#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 CS_INT *post, CS_INT *w, CS_INT **head, CS_INT **next)

{

    CS_INT 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 ;

    }

}

CS_INT *cs_counts (const cs *A, const CS_INT *parent, const CS_INT *post, CS_INT ata)

{

    CS_INT 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 (CS_INT)) ;    /* allocate result */

    w = cs_malloc (s, sizeof (CS_INT)) ;                   /* 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 */

}