Java Reference
In-Depth Information
for(i=0;i>=0;i++)
{}
2.5.3 Loop equivalence to universal
while
structures
As mentioned earlier, the three loop structures in Java are all equivalent to a
universal
while
structure. These different loop syntaxes are provided to help
programmers quickly write code.
for(instructionInit; booleanCondition; instructionUpdate) block instruction;
instructionInit;
while (booleanCondition)
block instruction3; instructionUpdate;
2.5.4 Breaking loops at any time with
break
We can voluntarily escape loops at
any time
by using the keyword
break
. This
special instruction is useful for example when we ask users to input any given
number of data.
2.5.5 Loops and program termination
Consider the following sequence
u
i
}
i
of integers numbers as follows:
u
n
+1
=
u
n
/
2
{
if
n
is even,
,
3
u
n
+ 1
otherwise.
initialized for any given
u
0
∈
N
.
For example, let
u
0
= 14. Then
u
1
= 14,
u
2
=7,
u
3
= 22,
u
4
= 11,
u
5
= 34,
u
6
= 17,
u
7
= 52,
u
8
= 26,
u
9
= 13,
u
10
= 40,
u
11
= 20,
u
12
= 10,
u
13
=5,
u
14
= 16,
u
15
=8,
u
16
=4,
u
17
=2,
u
18
= 1. Once 1 is reached the sequence
cycles 1
,
4
,
2
,
1
,
4
,
2
...
. It is conjectured but not yet proved that for any
u
0
≥
1
the sequence reaches in a finite step number 1. We can numerically check that
this conjecture holds for a given number
u
0
=
n
using the following
do
loop
structure:
Program 2.9
Syracuse's conjecture
do
{
if
( ( n%2)==0)
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