// CXSparse/Source/cs_scc: strongly connected components
// CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
// SPDX-License-Identifier: LGPL-2.1+
#include "cs.h"
/* find the strongly connected components of a square matrix */
csd *cs_scc (cs *A)     /* matrix A temporarily modified, then restored */
{
    CS_INT n, i, k, b, nb = 0, top, *xi, *pstack, *p, *r, *Ap, *ATp, *rcopy, *Blk ;
    cs *AT ;
    csd *D ;
    if (!CS_CSC (A)) return (NULL) ;                /* check inputs */
    n = A->n ; Ap = A->p ;
    D = cs_dalloc (n, 0) ;                          /* allocate result */
    AT = cs_transpose (A, 0) ;                      /* AT = A' */
    xi = cs_malloc (2*n+1, sizeof (CS_INT)) ;          /* get workspace */
    if (!D || !AT || !xi) return (cs_ddone (D, AT, xi, 0)) ;
    Blk = xi ; rcopy = pstack = xi + n ;
    p = D->p ; r = D->r ; ATp = AT->p ;
    top = n ;
    for (i = 0 ; i < n ; i++)   /* first dfs(A) to find finish times (xi) */
    {
        if (!CS_MARKED (Ap, i)) top = cs_dfs (i, A, top, xi, pstack, NULL) ;
    }
    for (i = 0 ; i < n ; i++) CS_MARK (Ap, i) ; /* restore A; unmark all nodes*/
    top = n ;
    nb = n ;
    for (k = 0 ; k < n ; k++)   /* dfs(A') to find strongly connnected comp */
    {
        i = xi [k] ;            /* get i in reverse order of finish times */
        if (CS_MARKED (ATp, i)) continue ;  /* skip node i if already ordered */
        r [nb--] = top ;        /* node i is the start of a component in p */
        top = cs_dfs (i, AT, top, p, pstack, NULL) ;
    }
    r [nb] = 0 ;                /* first block starts at zero; shift r up */
    for (k = nb ; k <= n ; k++) r [k-nb] = r [k] ;
    D->nb = nb = n-nb ;         /* nb = # of strongly connected components */
    for (b = 0 ; b < nb ; b++)  /* sort each block in natural order */
    {
        for (k = r [b] ; k < r [b+1] ; k++) Blk [p [k]] = b ;
    }
    for (b = 0 ; b <= nb ; b++) rcopy [b] = r [b] ;
    for (i = 0 ; i < n ; i++) p [rcopy [Blk [i]]++] = i ;
    return (cs_ddone (D, AT, xi, 1)) ;
}