#include "cs.h"
/* compute the etree of A (using triu(A), or A'A without forming A'A */
int *cs_etree (const cs *A, int ata)
{
    int 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 (int)) ;		/* allocate result */
    w = cs_malloc (n + (ata ? m : 0), sizeof (int)) ;	/* 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)) ;
}
