/* * The MIT License * * Copyright 2012 Abhijit Gaikwad <gaikwad.abhijit@gmail.com>. * * Permission is hereby granted, free of charge, to any person obtaining a copy * of this software and associated documentation files (the "Software"), to deal * in the Software without restriction, including without limitation the rights * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell * copies of the Software, and to permit persons to whom the Software is * furnished to do so, subject to the following conditions: * * The above copyright notice and this permission notice shall be included in * all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN * THE SOFTWARE. */ package com.gabhi.sorting; /** * * @author Abhijit Gaikwad <gaikwad.abhijit@gmail.com> * visit http://gabhi.com */ public class TopologicalSorting { //Topological sorting //In computer science, a topological sort (sometimes abbreviated topsort or toposort) or topological ordering of a directed graph is a linear ordering of its vertices such that, for every edge uv, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time. //L ← Empty list that will contain the sorted elements //S ← Set of all nodes with no incoming edges //while S is non-empty do // remove a node n from S // insert n into L // for each node m with an edge e from n to m do // remove edge e from the graph // if m has no other incoming edges then // insert m into S //if graph has edges then // return error (graph has at least one cycle) //else // return L (a topologically sorted order) }

# Topological Sorting

**11**
*Saturday*
Aug 2012

Posted Sorting

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