220
Step 1: set
F
=
0;
Step 2: for
i
=
1 to
n,
if
x
~
ai
and
F
=
0, output
x
and set
F
=
1;
output
ai.
Step 3: if
F
=
0, output
x.
Solutions to Exercises
The variable
F
introduced here is
ajlag,
whose purpose is to tell us whether or not
x
has been output.
At the end of the loop
in
Step 2, if
x
has not been output (that is,
x
is larger than all the
ai's),
then we
will know this, because
F
will not have changed from its initial value of 0; hence, we must output
x
as the final element. Note that the "and" in Step 2 is the logical "and" introduced in Section 0.1. We
output
x
and set
F
=
1 only if both
x
~
ai
and
F
=
0 are true.
13. The idea is to test each integer
x
between 0 and
n
 1 for the possibility
n
I
(ax

b).
After we have
checked
x
=
n
1, however, we need a way to ascertain whether or not any solutions have been found.
For this purpose, we introduce a flag
F
which is set initially to 0 and, if a solution to
ax
==
b
(mod
n)
is found, reset to 1.
If
the value of
F
at the end is still 0, we know there are no solutions. Here is an
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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