/* find the strongly connected components of a square matrix */ csd *cs_scc (cs *A) /* matrix A temporarily modified, then restored */ { 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 (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)) ; }
int cs_reach (cs *G, const cs *B, int k, int *xi, const int *pinv) { int p, n, top, *Bp, *Bi, *Gp ; if (!CS_CSC (G) || !CS_CSC (B) || !xi) return (-1) ; /* check inputs */ n = G->n ; Bp = B->p ; Bi = B->i ; Gp = G->p ; top = n ; for (p = Bp [k] ; p < Bp [k+1] ; p++) { if (!CS_MARKED (Gp, Bi [p])) /* start a dfs at unmarked node i */ { top = cs_dfs (Bi [p], G, top, xi, xi+n, pinv) ; } } for (p = top ; p < n ; p++) CS_MARK (Gp, xi [p]) ; /* restore G */ return (top) ; }