#include "cs.h"
/* breadth-first search for coarse decomposition (C0,C1,R1 or R0,R3,C3) */
static int cs_bfs (const cs *A, int n, int *wi, int *wj, int *queue,
    const int *imatch, const int *jmatch, int mark)
{
    int *Ap, *Ai, head = 0, tail = 0, j, i, p, j2 ;
    cs *C ;
    for (j = 0 ; j < n ; j++)		/* place all unmatched nodes in queue */
    {
	if (imatch [j] >= 0) continue ;	/* skip j if matched */
	wj [j] = 0 ;			/* j in set C0 (R0 if transpose) */
	queue [tail++] = j ;		/* place unmatched col j in queue */
    }
    if (tail == 0) return (1) ;		/* quick return if no unmatched nodes */
    C = (mark == 1) ? ((cs *) A) : cs_transpose (A, 0) ;
    if (!C) return (0) ;		/* bfs of C=A' to find R3,C3 from R0 */
    Ap = C->p ; Ai = C->i ;
    while (head < tail)			/* while queue is not empty */
    {
	j = queue [head++] ;		/* get the head of the queue */
	for (p = Ap [j] ; p < Ap [j+1] ; p++)
	{
	    i = Ai [p] ;
	    if (wi [i] >= 0) continue ;	/* skip if i is marked */
	    wi [i] = mark ;		/* i in set R1 (C3 if transpose) */
	    j2 = jmatch [i] ;		/* traverse alternating path to j2 */
	    if (wj [j2] >= 0) continue ;/* skip j2 if it is marked */
	    wj [j2] = mark ;		/* j2 in set C1 (R3 if transpose) */
	    queue [tail++] = j2 ;	/* add j2 to queue */
	}
    }
    if (mark != 1) cs_spfree (C) ;	/* free A' if it was created */
    return (1) ;
}

/* collect matched rows and columns into p and q */
static void cs_matched (int n, const int *wj, const int *imatch, int *p, int *q,
    int *cc, int *rr, int set, int mark)
{
    int kc = cc [set], j ;
    int kr = rr [set-1] ;
    for (j = 0 ; j < n ; j++)
    {
	if (wj [j] != mark) continue ;	    /* skip if j is not in C set */
	p [kr++] = imatch [j] ;
	q [kc++] = j ;
    }
    cc [set+1] = kc ;
    rr [set] = kr ;
}

/* collect unmatched rows into the permutation vector p */
static void cs_unmatched (int m, const int *wi, int *p, int *rr, int set)
{
    int i, kr = rr [set] ;
    for (i = 0 ; i < m ; i++) if (wi [i] == 0) p [kr++] = i ;
    rr [set+1] = kr ;
}

/* return 1 if row i is in R2 */
static int cs_rprune (int i, int j, double aij, void *other)
{
    int *rr = (int *) other ;
    return (i >= rr [1] && i < rr [2]) ;
}

/* Given A, compute coarse and then fine dmperm */
csd *cs_dmperm (const cs *A, int seed)
{
    int m, n, i, j, k, cnz, nc, *jmatch, *imatch, *wi, *wj, *pinv, *Cp, *Ci,
	*ps, *rs, nb1, nb2, *p, *q, *cc, *rr, *r, *s, ok ;
    cs *C ;
    csd *D, *scc ;
    /* --- Maximum matching ------------------------------------------------- */
    if (!CS_CSC (A)) return (NULL) ;		/* check inputs */
    m = A->m ; n = A->n ;
    D = cs_dalloc (m, n) ;			/* allocate result */
    if (!D) return (NULL) ;
    p = D->p ; q = D->q ; r = D->r ; s = D->s ; cc = D->cc ; rr = D->rr ;
    jmatch = cs_maxtrans (A, seed) ;		/* max transversal */
    imatch = jmatch + m ;			/* imatch = inverse of jmatch */
    if (!jmatch) return (cs_ddone (D, NULL, jmatch, 0)) ;
    /* --- Coarse decomposition --------------------------------------------- */
    wi = r ; wj = s ;				/* use r and s as workspace */
    for (j = 0 ; j < n ; j++) wj [j] = -1 ;	/* unmark all cols for bfs */
    for (i = 0 ; i < m ; i++) wi [i] = -1 ;	/* unmark all rows for bfs */
    cs_bfs (A, n, wi, wj, q, imatch, jmatch, 1) ;	/* find C1, R1 from C0*/
    ok = cs_bfs (A, m, wj, wi, p, jmatch, imatch, 3) ;	/* find R3, C3 from R0*/
    if (!ok) return (cs_ddone (D, NULL, jmatch, 0)) ;
    cs_unmatched (n, wj, q, cc, 0) ;			/* unmatched set C0 */
    cs_matched (n, wj, imatch, p, q, cc, rr, 1, 1) ;	/* set R1 and C1 */
    cs_matched (n, wj, imatch, p, q, cc, rr, 2, -1) ;	/* set R2 and C2 */
    cs_matched (n, wj, imatch, p, q, cc, rr, 3, 3) ;	/* set R3 and C3 */
    cs_unmatched (m, wi, p, rr, 3) ;			/* unmatched set R0 */
    cs_free (jmatch) ;
    /* --- Fine decomposition ----------------------------------------------- */
    pinv = cs_pinv (p, m) ;	    /* pinv=p' */
    if (!pinv) return (cs_ddone (D, NULL, NULL, 0)) ;
    C = cs_permute (A, pinv, q, 0) ;/* C=A(p,q) (it will hold A(R2,C2)) */
    cs_free (pinv) ;
    if (!C) return (cs_ddone (D, NULL, NULL, 0)) ;
    Cp = C->p ;
    nc = cc [3] - cc [2] ;	    /* delete cols C0, C1, and C3 from C */
    if (cc [2] > 0) for (j = cc [2] ; j <= cc [3] ; j++) Cp [j-cc[2]] = Cp [j] ;
    C->n = nc ;
    if (rr [2] - rr [1] < m)	    /* delete rows R0, R1, and R3 from C */
    {
	cs_fkeep (C, cs_rprune, rr) ;
	cnz = Cp [nc] ;
	Ci = C->i ;
	if (rr [1] > 0) for (k = 0 ; k < cnz ; k++) Ci [k] -= rr [1] ;
    }
    C->m = nc ;
    scc = cs_scc (C) ;		    /* find strongly connected components of C*/
    if (!scc) return (cs_ddone (D, C, NULL, 0)) ;
    /* --- Combine coarse and fine decompositions --------------------------- */
    ps = scc->p ;		    /* C(ps,ps) is the permuted matrix */
    rs = scc->r ;		    /* kth block is rs[k]..rs[k+1]-1 */
    nb1 = scc->nb  ;		    /* # of blocks of A(R2,C2) */
    for (k = 0 ; k < nc ; k++) wj [k] = q [ps [k] + cc [2]] ;
    for (k = 0 ; k < nc ; k++) q [k + cc [2]] = wj [k] ;
    for (k = 0 ; k < nc ; k++) wi [k] = p [ps [k] + rr [1]] ;
    for (k = 0 ; k < nc ; k++) p [k + rr [1]] = wi [k] ;
    nb2 = 0 ;			    /* create the fine block partitions */
    r [0] = s [0] = 0 ;
    if (cc [2] > 0) nb2++ ;	    /* leading coarse block A (R1, [C0 C1]) */
    for (k = 0 ; k < nb1 ; k++)	    /* coarse block A (R2,C2) */
    {
	r [nb2] = rs [k] + rr [1] ; /* A (R2,C2) splits into nb1 fine blocks */
	s [nb2] = rs [k] + cc [2] ;
	nb2++ ;
    }
    if (rr [2] < m)
    {
	r [nb2] = rr [2] ;	    /* trailing coarse block A ([R3 R0], C3) */
	s [nb2] = cc [3] ;
	nb2++ ;
    }
    r [nb2] = m ;
    s [nb2] = n ;
    D->nb = nb2 ;
    cs_dfree (scc) ;
    return (cs_ddone (D, C, NULL, 1)) ;
}
