calls a recursive function named topologicalSortUtil() that consists of the actual logic of the topological sorting of the graph. Once the topological sorting is performed on the graph, the graph's nodes are printed due to the topological operation. Advantages of Topological SortingTopological Sorting is mostly used to schedule jobs based on their dependencies. Instruction scheduling, ordering formula cell evaluation when recomputing formula values in spreadsheets, logic synthesis, determining the order of compilation tasks to perform in make files, data serialization, and resolving symbol dependencies in linker are all examples of applications of this type in computer science.
Next TopicTernary Search Tree |
Each node has a left and a right subtree in a binary tree. Any binary tree, including empty, single-node trees, and subtrees, can exist. If the right subtree and the left subtree of the root node are mirror images of each other, then a binary tree...
3 min read
Print greater number of Q queries The field of algorithmic problem-solving is constantly expanding and improving, opening new avenues for creativity and technical breakthroughs. The problem of determining the greater number for a given set of numbers is one of these challenges. Despite its apparent...
5 min read
What Is an AVL Tree? Adelson-Velskii and Landis are the people who discovered it, so the name came from their names i.e., AVL. It is commonly referred to as a height binary tree. An AVL tree is one that has one of the following characteristics at each...
18 min read
The Lowest Common Ancestor (LCA) is a term in graph theory and computer science that is frequently employed in the context of trees, particularly binary trees. The LCA of two nodes in a tree is defined as the lowest (deepest) node that is an ancestor of...
7 min read
Skip list in Data structure What is a skip list? A skip list is a probabilistic data structure. The skip list is used to store a sorted list of elements or data with a linked list. It allows the process of the elements or data to view...
5 min read
Introduction: In a Bipartite graph, we can say that the matching is a type of set of edges that is chosen in such a way that one endpoint doesn't share more than one edge. We can also say that the matching of the maximum number of edges...
6 min read
Introduction An effective algorithmic technique for effectively resolving problems involving arrays and strings is the sliding window approach. Finding contiguous subarrays or substrings that meet specific requirements is a task that it is particularly well suited for. The sliding window technique enables us to efficiently update the window...
5 min read
In this article, we investigate various strategies for achieving this visual representation and examine their application and importance. Binary trees are basic data structures used in computer science for a variety of purposes, including database indexing, file system organisation, and sorting algorithms. While knowing binary trees conceptually...
4 min read
Various data structures in computer science aid in the organization of data in various forms. Trees are popular abstract data structures that simulate a hierarchical tree structure. A tree typically has a root value and subtrees formed by child nodes from parent nodes. Non-linear data structures...
7 min read
In this article, we will learn about the differences between internal sorting and external sorting in detail. Sorting is a technique used for arranging the data in ascending or descending order. The main purpose of sorting technique is to comparison and interchanging position of elements. There...
2 min read
We request you to subscribe our newsletter for upcoming updates.
We provides tutorials and interview questions of all technology like java tutorial, android, java frameworks
G-13, 2nd Floor, Sec-3, Noida, UP, 201301, India