Algorithm and Program
Introduction
Algorithms are important for mathematics and other sciences.
An algorithm allows a process to be explained in detail in a structured, clear and precise manner.
An algorithm is a sequence of instructions that can be executed by humans or machines.
A machine, usually a computer, executes instructions given to it in a language called a programming language.
Algorithm and Program
An algorithm is a finite sequence of instructions that performs a task to solve a problem.
Example
When we want to calculate the sum of two whole numbers by hand, we use the fixed addition algorithm.
We use a pseudo-language to write an algorithm.
A program is an algorithm translated and written using a programming language.
A program consists of a finite sequence of instructions.
A computer executes the instructions that make up a program.
Programming means writing several instructions in sequence.
It is very important to approach the task of writing a program in a structured and well-thought-out manner.
Structured programming
Structured programming is based on the concept that any program can be written using only three basic structures:
- the sequence (chaining into processing sequence)
- the conditional structure (the alternative): allows you to decide on the processing to be carried out depending on whether a condition is satisfied or not
if ... then ... else ...
- The iterative structure (loop or repetition): allows a process to be carried out several times in a row
while ... do ...repeat ... until ...
Example of using basic structures: the algorithm of fixed addition.
Pseudo-language
The pseudo-language used to write an algorithm includes the basic structures used in structured programming.
In this course, we will use the Pascal programming language to translate an algorithm written in pseudo-language.
PASCAL : primary algorithmic scientific commercial application language.
Pascal is an algorithmic language that can be used as a pseudo-language to write algorithms.
Pascal is an educational language suitable for implementing algorithms and structured programming.
Concept of variable
Example: The area of a rectangle can be expressed by the following literal expression:area = length x width
length can be assigned different values.
The value assigned to length varies, and thus length is a variable.
In an algorithm, a variable is a name intended to identify a mathematical object characterized by its value and its type (numeric, character, boolean, etc.)
In programming, as in algebra, we use variables (like length and width) to hold values.
In programming, as in algebra, we use variables in expressions.
Variable in a program
In a program, a variable is a name (identifier) used to reference a location in the computer volatile memory (RAM: Random Access Memory). This memory location holds the value assigned to the variable.
When executing a program, the computer accesses the memory location referenced by a variable to perform the required operations there.
The program can use variables of different types: numbers, characters, booleans, etc.
A variable is declared in the program by specifying its type.
The type of a variable determines the size of the memory location referenced by the variable; the range of values that can be stored in that memory location; and the set of operations that can be applied to the variable.
Design an algorithm
To design an algorithm, we follow these steps:
Step 1
Read and understand the statement of the problem to be solved.
Step 2
- Define the problem results (outputs).
- Define the problem data (inputs).
- Define the processing (the operations to obtain the results from the data.)
Step 3
Write the algorithm using the pseudo-language, while respecting the structure and syntax of the pseudo-language.
The structure of writing an algorithm in pseudo-language consists of the following parts:
- The header.
- The declarations.
- The body.
An example of an algorithm
Write an algorithm that asks for the value of the radius of a circle, then calculates the value of the area of the circle.
Algorithm in pseudo-language
Algorithm circle_area;
Constants
pi = 3.14;
Variables
radius, area : Real;
Begin
Write('enter value of radius');
Read(radius);
area ← pi * radius * radius;
Write('area is : ', area);
End.
{ header }
{ declarations }
{ body }
{ write }
{ read }
{ assign }
A comment can be placed in an algorithm above or next to an instruction.
A comment is enclosed in curly braces: {comment}.
An example of a program written in Pascal
program circle_area;
const
pi = 3.14;
var
radius, area : real;
begin
writeln('enter value of radius');
readln(radius);
area := pi * radius * radius;
writeln('area is : ', area);
end.
{ header }
{ declarations }
{ body }
{ write }
{ read }
{ assign }
The structure of a Pascal program consists of three parts:
- the name of the program,
- the declaration of constants and variables,
- the body of the program, which is a sequence of instructions.
A comment can be placed in an program above or next to an instruction.
A comment is enclosed in curly braces: {comment}.
Running a program
To run a Pascal program on a computer, it must first go through a phase called compilation performed by a compiler.
A compiler is a software program that reads and analyzes a program, then translates it into machine code that can be directly executed by the computer’s processor.
A comment in a program is ignored when compiling the program.