// CSparse/Source/cs_etree: compute the elimination tree
// CSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
// SPDX-License-Identifier: LGPL-2.1+
#include "cs.h"
/* compute the etree of A (using triu(A), or A'A without forming A'A */
csi *cs_etree (const cs *A, csi ata)
{
    csi i, k, p, m, n, inext, *Ap, *Ai, *w, *parent, *ancestor, *prev ;
    if (!CS_CSC (A)) return (NULL) ;        /* check inputs */
    m = A->m ; n = A->n ; Ap = A->p ; Ai = A->i ;
    parent = cs_malloc (n, sizeof (csi)) ;              /* allocate result */
    w = cs_malloc (n + (ata ? m : 0), sizeof (csi)) ;   /* get workspace */
    if (!w || !parent) return (cs_idone (parent, NULL, w, 0)) ;
    ancestor = w ; prev = w + n ;
    if (ata) for (i = 0 ; i < m ; i++) prev [i] = -1 ;
    for (k = 0 ; k < n ; k++)
    {
        parent [k] = -1 ;                   /* node k has no parent yet */
        ancestor [k] = -1 ;                 /* nor does k have an ancestor */
        for (p = Ap [k] ; p < Ap [k+1] ; p++)
        {
            i = ata ? (prev [Ai [p]]) : (Ai [p]) ;
            for ( ; i != -1 && i < k ; i = inext)   /* traverse from i to k */
            {
                inext = ancestor [i] ;              /* inext = ancestor of i */
                ancestor [i] = k ;                  /* path compression */
                if (inext == -1) parent [i] = k ;   /* no anc., parent is k */
            }
            if (ata) prev [Ai [p]] = k ;
        }
    }
    return (cs_idone (parent, NULL, w, 1)) ;
}