amd_postorder.c
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/* ========================================================================= */
/* === 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
) ;
}
}
}