<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
problem	O
is	O
said	O
to	O
have	O
overlapping	B-Algorithm
subproblems	I-Algorithm
if	O
the	O
problem	O
can	O
be	O
broken	O
down	O
into	O
subproblems	O
which	O
are	O
reused	O
several	O
times	O
or	O
a	O
recursive	O
algorithm	O
for	O
the	O
problem	O
solves	O
the	O
same	O
subproblem	O
over	O
and	O
over	O
rather	O
than	O
always	O
generating	O
new	O
subproblems	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
problem	O
of	O
computing	O
the	O
Fibonacci	B-Algorithm
sequence	I-Algorithm
exhibits	O
overlapping	B-Algorithm
subproblems	I-Algorithm
.	O
</s>
<s>
The	O
problem	O
of	O
computing	O
the	O
nth	O
Fibonacci	B-Algorithm
number	I-Algorithm
F(n )	O
,	O
can	O
be	O
broken	O
down	O
into	O
the	O
subproblems	O
of	O
computing	O
F(n1 )	O
and	O
F(n2 )	O
,	O
and	O
then	O
adding	O
the	O
two	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
computation	O
of	O
F(n2 )	O
is	O
reused	O
,	O
and	O
the	O
Fibonacci	B-Algorithm
sequence	I-Algorithm
thus	O
exhibits	O
overlapping	B-Algorithm
subproblems	I-Algorithm
.	O
</s>
<s>
If	O
the	O
problem	O
also	O
shares	O
an	O
optimal	B-Algorithm
substructure	I-Algorithm
property	O
,	O
dynamic	B-Algorithm
programming	I-Algorithm
is	O
a	O
good	O
way	O
to	O
work	O
it	O
out	O
.	O
</s>
<s>
Consider	O
the	O
following	O
C	B-Language
code	O
:	O
</s>
