/*
 * 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)

}

Advertisements