/* ========================================================================= */
/* === AMD_post_tree ======================================================= */
/* ========================================================================= */

/* ------------------------------------------------------------------------- */
/* 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                          */
/* ------------------------------------------------------------------------- */

/* Post-ordering of a supernodal elimination tree.  */

#include "amd_internal.h"

GLOBAL Int AMD_post_tree
(
    Int root,                   /* root of the tree */
    Int k,                      /* start numbering at k */
    Int Child [ ],              /* input argument of size nn, undefined on
                                 * output.  Child [i] is the head of a link
                                 * list of all nodes that are children of node
                                 * i in the tree. */
    const Int Sibling [ ],      /* input argument of size nn, not modified.
                                 * If f is a node in the link list of the
                                 * children of node i, then Sibling [f] is the
                                 * next child of node i.
                                 */
    Int Order [ ],              /* output order, of size nn.  Order [i] = k
                                 * if node i is the kth node of the reordered
                                 * tree. */
    Int Stack [ ]               /* workspace of size nn */
#ifndef NDEBUG
    , Int nn                    /* nodes are in the range 0..nn-1. */
#endif
)
{
    Int f, head, h, i ;

#if 0
    /* --------------------------------------------------------------------- */
    /* recursive version (Stack [ ] is not used): */
    /* --------------------------------------------------------------------- */

    /* this is simple, but can caouse stack overflow if nn is large */
    i = root ;
    for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
    {
        k = AMD_post_tree (f, k, Child, Sibling, Order, Stack, nn) ;
    }
    Order [i] = k++ ;
    return (k) ;
#endif

    /* --------------------------------------------------------------------- */
    /* non-recursive version, using an explicit stack */
    /* --------------------------------------------------------------------- */

    /* push root on the stack */
    head = 0 ;
    Stack [0] = root ;

    while (head >= 0)
    {
        /* get head of stack */
        ASSERT (head < nn) ;
        i = Stack [head] ;
        AMD_DEBUG1 (("head of stack "ID" \n", i)) ;
        ASSERT (i >= 0 && i < nn) ;

        if (Child [i] != EMPTY)
        {
            /* the children of i are not yet ordered */
            /* push each child onto the stack in reverse order */
            /* so that small ones at the head of the list get popped first */
            /* and the biggest one at the end of the list gets popped last */
            for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
            {
                head++ ;
                ASSERT (head < nn) ;
                ASSERT (f >= 0 && f < nn) ;
            }
            h = head ;
            ASSERT (head < nn) ;
            for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
            {
                ASSERT (h > 0) ;
                Stack [h--] = f ;
                AMD_DEBUG1 (("push "ID" on stack\n", f)) ;
                ASSERT (f >= 0 && f < nn) ;
            }
            ASSERT (Stack [h] == i) ;

            /* delete child list so that i gets ordered next time we see it */
            Child [i] = EMPTY ;
        }
        else
        {
            /* the children of i (if there were any) are already ordered */
            /* remove i from the stack and order it.  Front i is kth front */
            head-- ;
            AMD_DEBUG1 (("pop "ID" order "ID"\n", i, k)) ;
            Order [i] = k++ ;
            ASSERT (k <= nn) ;
        }

#ifndef NDEBUG
        AMD_DEBUG1 (("\nStack:")) ;
        for (h = head ; h >= 0 ; h--)
        {
            Int j = Stack [h] ;
            AMD_DEBUG1 ((" "ID, j)) ;
            ASSERT (j >= 0 && j < nn) ;
        }
        AMD_DEBUG1 (("\n\n")) ;
        ASSERT (head < nn) ;
#endif

    }
    return (k) ;
}