/* ========================================================================= */
/* === AMD_postorder ======================================================= */
/* ========================================================================= */

/* ------------------------------------------------------------------------- */
/* AMD, Copyright (c) Timothy A. Davis,                                      */
/* Patrick R. Amestoy, and Iain S. Duff.  See ../README.txt for License.     */
/* email: davis at cise.ufl.edu    CISE Department, Univ. of Florida.        */
/* web: http://www.cise.ufl.edu/research/sparse/amd                          */
/* ------------------------------------------------------------------------- */

/* Perform a postordering (via depth-first search) of an assembly tree. */

#include "amd_internal.h"

GLOBAL void AMD_postorder
(
    /* inputs, not modified on output: */
    Int nn,             /* nodes are in the range 0..nn-1 */
    Int Parent [ ],     /* Parent [j] is the parent of j, or EMPTY if root */
    Int Nv [ ],         /* Nv [j] > 0 number of pivots represented by node j,
                         * or zero if j is not a node. */
    Int Fsize [ ],      /* Fsize [j]: size of node j */

    /* output, not defined on input: */
    Int Order [ ],      /* output post-order */

    /* workspaces of size nn: */
    Int Child [ ],
    Int Sibling [ ],
    Int Stack [ ]
)
{
    Int i, j, k, parent, frsize, f, fprev, maxfrsize, bigfprev, bigf, fnext ;

    for (j = 0 ; j < nn ; j++)
    {
        Child [j] = EMPTY ;
        Sibling [j] = EMPTY ;
    }

    /* --------------------------------------------------------------------- */
    /* place the children in link lists - bigger elements tend to be last */
    /* --------------------------------------------------------------------- */

    for (j = nn-1 ; j >= 0 ; j--)
    {
        if (Nv [j] > 0)
        {
            /* this is an element */
            parent = Parent [j] ;
            if (parent != EMPTY)
            {
                /* place the element in link list of the children its parent */
                /* bigger elements will tend to be at the end of the list */
                Sibling [j] = Child [parent] ;
                Child [parent] = j ;
            }
        }
    }

#ifndef NDEBUG
    {
        Int nels, ff, nchild ;
        AMD_DEBUG1 (("\n\n================================ AMD_postorder:\n"));
        nels = 0 ;
        for (j = 0 ; j < nn ; j++)
        {
            if (Nv [j] > 0)
            {
                AMD_DEBUG1 (( ""ID" :  nels "ID" npiv "ID" size "ID
                    " parent "ID" maxfr "ID"\n", j, nels,
                    Nv [j], Fsize [j], Parent [j], Fsize [j])) ;
                /* this is an element */
                /* dump the link list of children */
                nchild = 0 ;
                AMD_DEBUG1 (("    Children: ")) ;
                for (ff = Child [j] ; ff != EMPTY ; ff = Sibling [ff])
                {
                    AMD_DEBUG1 ((ID" ", ff)) ;
                    ASSERT (Parent [ff] == j) ;
                    nchild++ ;
                    ASSERT (nchild < nn) ;
                }
                AMD_DEBUG1 (("\n")) ;
                parent = Parent [j] ;
                if (parent != EMPTY)
                {
                    ASSERT (Nv [parent] > 0) ;
                }
                nels++ ;
            }
        }
    }
    AMD_DEBUG1 (("\n\nGo through the children of each node, and put\n"
                 "the biggest child last in each list:\n")) ;
#endif

    /* --------------------------------------------------------------------- */
    /* place the largest child last in the list of children for each node */
    /* --------------------------------------------------------------------- */

    for (i = 0 ; i < nn ; i++)
    {
        if (Nv [i] > 0 && Child [i] != EMPTY)
        {

#ifndef NDEBUG
            Int nchild ;
            AMD_DEBUG1 (("Before partial sort, element "ID"\n", i)) ;
            nchild = 0 ;
            for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
            {
                ASSERT (f >= 0 && f < nn) ;
                AMD_DEBUG1 (("      f: "ID"  size: "ID"\n", f, Fsize [f])) ;
                nchild++ ;
                ASSERT (nchild <= nn) ;
            }
#endif

            /* find the biggest element in the child list */
            fprev = EMPTY ;
            maxfrsize = EMPTY ;
            bigfprev = EMPTY ;
            bigf = EMPTY ;
            for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
            {
                ASSERT (f >= 0 && f < nn) ;
                frsize = Fsize [f] ;
                if (frsize >= maxfrsize)
                {
                    /* this is the biggest seen so far */
                    maxfrsize = frsize ;
                    bigfprev = fprev ;
                    bigf = f ;
                }
                fprev = f ;
            }
            ASSERT (bigf != EMPTY) ;

            fnext = Sibling [bigf] ;

            AMD_DEBUG1 (("bigf "ID" maxfrsize "ID" bigfprev "ID" fnext "ID
                " fprev " ID"\n", bigf, maxfrsize, bigfprev, fnext, fprev)) ;

            if (fnext != EMPTY)
            {
                /* if fnext is EMPTY then bigf is already at the end of list */

                if (bigfprev == EMPTY)
                {
                    /* delete bigf from the element of the list */
                    Child [i] = fnext ;
                }
                else
                {
                    /* delete bigf from the middle of the list */
                    Sibling [bigfprev] = fnext ;
                }

                /* put bigf at the end of the list */
                Sibling [bigf] = EMPTY ;
                ASSERT (Child [i] != EMPTY) ;
                ASSERT (fprev != bigf) ;
                ASSERT (fprev != EMPTY) ;
                Sibling [fprev] = bigf ;
            }

#ifndef NDEBUG
            AMD_DEBUG1 (("After partial sort, element "ID"\n", i)) ;
            for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
            {
                ASSERT (f >= 0 && f < nn) ;
                AMD_DEBUG1 (("        "ID"  "ID"\n", f, Fsize [f])) ;
                ASSERT (Nv [f] > 0) ;
                nchild-- ;
            }
            ASSERT (nchild == 0) ;
#endif

        }
    }

    /* --------------------------------------------------------------------- */
    /* postorder the assembly tree */
    /* --------------------------------------------------------------------- */

    for (i = 0 ; i < nn ; i++)
    {
        Order [i] = EMPTY ;
    }

    k = 0 ;

    for (i = 0 ; i < nn ; i++)
    {
        if (Parent [i] == EMPTY && Nv [i] > 0)
        {
            AMD_DEBUG1 (("Root of assembly tree "ID"\n", i)) ;
            k = AMD_post_tree (i, k, Child, Sibling, Order, Stack
#ifndef NDEBUG
                , nn
#endif
                ) ;
        }
    }
}