Algorithms and
Programming
Lect 3
Algorithm


An algorithm is a finite step-by-step
sequence of instructions for carrying out
some task
Algorithms predate computers, e.g.


Euclid's algorithm for finding the greatest
common factor
Find average of some values
Finding the Oldest (1)
1. ask the first person to state his or her
name and birthday, then write this
information down on a piece of paper
2. for each successive person in line:
• ask the person for his or her name
and birthday
• if the stated birthday is earlier than
the birthday on the paper, cross out
old information and write down the
new
3. at the end of the line, the name and
birthday of the oldest person will be on
the paper
Oldest (1)
Find the Oldest (2)
1.
2.
line up all the people along one wall
as long as there is more than one person in
the line, repeatedly
•
have the people pair up– if there is an
odd number of people, the last person will
be without a partner
•
ask each pair of people to compare their
birthdays and request that the younger of
the two leave the line
3. when there is only one person left in line,
that person is the oldest
Oldest(2)
Algorithm Analysis

algorithm 1 involves asking each person’s
birthday and then comparing it to the
birthday written on the page
 the amount of time to find the oldest
person is proportional to the number of
people
 if you double the amount of people, the
time needed to find the oldest person will
also double
Algorithm Analysis

algorithm 2 allows you to perform multiple
comparisons simultaneously
 the time needed to find the oldest person is
proportional to the number of rounds it takes to
shrink the line down to one person -- the
logarithm (base 2) of the number of people
 if you double the number of people, the time
increases by the cost of one more comparison
 requires carrying out comparisons in parallel
(special hardware is the price you have to pay)
algorithm vs. logarithm

the words algorithm and logarithm are similar
– do not be confused
algorithm:
a finite step-by-step sequence of
instructions for carrying out a task
logarithm: the exponent to which a base is raised to
produce a number
e.g., 210 = 1024, so log2(1024) = 10
Searching
A common problem in computer science
involves storing and maintaining large
amounts of data, and then searching the
data for particular value.
Searching
There are two commonly used algorithms for
searching a list of items
1.sequential search
• general purpose
• relatively slow
2.binary search
• data must be sorted
• faster
• guess my number
Searching


Algorithm 1 takes time proportional to the
number of values
Algorithm 2 is again proportional to the log2.
Algorithms

There may be many algorithms to solve a
given problem.


Some algorithms may be faster than others
some algorithms may require different
resources (memory, special hardware).
Programming
In order to use a computer to solve a problem,
we go through a series of steps.
 Determine how to solve the problem and
come up with an algorithm (a finite sequence
of steps to solve the problem).
 Formulate the algorithm in a way that a
computer can use to carry out the steps.
A program is a set of instructions to solve a
problem written in a manner that a computer
can use (not in English).

Programming



A computer understands only its own
machine language.
We write the program in a high-level
language. It uses English-like words.
A program called a compiler or
interpreter "translates" the program
written in the high-level programming
language to machine language.
Machine Language

machine language consists of instructions that
correspond directly to the hardware operations
of a particular machine i.e., instructions deal
directly with the computer’s physical
components
 machine language instructions are written in
binary
 programming in machine language is tedious
and error prone
 code is nearly impossible to understand and
debug
 Each machine has its own machine language.
Languages


in the early 1950’s, assembly languages evolved
from machine languages
 substitute words for binary codes
 much easier to remember and use, but still a
low level of abstraction
in the late 1950's, high-level languages were
introduced
 allow the programmer to write code closer to
the way humans think
 a much more natural way to solve problems
 programs are machine independent
Translation



Using a high-level language, the programmer is
able to reason at a high-level of abstraction
But programs must still be translated into
machine language that the computer hardware
can understand/execute. Inside a computer,
everything is binary.
Two standard approaches to program translation
 Interpreter – translate and execute each
instruction
 Compiler -- translate entire program
Translating a speech

an interpreter can be used to provide real-time
translation

the interpreter hears a phrase, translates,
and immediately speaks the translation

ADVANTAGE: the translation is immediate

DISADVANTAGE: if you want to hear the
speech again, must interpret all over again
Translating a speech

a translator (or compiler) translates the entire
speech offline

the translator takes a copy of the speech
and translates the entire speech

ADVANTAGE: once translated, it can be
read over and over very quickly

DISADVANTAGE: must wait for the entire
speech to be translated
Compiler vs. Interpreter



Compilation is done once and then the compiled
version can be reused many times. Often, that’s
what’s sold.
Interpretation can be done before the whole
program is available, but has to be repeated each
time the program is used.
Interpreter is suitable for Javascript, because the
program can be interpreted as the page is being
loaded, doesn't have to wait for the whole page to
download.
Debugging



A bug is an error in a program
Debugging is removing the errors without
introducing new ones.
The compiler may find errors - mistakes in
the way the program was formulated - and
will not be able to complete the translation
process. Fix the errors and repeat the
process until the program compiles
successfully.
Debugging


Run (or execute) the program. At this point,
we may find other errors and we may have to
correct the program again.
Test the program. Test it and see if there are
any mistakes. Fix errors and test again.
Software Life-Cycle






Determine an algorithm to solve the problem
Write a program to implement the algorithm:
 use very specific, detailed instructions
 use a “language” the computer understands.
Compile the program:
 A compiler translates the program into machine language.
 Fix any syntax errors that the compiler finds.
Run (or execute) the program:
 At this time we may find other errors that must be corrected.
Test the program:
 Test the program and fix any errors.
Maintain the program:
 Keep monitoring the program for unexpected errors.
 Make changes
Examples of Bugs


The Mars Climate Orbiter was lost in space in
1999. In the calculation of its route, some
programmers used the metric system while
others used English units!
A Patriot missile failed to intercept a scud
fired at US troops in 1991. The time in tenths
of a second, as measured by the system’s
internal clock, was multiplied by 10 to
produce the time in seconds.
For the future
A recipe is a good analogy for a program:
 ingredients
 Constants, variables
 data types, integer and real numbers, characters
 detailed step-by-step-instructions
 statements
 repeated actions (e.g., separate 5 eggs)
 loops
 decisions (e.g., bake until brown, beat until firm, etc.)
 pre defined actions (e.g., saute, puree, etc.)
 functions, parameters