// CSparse/Source/cs_counts: column counts for sparse Cholesky
// CSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
// SPDX-License-Identifier: LGPL-2.1+
#include "cs.h"
/* column counts of LL'=A or LL'=A'A, given parent & post ordering */
#define HEAD(k,j) (ata ? head [k] : j)
#define NEXT(J)   (ata ? next [J] : -1)
static void init_ata (cs *AT, const csi *post, csi *w, csi **head, csi **next)
{
    csi i, k, p, m = AT->n, n = AT->m, *ATp = AT->p, *ATi = AT->i ;
    *head = w+4*n, *next = w+5*n+1 ;
    for (k = 0 ; k < n ; k++) w [post [k]] = k ;    /* invert post */
    for (i = 0 ; i < m ; i++)
    {
        for (k = n, p = ATp[i] ; p < ATp[i+1] ; p++) k = CS_MIN (k, w [ATi[p]]);
        (*next) [i] = (*head) [k] ;     /* place row i in linked list k */
        (*head) [k] = i ;
    }
}
csi *cs_counts (const cs *A, const csi *parent, const csi *post, csi ata)
{
    csi i, j, k, n, m, J, s, p, q, jleaf, *ATp, *ATi, *maxfirst, *prevleaf,
        *ancestor, *head = NULL, *next = NULL, *colcount, *w, *first, *delta ;
    cs *AT ;
    if (!CS_CSC (A) || !parent || !post) return (NULL) ;    /* check inputs */
    m = A->m ; n = A->n ;
    s = 4*n + (ata ? (n+m+1) : 0) ;
    delta = colcount = cs_malloc (n, sizeof (csi)) ;    /* allocate result */
    w = cs_malloc (s, sizeof (csi)) ;                   /* get workspace */
    AT = cs_transpose (A, 0) ;                          /* AT = A' */
    if (!AT || !colcount || !w) return (cs_idone (colcount, AT, w, 0)) ;
    ancestor = w ; maxfirst = w+n ; prevleaf = w+2*n ; first = w+3*n ;
    for (k = 0 ; k < s ; k++) w [k] = -1 ;      /* clear workspace w [0..s-1] */
    for (k = 0 ; k < n ; k++)                   /* find first [j] */
    {
        j = post [k] ;
        delta [j] = (first [j] == -1) ? 1 : 0 ;  /* delta[j]=1 if j is a leaf */
        for ( ; j != -1 && first [j] == -1 ; j = parent [j]) first [j] = k ;
    }
    ATp = AT->p ; ATi = AT->i ;
    if (ata) init_ata (AT, post, w, &head, &next) ;
    for (i = 0 ; i < n ; i++) ancestor [i] = i ; /* each node in its own set */
    for (k = 0 ; k < n ; k++)
    {
        j = post [k] ;          /* j is the kth node in postordered etree */
        if (parent [j] != -1) delta [parent [j]]-- ;    /* j is not a root */
        for (J = HEAD (k,j) ; J != -1 ; J = NEXT (J))   /* J=j for LL'=A case */
        {
            for (p = ATp [J] ; p < ATp [J+1] ; p++)
            {
                i = ATi [p] ;
                q = cs_leaf (i, j, first, maxfirst, prevleaf, ancestor, &jleaf);
                if (jleaf >= 1) delta [j]++ ;   /* A(i,j) is in skeleton */
                if (jleaf == 2) delta [q]-- ;   /* account for overlap in q */
            }
        }
        if (parent [j] != -1) ancestor [j] = parent [j] ;
    }
    for (j = 0 ; j < n ; j++)           /* sum up delta's of each child */
    {
        if (parent [j] != -1) colcount [parent [j]] += colcount [j] ;
    }
    return (cs_idone (colcount, AT, w, 1)) ;    /* success: free workspace */
} 
