1. Loops (iterations, repetitions)

2. Three fundamental structures:
sequence,
condition,
iteration

3. Iterative Constructs: iteration or loop
A loop repeats a statement or a sequence of statements a number of times.
The fundamental iteration construct:
‘while’ statement

4. The fundamental while Statement
Syntax
while (bool expression) {
Action }
How it works:
If Expression is true then execute Action
Repeat this process until Expression evaluates to false
Action is either a single statement or a group of statements within braces
Expression
true
false
Action

5. The first example: int n; n=5; while (n < 10) {
cout << n << endl;
n=n+1; }
n=5;
(5<10); n=n+1;
(6<10); n=n+1;
(7<10); n=n+1;
(8<10); n=n+1;
(9<10); n=n+1;
(10<10)  false; finish;
10;

6. N! (while) int number, factorial, n; cout << "Enter number: ";
cin >> number;
factorial = 1;
n = 1;
while (n <= number) {
factorial = factorial*n;
n=n+1; }
cout << "The factorial of " << number
<< " is " << factorial << endl;

7. 2N (while) int number, result, n; cout << "Enter number: ";
cin >> number;
result = 1;
n = 1;
while (n <= number) {
result = result*2;
n=n+1; }
cout << "Two raised to the " << number
<< " power is " << result << endl;

8. while loop summary while (condition) action initialisation(V)
while (condition(V))
action-and-update(V)
Initialisation of a set of variables V
Condition on V
Action: V = f(V)
init
first action
second action
n=1,fac=1
fac=2,n=2
fac=6,n=3
fac=fac*n;n=n+1;
fac=fac*n;n=n+1;
fac=fac*n;n=n+1;

9. GCD (the greatest comon divisor) example
GCD(a,b) is the largest number that divides both a and b without leaving a remainder
GCD(25,0)=?
GCD(12,18) =?
GCD(5,7)=?
GCD(a,b)=GCD(a-b,b) if a>b
GCD(a,b-a) if b>a
GCD(a,b)=GCD(b,a mod b)
GCD(a,0)=a
Euclid method  iterative

10. GCD with subtraction int a,b,gcd; cin >> a; cin >> b;
if (a==0) gcd=b;
else {
while (b != 0) {
if (a>b) a = a-b;
else b = b-a; }
gcd=a;
cout << “GCD is:” << gcd << endl;

11. GCD with the remainder cin >> a; cin >> b;
while (b != 0) {
t = b;
b = a % b;
a = t; }
gcd=a;
cout << “GCD is:” << gcd << endl;

12. Key points of a loop:
Make sure there is a statement that will eventually stop the loop (condition)
Make sure to initialize loop counters correctly (initialisation)
Have a clear purpose for the loop (action)

13. How to Stop a Loop Known number of iterations before the loop stops
Test for a user-controlled
condition before or after
each iteration

14. Common Loop Errors while(balance != 0.0) { balance = balance - amount;}
This will lead to an infinite loop!
balance may not become equal zero due to numerical inaccuracies
while(balance != 0.0);

15. Common Loop Errors product=? while(n <= 1000){
product = product*n;
n=n+1; }
sum=?
while(n <= 1000) {
sum = sum+n;
Be sure to initialize to 0 a variable used for sums
Be sure to initialize to 1 a variable used for products

16. Nested Loops
Nested loops are loops within loops. They are similar in principle to nested if-else statements.
Many applications require nested loops.

17. Multiplication Table (while)
// Program to output the
// multiplication table
int i; //Outer loop counter
int j; //Inner loop counter
i=1;
while (i<=10) {
j=1;
while (j<=10) {
cout << i*j << “ “;
j=j+1; }
cout << endl;
i=i+1;

18. Diamond Pattern Print out the following diamond pattern * * * *
* * * * *
* * * * * * *
* * * * * * * * *

19. Diamond Pattern Subproblem: print out the upper half
print out the lower half

20. Upper triangular Pattern
Print out triangular pattern:
row 1: print 4 spaces, 1 star;
row 2: print 3 spaces, 3 stars;
row 3: print 2 spaces, 5 stars;
row 4: print 1 space, 7 stars;
row 5: print 0 spaces, 9 stars;
Algorithm Refinement:
row 1: print (5-row) spaces, (2*row - 1) stars;
row 2: print (5-row) spaces, (2*row - 1) stars;
row 3: print (5-row) spaces, (2*row - 1) stars;
row 4: print (5-row) spaces, (2*row - 1) stars;
row 5: print (5-row) spaces, (2*row - 1) stars; *
* * *
* * * * *
* * * * * * *
* * * * * * * * *

21. Upper Triangular Pattern
int row, space, star;
row=1;
while(row<=5){
space=1;
while(space<=5-row) {
cout << " ";
space=space+1; }
star=1;
while(star<=2*row-1) {
cout << "*";
star=star+1;
cout << endl ;
row=row+1;

22. Diamond Pattern Subproblem: Print out lower half:
print out the upper half
print out the lower half
Print out lower half:
Row 6 (row 4): print 1 spaces, 7 stars;
Row 7 (row 3): print 2 spaces, 5 stars;
Row 8 (row 2): print 3 space, 3 stars;
Row 9 (row 1): print 4 spaces, 1 stars;
Algorithm Refinement:
row 4: print (5-row) spaces, (2*row - 1) stars;
row 3: print (5-row) spaces, (2*row - 1) stars;
row 2: print (5-row) spaces, (2*row - 1) stars;
row 1: print (5-row) spaces, (2*row - 1) stars;

23. Diamond Pattern int row, space, star; … // top half
while(row>=1){ //bottom half
space=1;
while(space<=5-row) {
cout << " ";
space=space+1; }
star=1;
while(star<=2*row-1) {
cout << "*";
star=star+1;
cout << endl ;
row=row-1;