1. Computer Programming Fundamentals
Algorithms

2. Agenda What is an algorithm? How do we record an algorithm? An example
The basic building blocks
How do we record an algorithm?
Flow charts
Pseudocode
An example
Sieve of Eratosthenes 1

3. Basic building blocks Four principal programming structures
Sequence
Selection (if … else …)
Iteration (loops)
Sub-programs (functions)
Can construct any algorithm from these basics

4. What is an algorithm? A ‘recipe’ you use to complete a task
Use combinations of the basic building blocks
For many common tasks algorithms are already known
Eratosthenes 276 – 194 BC
Many still to be discovered
Factorisation of large numbers

5. Recording algorithms Flowcharts Pseudocode
We have already seen how to describe each of the basic building blocks as a flowchart
Graphical
They can get cumbersome for more complex algorithms
Pseudocode
An alternative to flowcharts
A generic form of the basic code building blocks
Text-based
No special software required

6. Pseudocode Like writing code but….
No predefined format
No formal syntax
Although it should be unambiguous
Allows you to defer decisions about details
No compiler or interpreter !!
Relatively easy to convert into ‘real’ code
In most target languages

7. Building blocks Sequence Selection Iteration IF - THEN - ELSE
SELECT - ENDSELECT
Iteration
FOR - NEXT
WHILE - ENDWHILE
REPEAT - UNTIL

8. Building blocks - sequence
Variables A and B each have a value
How do we exchange the two?
Exchange A and B:
Exchange the values
in variables A and B:
temp = A
A = B
B = temp
Start
Finish
temp = A
A = B
B = temp

9. Building blocks - selection
IF-THEN-ELSE
Set MAX equal to the larger value in
variables A and B:
IF A > B THEN
MAX = A
ELSE
MAX = B
ENDIF
# Set MAX equal to the larger value
# in variables A and B:
if A > B:
MAX = A
else:
MAX = B 8

10. Building blocks - selection
# Process direction variable:
# SELECT CASE direction OF
# north: move up
if direction == 'NORTH':
move("UP")
# south: move down
elif direction == 'SOUTH':
move("DOWN")
# east: move right
elif direction == 'EAST':
move("RIGHT")
# west: move left
elif direction == 'WEST':
move("LEFT")
# OTHERWISE error
else:
bad_move(direction)
SELECT
Process direction variable:
SELECT CASE direction OF
north: move up
south: move down
east: move right
west: move left
OTHERWISE error
ENDSELECT 9

11. Building blocks - iteration
FOR - NEXT
A = [1,…]
# Process each element
# in an Array ‘A’:
#FOR k = 0 TO (size_of_A - 1)
# process A(k)
for k in range(len(A)):
process_item(A[k])
Process each element
in an Array ‘A’:
FOR k = 0 TO (size_of_A - 1)
process A(k)
NEXT k 10

12. Building blocks - iteration
WHILE - ENDWHILE
# Print Fibonacci numbers
# less than MAX :
A = 0
B = 1
#WHILE B less than MAX
while B < MAX :
print (B)
temp = A+B
A = B
B = temp
Print Fibonacci numbers less than MAX :
A = 0, B = 1
WHILE B less than MAX
print B
temp =A+B
A = B
B = temp
ENDWHILE 11

13. Building blocks - iteration
REPEAT - UNTIL
#Calculate average of entered values:
count = 0
total = 0
#REPEAT
while True:
# INPUT x
x = int(input("Enter integer:"))
count += 1
total += x
# INPUT more
more = (input("Any more? [Y or N]")).upper()
# UNTIL more is not 'yes'
if more[0] != 'Y':
break
#Calculate average
print ("Average is ",total/count)
Calculate average of entered values:
count = 0, total = 0
REPEAT
INPUT in
count = count + 1
total = total + in
INPUT more
UNTIL more is not ‘yes’
Calculate average 12

14. Example Finding prime numbers Sieve of Eratosthenes
Finds all primes less than a particular value 13

15. Sieve of Eratosthenes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 29 40 41 42 43 44 45 46 47 48 49

16. The sieve in pseudocode
Generate primes using sieve method:
INPUT maxprime
Create integer array called primes with maxprime elements
Initialise primes so that for all x primes[x] = x (…primes[3] = 3, primes[4] = 4, … etc.)
Show 1 is not prime by setting primes[1] =0
Initialise current_prime = 2
WHILE current_prime is less than length of primes
IF primes[current_prime] indicates a prime (it is not 0) THEN
Initialise counter to square of current_prime
WHILE counter less than length of primes
mark primes[counter] as not prime by setting to 0
increment counter by current_prime
END WHILE
END IF
increment current_prime by 1
ENDWHILE
Now print the results:
FOR k = 0 TO size of primes
IF primes[k] is not 0 THEN
k must be a prime so print it
NEXT k

17. Exercises Implement some algorithms defined in pseudocode
Implement the ‘Sieve of Eratosthenes’ algorithm