<s>
The	O
Hoshen	B-Algorithm
–	I-Algorithm
Kopelman	I-Algorithm
algorithm	I-Algorithm
is	O
a	O
simple	O
and	O
efficient	O
algorithm	O
for	O
labeling	O
clusters	B-Algorithm
on	O
a	O
grid	O
,	O
where	O
the	O
grid	O
is	O
a	O
regular	O
network	B-Architecture
of	O
cells	O
,	O
with	O
the	O
cells	O
being	O
either	O
occupied	O
or	O
unoccupied	O
.	O
</s>
<s>
This	O
algorithm	O
is	O
based	O
on	O
a	O
well-known	O
union-finding	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Percolation	O
theory	O
is	O
the	O
study	O
of	O
the	O
behavior	O
and	O
statistics	O
of	O
clusters	B-Algorithm
on	O
lattices	O
.	O
</s>
<s>
we	O
consider	O
the	O
4-connected	B-Algorithm
neighborhood	I-Algorithm
that	O
is	O
top	O
,	O
bottom	O
,	O
left	O
and	O
right	O
.	O
</s>
<s>
The	O
number	O
of	O
clusters	B-Algorithm
,	O
the	O
size	O
of	O
each	O
cluster	O
and	O
their	O
distribution	O
are	O
important	O
topics	O
in	O
percolation	O
theory	O
.	O
</s>
<s>
(	O
For	O
this	O
we	O
are	O
going	O
to	O
use	O
Union-Find	B-Algorithm
Algorithm	I-Algorithm
which	O
is	O
explained	O
in	O
the	O
next	O
section	O
.	O
)	O
</s>
<s>
Following	O
pseudocode	B-Language
is	O
referred	O
from	O
implementation	O
of	O
the	O
same	O
algorithm	O
.	O
</s>
<s>
union(left,above )	O
;	O
/	O
*	O
Link	O
the	O
left	O
and	O
above	O
clusters	B-Algorithm
.	O
</s>
<s>
So	O
by	O
running	O
H	O
–	O
K	O
algorithm	O
on	O
this	O
input	O
we	O
would	O
get	O
the	O
output	O
as	O
shown	O
in	O
figure	O
(	O
b	O
)	O
with	O
all	O
the	O
clusters	B-Algorithm
labeled	O
.	O
</s>
<s>
grid[1][3]	O
is	O
occupied	O
so	O
check	O
cell	O
to	O
the	O
left	O
and	O
above	O
,	O
both	O
the	O
cells	O
are	O
occupied	O
,	O
so	O
merge	O
the	O
two	O
clusters	B-Algorithm
and	O
assign	O
the	O
cluster	O
label	O
of	O
the	O
cell	O
above	O
to	O
the	O
cell	O
on	O
the	O
left	O
and	O
to	O
this	O
cell	O
i.e.	O
</s>
<s>
grid[4][3]	O
is	O
occupied	O
so	O
check	O
cell	O
to	O
the	O
left	O
and	O
above	O
,	O
both	O
,	O
cell	O
to	O
the	O
left	O
and	O
above	O
are	O
occupied	O
so	O
merge	O
the	O
two	O
clusters	B-Algorithm
and	O
assign	O
the	O
cluster	O
label	O
of	O
the	O
cell	O
above	O
to	O
the	O
cell	O
on	O
the	O
left	O
and	O
to	O
this	O
cell	O
i.e.	O
</s>
<s>
grid[5][5]	O
is	O
occupied	O
so	O
check	O
cell	O
to	O
the	O
left	O
and	O
above	O
,	O
both	O
,	O
cell	O
to	O
the	O
left	O
and	O
above	O
are	O
occupied	O
so	O
merge	O
the	O
two	O
clusters	B-Algorithm
and	O
assign	O
the	O
cluster	O
label	O
of	O
the	O
cell	O
above	O
to	O
the	O
cell	O
on	O
the	O
left	O
and	O
to	O
this	O
cell	O
i.e.	O
</s>
<s>
Figure	O
(	O
a	O
)	O
,	O
This	O
is	O
the	O
input	O
to	O
the	O
Hoshen	B-Algorithm
–	I-Algorithm
Kopelman	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Figure	O
(	O
b	O
)	O
,	O
This	O
is	O
the	O
output	O
of	O
the	O
algorithm	O
with	O
all	O
the	O
clusters	B-Algorithm
labeled	O
.	O
</s>
