- Basic property of a computer (a machine):
- Computers do
what we tell them to do
- Unfortunately,
computer do not
necessarily do
what we want them to do....
(Because we can make mistake in telling the computer what we want to do...
These mistakes are called "bugs")
- Computers do
what we tell them to do
- Definition: algorithm
- Dictionary definition:
- Algorithm = a step-by-step procedure for solving a problem or accomplishing some task, especially by means of a computer
- Dictionary definition:
- Computer Algorithm:
- is an algorithm that can be executed by a computer
- Properties of computer algorithms:
- The steps in an
algorithm must be consists
of operations that
can be executed by
a computer
- The step in an
algorithm must be
unambiguous
(Remember that a dumb machine like a computer will do what it is told to do.
- Computers cannot think.
Resolving ambiguity requires some thinking (intelligence) which computers cannot do !)
- The steps in an
algorithm must be consists
of operations that
can be executed by
a computer
- We will now illustrate the
process of
developing an algorithm
- An algorithm
always accomplishes
some well-defined task
or solves some
well-defined problem
- The task/problem that we will use
to illustrate
the process of
developing an algorithm is:
- Replacing a burned out light bulb
- Typical instructions given to humans on how to replace
a light bulb:
- Remove the burned-out bulb
- Insert a new bulb
These brief instructions assume a lot of common sense knowledge that a machine does not have !!!
- What can go wrong if a machine
uses these instructions:
- A machine does not know how
to remove a bulb
It could yank the bulk out of its socket and damage the fixture in the process.
- A machine does not know
how
to insert a bulb
- A machine can replace the bulb with one that has an inadequate wattage (too bright or too dim)
- A machine does not know how
to remove a bulb
- Computers have
no common sense knowledge
(really dumb)
Instructions for computers must be given very explicitly (in "baby steps")
- Example of how you would
instruct a
computer to
change a light bulb:
[The following instructions will remove the burn-out bulb] repeat until (bulb comes free of socket) { turn bulb in counter-clockwise direction } [The following instructions will find a suitable bulb] select a new bulb repeat until (wattage of bulb selected = wattage of old bulb) { discard the selected bulb select another bulb } [The following instructions will insert the new bulb] repeat until (bulb is secure in socket) { turn bulb in clockwise direction }
- Here is a famous algorithm that
you can try out:
- Take 2 pieces of paper and
write on one piece "A" and
on the other piece "B":
- Write a positive integer
on each piece of paper.
- Euclid's Algorithm:
(
see Wikipedia)
As long as neither number is zero (0) do { if ( number on A ≥ number on B ) replace the number on A by the value (A - B) otherwise replace the number on B by the value (B - A) } The Greatest Common Divisor (GCD) = B
- Example of the Euclid Algorithm:
- We start with the following 2 number:
- Since number on A < number on B,
we replace the number on
B (= 36)
by the value
(B − A) = 8:
- Now number on A ≥ number on B,
so we replace the number on
A (= 28)
by the value
(A − B) = 20:
- Again, number on A ≥ number on B,
so we replace the number on
A (= 20)
by the value
(A − B) = 12:
- Yet again, number on A ≥ number on B,
so we replace the number on
A (= 12)
by the value
(A − B) = 4:
- This time, number on B > number on A,
so we replace the number on
B (= 8)
by the value
(B − A) = 4:
- Now, number on A ≥ number on B,
so we replace the number on
A (= 4)
by the value
(B − A) = 0:
- One of the number on the papers is now
zero
According to the Euclid's Algorithm, the other number (= 4) is equal to the GCD of (28, 36)
- We start with the following 2 number:
- Take 2 pieces of paper and
write on one piece "A" and
on the other piece "B":