1. Every step in an algorithm has two basic components:
Algorithms
An algorithm is an ordered set of unambiguous, executable steps that ultimately terminate if followed.
In computer programming, an algorithm is the sequence of steps (i.e., the “recipe”) for accomplishing a task.
Every step in an algorithm has two basic components:
Semantics: The meaning of the step
Syntax: The format of the step
Semantics
Syntax
Get a value from the user
Double that value
Return the result to the user
Program DoubleIt;
var x, y integer;
begin
write(“Input your number: ”);
read(x);
y = 2*x;
writeln(“The doubled number is ”, y);
end. CS
Chapter 5 – Algorithms

2. Pseudocode
Pseudocode is an informal notation for expressing an algorithm.
Example: Which years in have New Year’s Eve on Saturday?
Procedure Sat1231A
Set year to 2006
Set month to January
Set day to first Saturday in January 2006
While (year < 2021) Do {
Increment day by 7
If date is New Year’s Eve
Then display year as having a Saturday New Year’s Eve
If day > (number of days in month)
Then
Adjust day by subtracting the number of days in month
If month is December
Increment year by 1 }
Else
Increment month by one CS
Chapter 5 – Algorithms

3. Of course, it is possible to devise many algorithms to solve the same problem.
Alternative pseudocode to determine which years in have New Year’s Eve on Saturday:
Procedure Sat1231B
Set day_of_week to 12/31/2005
Set year to 2006
While (year < 2021) Do {
If year is a leap year
Then increment day_of_week by 2
Else increment day_of_week by 1
If day_of_week is Saturday
Then display year as having a Saturday New Year’s Eve
Increment year by 1 }
Both algorithms work, but which is better?
Which is easier to code?
Which runs more efficiently? CS
Chapter 5 – Algorithms

4. Iteration (Looping)
When an algorithm involves repetitive actions, iteration may be a practical approach.
Pseudocode to implement the search for a specific name in an alphabetized phonebook:
Procedure SeqSearch(phonebook, sought_name)
Set test_name to first name in phonebook
While (test_name is alphabetically before sought_name AND
there are stillmore names in phonebook) Do
Set test_name to the next name in phonebook
If test_name is sought_name
Then return the corresponding phone number
Else return “Unlisted” message
Notice that this algorithm always starts at the top of the phonebook list and checks each name against sought_name until it either locates it or (if it’s not in the phonebook) passes it. CS
Chapter 5 – Algorithms

5. Calling SeqSearch(phonebook, sought_name) where sought_name is “Rubeus Hagrid” and phonebook is the list below:
Name
Number
Black, Sirius
Chang, Cho
Dumbledore, Albus
Dursley, Dudley
Filch, Argus
Fudge, Cornelius
Granger, Hermione
Hagrid, Rubeus
Lockhart, Gilderoy
Longbottom, Neville
Malfoy, Draco
McGonagall, Minerva
Pettigrew, Peter
Pomfrey, Poppy
Snape, Severus
Trelawney, Sybill
Weasley, Ron
Wood, Oliver
1. test_name is Sirius Black, so iterate again
2. test_name is Cho Chang, so iterate again
3. test_name is Albus Dumbledore, so iterate again
4. test_name is Dudley Dursley, so iterate again
5. test_name is Argus Filch, so iterate again
6. test_name is Cornelius Fudge, so iterate again
7. test_name is Hermione Granger, so iterate again
8. test_name is Rubeus Hagrid, so return CS
Chapter 5 – Algorithms

6. Recursion (“Divide & Conquer”)
Another common approach in algorithms is to employ recursion, which repeatedly reduces the size of a problem until it becomes manageable.
Pseudocode to recursively take a base number to a specified power:
Procedure Exponentiate(base, power)
If base is 0
Then return 0
Else If power < 0
Then return Exponentiate(base, power+1)/base
Else If power is 0
Then return 1
Else return base * Exponentiate(base, power-1)
Notice that this algorithm returns 0 if the value of base is 0, 1 if the value of power is 0, base if the value of power is 1, 1/base if the value of power is -1, and so on. CS
Chapter 5 – Algorithms

7. A Recursive Search Algorithm
Pseudocode to recursively implement the search for a specific name in an alphabetized phonebook:
Procedure BinarySearch(phonebook, sought_name)
Set test_name to the middle name in phonebook
If test_name is sought_name
Then return corresponding phone number
Else If phonebook has only one remaining entry
Then return “Unlisted” message
If test_name is alphabetically before sought_name
Then apply BinarySearch to the portion of phonebook after test_name
Else apply BinarySearch to the portion of phonebook before test_name
Notice that this algorithm starts at the middle of the phonebook list, and keeps splitting what’s left of the phonebook in half until it either locates sought_name or runs out of names to check. CS
Chapter 5 – Algorithms

8. Calling BinarySearch(phonebook, sought_name) where sought_name is “Rubeus Hagrid” and phonebook is the list below:
Name
Number
Black, Sirius
Chang, Cho
Dumbledore, Albus
Dursley, Dudley
Filch, Argus
Fudge, Cornelius
Granger, Hermione
Hagrid, Rubeus
Lockhart, Gilderoy
Longbottom, Neville
Malfoy, Draco
McGonagall, Minerva
Pettigrew, Peter
Pomfrey, Poppy
Snape, Severus
Trelawney, Sybill
Weasley, Ron
Wood, Oliver
2. test_name: Dudley Dursley, so use 2nd quarter
3. test_name: Cornelius Fudge, so use 4th eighth
4. test_name: Hermione Granger, so use 8th sixteenth
5. test_name: Rubeus Hagrid, so return
1. test_name: Gilderoy Lockhart, so use 1st half CS
Chapter 5 – Algorithms