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CS100A, Lecture 8, 24 Sept 1997
Iteration
(We’ll spend a few lectures on iteration)
Reading: Holmes, Chapter 4, p. 112-140
Iterate: Reiterate
Reiterate: to say or do over again or repeatedly; repeat
often or continually, sometimes with a wearying effect.
Iteration: the action of repeating or reiterating:
repetition, reiteration.
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Sept. 1998
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Views on Iteration, Repetition
Like warmed-up cabbage served at each repast,
The repetition kills the wretch at last.
Juvenal, Satires
Use not vain repetitions, as the heathens do.
Matthew vi, 7
Oh, thou hast damnable iteration, and art indeed able to
corrupt a saint.
Shakespeare, Henry IV
Iteration, like friction, is likely to generate heat instead
of progress.
George Eliot, The Mill on the Floss
A languid, leaden iteration reigns,
And ever must, o’er those whose joys are joys
Of sight, smell, taste
Young, Night Thoughts
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// Write out the numbers 0..9, each on a
// separate line
System.out.println(0);
System.out.println(1);
System.out.println(2);
System.out.println(3);
System.out.println(4);
System.out.println(5);
System.out.println(6);
System.out.println(7);
System.out.println(8);
System.out.println(9);
The while loop allows us to do this more tersely.
i= 0;
while (i<10) {
System.out.println(i);
i= i+1;
}
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Syntax of the Java while loop:
while ( <boolean expression> )
statement
called the “body”
of the loop
called the
“condition”
Example:
i= 0;
// General picture: integers 0..i-1 have been
// printed
while (i<10) {
System.out.println(i);
i= i+1;
}
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Execution of the while loop
while ( B )
S
flowchart
Evaluate B
true Execute S
false
Execution of a while loop: Evaluate condition B;
if it is true, execute body S and repeat the process.
The first execution of S is called iteration 0.
The second execution of S is called iteration 1.
The third execution of S is called iteration 2.
...
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Another example:
// Store 1 + 2 + 3 + 4 in s
s= 0; i= 1;
// General picture: s= 1 + 2 + … + i-1.
while (i != 5)
{s= s + i; i= i+1;}
Execution:
i |? |1 |
|2 |
|3 |
|4 |
|5 |
s |0 |
|1 |
|3 |
|6 |
| 10 |
|
Execute on computer.
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// Store 1 + 2 + 3 + 4 in s
s= 0; i= 1; // Initialization
// General picture: s = 1 + 2 + … + i-1.
while (i != 5)
{s= s + i; i= i+1;}
The “General picture”, or “invariant” is a relation that
shows how the values of the variables are related just
before and just after each iteration. It gives the meaning
of the variables before and after each iteration. It helps
us understand what the loop is doing.
For each loop, write an invariant, which shows the state
of affairs before and after each iteration. The invariant
gives the meaning of the variables during execution of
the loop.
•The initialization “truthifies” the invariant (makes it
true).
•Each iteration “maintains” the invariant (keeps it true).
•Condition is written so that when the loop terminates,
the general picture helps us see that the desired answer
has been obtained.
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Note the indentation used below:
1 // Store 1 + 2 + 3 + 4 in s
2
s= 0; i= 1;
3
// Invariant: s = 1 + 2 + … + i-1
4
while (i != 5) {
5
s= s + i;
6
i= i+1;
7
}
Line 1 is a statement-comment: a statement to be
executed that it is written in English, so it is a
comment. The statement-comment says WHAT to do.
Lines 2-7 are the implementation of the statement
comment. They are indented beneath it.
Lines 5-7 are the body of the while loop; they form a
substatement of the loop. They are indented.
Rule: Indent substatements of a statement!
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Develop another algorithm for same task
// Store 1 + 2 + 3 + 4 in s
Use invariant
s= 0 + 1 + 2 + … + i.
To make it true, use initialization: s= 0; i= 0;
When will s = 1+2+3+4 be true? When i=4.
Use condition i != 4
Body of loop: Make “progress” by increasing i and
changing s to maintain the invariant:
i= i+1; s= s+i;
Loop:
s= 0; i= 0;
// Invariant: s = 1+2+3+4
while (i !=4)
{i= i+1; s= s+i;}
Invariant is different, so loop is different!
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Another Example: (Assume that n has been declared and
assigned a variable before the following program segment
is to be executed.)
// Print the factors of integer n
int i= 1;
// Invariant: the factors of n that are less than
// i have been printed, and 1 <= i <= n+1
while (i <= n) {
if (n % i == 0)
System.out.println(i);
i= i+1;
}
x % y yields the remainder when x is divided by y.
Example: 13 % 1 = 0
13 % 2 = 1
13 % 3 = 1
13 % 5 = 3
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MEMORIZE THE DEFINITIONS
OF THESE TERMS!
Iterate. Slide 1
While loop. Slide 3
Body of a while loop. Slide 3
Condition of a while loop. Slide 3
How to execute a while loop. Slide 5
Iteration of a while loop. Slide 5
Invariant of a loop. Slide 7
A statement “truthifies” a relation. Slide 7
A statement “maintains” a relation. Slide 7
Statement-comment. Slide 8
Implementation of a statement-comment. Slide 8
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PRELIM MONDAY EVENING
You MUST know precise meanings of following!
Type (e.g. int, bool)
Class
Subclass
Field (of a class) or instance variable
Static field (of a class) or class variable
Instance of a class –also called an object
Method
function
procedure
constructor
Local variable (of a method)
Parameter (of a method)
Method call –how each of the three kinds of
methods is called
Argument (of a method call)
How to execute an assignment, if statement.
How to execute a method call
How to evaluate expression new C(…)
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