EulerTour version 1.0
=======================

FULL NAME:

Euler Tour Tree Representation 





DESCRIPTION:

The Euler tour tree representation is a program for representing trees (including subtrees) as euler circuts of directed graphs produced by converting a tree (undirected graph) into a directed graph. The procedure is achieved by replacing each undirected edge in a tree with two directed ones. As a result a list of vertices is computed as they are visited during the traversal of one such graph.





SYNOPSIS:

    #include<vector>
    #include<EulerTour.hpp>

    vector<int|long|unsigned|double> parent {0,1,1,2,1,2,3,4,6,3,2,67,67};    
    vector<int|long|unsigned|double> child  {1,2,4,8,5,67,6,14,15,68,3,11,17};

/* Make Graph */

    /* Construction */
    Graph<int|long|unsigned|double> graph(parent,child);
    /*  OR  */
    Graph<int|long|unsigned|double> graph;
    graph.make(parent,child);

/*  Make ET  */

    /* Construction */
    EulerTour<int|long|unsigned|double> et(0,parent,child);
    /*  OR  */
    EulerTour<int|long|unsigned|double> et(parent,child);
    /*  OR  */
    EulerTour<int|long|unsigned|double> et;
    et.make(0,parent,child);
      /*  or  */
    et.make(parent,child);

/*  Functions */

    et.Traverse(2)        // traverses the tree with 2 as a start and stop point

    et.Clean()            // cleans the treversed path (both dept and value)

    et.GetDepthVec()      // returns the depth vector
                          //    result for 2:      0 1 0 1 2 1 2 1 0 1 2 3 2 1 2 1 0
    et.GetVertexIdVec()   // returns the set of vertices (vector)
                          //    result for 2:      2 8 2 67 11 67 17 67 2 3 6 15 6 3 68 3 2



CONSTRUCTION AND RUNTIME COMPLEXITY:

For: 

|p| - number of elements in parent vector
|c| - number of elements in child vector 

     Graph construction:                        O(|p|+|c|)
     Euler circut computation:                  O(|p|+|c|)


ACKNOWLEDGMENTS:

     -


AUTHOR:

Robert Bakaric <rbakaric@irb.hr>, <bakaric@evolbio.mpg.de>

COPYRIGHT AND LICENSE:

 * Copyright 2015 Robert Bakaric
 * 
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
 * MA 02110-1301, USA.