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#include "cs.h"
/* find an augmenting path starting at column k and extend the match if found */
static void cs_augment (csi k, const cs *A, csi *jmatch, csi *cheap, csi *w,
csi *js, csi *is, csi *ps)
{
csi found = 0, p, i = -1, *Ap = A->p, *Ai = A->i, head = 0, j ;
js [0] = k ; /* start with just node k in jstack */
while (head >= 0)
{
/* --- Start (or continue) depth-first-search at node j ------------- */
j = js [head] ; /* get j from top of jstack */
if (w [j] != k) /* 1st time j visited for kth path */
{
w [j] = k ; /* mark j as visited for kth path */
for (p = cheap [j] ; p < Ap [j+1] && !found ; p++)
{
i = Ai [p] ; /* try a cheap assignment (i,j) */
found = (jmatch [i] == -1) ;
}
cheap [j] = p ; /* start here next time j is traversed*/
if (found)
{
is [head] = i ; /* column j matched with row i */
break ; /* end of augmenting path */
}
ps [head] = Ap [j] ; /* no cheap match: start dfs for j */
}
/* --- Depth-first-search of neighbors of j ------------------------- */
for (p = ps [head] ; p < Ap [j+1] ; p++)
{
i = Ai [p] ; /* consider row i */
if (w [jmatch [i]] == k) continue ; /* skip jmatch [i] if marked */
ps [head] = p + 1 ; /* pause dfs of node j */
is [head] = i ; /* i will be matched with j if found */
js [++head] = jmatch [i] ; /* start dfs at column jmatch [i] */
break ;
}
if (p == Ap [j+1]) head-- ; /* node j is done; pop from stack */
} /* augment the match if path found: */
if (found) for (p = head ; p >= 0 ; p--) jmatch [is [p]] = js [p] ;
}
/* find a maximum transveral */
csi *cs_maxtrans (const cs *A, csi seed) /*[jmatch [0..m-1]; imatch [0..n-1]]*/
{
csi i, j, k, n, m, p, n2 = 0, m2 = 0, *Ap, *jimatch, *w, *cheap, *js, *is,
*ps, *Ai, *Cp, *jmatch, *imatch, *q ;
cs *C ;
if (!CS_CSC (A)) return (NULL) ; /* check inputs */
n = A->n ; m = A->m ; Ap = A->p ; Ai = A->i ;
w = jimatch = cs_calloc (m+n, sizeof (csi)) ; /* allocate result */
if (!jimatch) return (NULL) ;
for (k = 0, j = 0 ; j < n ; j++) /* count nonempty rows and columns */
{
n2 += (Ap [j] < Ap [j+1]) ;
for (p = Ap [j] ; p < Ap [j+1] ; p++)
{
w [Ai [p]] = 1 ;
k += (j == Ai [p]) ; /* count entries already on diagonal */
}
}
if (k == CS_MIN (m,n)) /* quick return if diagonal zero-free */
{
jmatch = jimatch ; imatch = jimatch + m ;
for (i = 0 ; i < k ; i++) jmatch [i] = i ;
for ( ; i < m ; i++) jmatch [i] = -1 ;
for (j = 0 ; j < k ; j++) imatch [j] = j ;
for ( ; j < n ; j++) imatch [j] = -1 ;
return (cs_idone (jimatch, NULL, NULL, 1)) ;
}
for (i = 0 ; i < m ; i++) m2 += w [i] ;
C = (m2 < n2) ? cs_transpose (A,0) : ((cs *) A) ; /* transpose if needed */
if (!C) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, NULL, 0)) ;
n = C->n ; m = C->m ; Cp = C->p ;
jmatch = (m2 < n2) ? jimatch + n : jimatch ;
imatch = (m2 < n2) ? jimatch : jimatch + m ;
w = cs_malloc (5*n, sizeof (csi)) ; /* get workspace */
if (!w) return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 0)) ;
cheap = w + n ; js = w + 2*n ; is = w + 3*n ; ps = w + 4*n ;
for (j = 0 ; j < n ; j++) cheap [j] = Cp [j] ; /* for cheap assignment */
for (j = 0 ; j < n ; j++) w [j] = -1 ; /* all columns unflagged */
for (i = 0 ; i < m ; i++) jmatch [i] = -1 ; /* nothing matched yet */
q = cs_randperm (n, seed) ; /* q = random permutation */
for (k = 0 ; k < n ; k++) /* augment, starting at column q[k] */
{
cs_augment (q ? q [k]: k, C, jmatch, cheap, w, js, is, ps) ;
}
cs_free (q) ;
for (j = 0 ; j < n ; j++) imatch [j] = -1 ; /* find row match */
for (i = 0 ; i < m ; i++) if (jmatch [i] >= 0) imatch [jmatch [i]] = i ;
return (cs_idone (jimatch, (m2 < n2) ? C : NULL, w, 1)) ;
}
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