Recursion is the procedure of solving a problem by breaking it down into a smaller version of itself. It is similar to factorial notation of a nonnegative number in algebra. Below are the equations that define algebraic factorial notation.

Equation 1:0! = 1
Equation 2:n! = n * (n - 1)! If n > 0

These equations can be used to help define the concept of recursion in computer programming. A further explanation of them is needed to better understand how they can help. Equation 1 is known as the base case while equation 2 is known as the general case. Equation 1 contains no factorial notation while equation 2 is a smaller version of itself. These two equations are known as recursive definition. The following can be derived from recursive definition:

1. Every recursive definition must have one (or more) base cases.

2. The general case must eventually be reduced to a base case.

3. The base case stops the recursion. (Malik 357)

Using the information learned from above, a computer programmer can solve a problem by using a recursive algorithm or recursive function. A recursive algorithm has to have one or more base cases as well as the general solution being eventually reduced to a base case. A recursive function contains a statement that calls itself before the current call is completed. Recursive functions are used to implement recursive algorithms. Keep in mind that having a recursive function in a program allows the program to have an unlimited number of copies of that function. Also that every recursive call to a recursive function has its own set of variables and parameters as well as its own code. Finally remember that control goes back to the calling environment after it completes a recursive call. Before control can go back to the previous call, the current recursive call must finish executing. The previous call will resume execution at the point immediately following where the current recursive call has...

...For (i=0,i<index,i++
Hanly, Chapter 8, Self-Check Exercises (p. 396), numbers 1-2
1.sqrt (xi+1-xi)pow(x,2) + (yi+1-yi)pow(y,2)
2.int LIST_SIZE[6];
Int odd;
Int sum, I;
For(i=0,i<=LIST_SIZE,++i)
Sum=i+ odd;
Hanly, Chapter 8, Programming (pp. 396-397), number 1
1. #include<stdio.h>
Int main <void>
Int list{11};
Int n, I, sum;
Double %_of_total;
{
Printf(“please enter values\n”)
Scanf(“%d”,&n)
For(i=0,i<=n,++i)
Sum=n/10;
%_of_total = sum;
Printf(“The%d is the %_of_total %d\n”, n, %_of_total);
Return (0);
}
Hanly, Chapter 8, Self-Check Exercises (p. 410), numbers 3-4
3.return (int, 1= I <=in_use, 0= I =in_use);
4.for(i=0, i<=data, ++i)
Hanly, Chapter 8, Programming (p. 410), numbers 1, 3
1. Int multiply [5]
3.(double values ([10], int n)
Hanly, Chapter 8, Programming (p. 416), number 3
3.index_of_mass = get_max_range(list,fill, n-1);
Hanly, Chapter 8, Review Questions (p. 435-436), numbers 1, 6
1.for (i=0, i<=8, ++I)
6. const reverse (int x {},
Int ysum[],
Int n)
Ysum= getx[](n-1)
Hanly, Chapter 9, Self-Check Exercises (pp. 453-454), numbers 1-3
1. C
2. It displays the values in memory until it finds a null character or it finds value in memory not stored to the program and causes a run time error.
3. char_[30][29]= {_;}
Hanly, Chapter 9, Programming (p. 454), number 1
1. #include <stdio.h>
Int main(void)
{
Char fractal[25][24]= {fractal stars with the letter f;}
Printf”%s”,fractal);
1. Write the correct syntax for...

...AND TECHNOLOGY
ICS 2102 Introduction to ComputerProgramming ~ Course Outline
Course Objective
The students will understand the concepts of structured programming and learn how to write programs for
problem solving using structured programming language (C).
Learning Outcomes
By the end of the unit, the student should be able to:
a)
b)
c)
d)
e)
f)
To understand principles of good program design
To understand the concept of a variable holding a value, how a variable is declared and how it can
change
To be able to use a conditional statement to select a choice from two or more alternatives
To understand the concept of a loop – that is, a series of statements which is written once but
executed repeatedly- and how to use it in a programming language
To be able to break a large problem into smaller parts, writing each part as a module or function
To be able to use an array to store multiple pieces of homogeneous data, and use a structure to
store multiple pieces of heterogeneous data
Course Description
Structured programming: problem solving techniques, algorithms, pseudo code, syntax, semantics, data
types, expressions, statements, input/output and control structures. Basic sequencing, alternation, and looping
control constructs. Subprograms: functional and procedural abstractions and data abstraction.
Course Content and...

...Computer Programmers
Computer programmers held about 568,000 jobs in 1996. Programmers are employed in almost every industry but the largest amount is in the computer and data processing industry that includes companies that write and sell software. Allot of programmers can also be found working for companies that provide engineering and management services, manufacturers of computer and office equipment, financial institutions, insurance carriers, educational institutions, and government agencies. A growing number of computer programmers are employed on a temporary, a contract basis, or work as independent workers because allot of companies demand expertise with newer programming languages or more specialized areas of application. Rather than hiring programmers as permanent employees and then laying them off after a job is completed, employers can contract with temporary help agencies, consulting firms, or directly with programmers themselves. A marketing company may only need the services of several programmers to write and debug the software necessary to get a new database management system running. This practice also enables companies to bring in people with a specific set of skills. Bringing in an independent contractor with a certain level of experience in a new or advanced programming language enables an establishment to complete a particular job without...

...Computerprogramming (often shortened to programming) is a process that leads from an original formulation of a computing problem to executable programs. It involves activities such as analysis, understanding, thinking, and generically solving such problems resulting in an algorithm, verification of requirements of the algorithm including its correctness and its resource consumption, implementation (commonly referred to as coding[1][2]) of the algorithm in a target programming language. Source code is written in one or more programming languages (such as C, C++, C#,Java, Python, Smalltalk, JavaScript, etc.). The purpose of programming is to find a sequence of instructions that will automate performing a specific task or solve a given problem.[citation needed] The process of programming thus often requires expertise in many different subjects, including knowledge of the application domain, specialized algorithmsand formal logic.
Related tasks include testing, debugging, and maintaining the source code, implementation of the build system, and management of derived artifacts such as machine code of computer programs. These might be considered part of the programming process, but often the term "software development" is used for this larger process with the term "programming", "implementation", or "coding" reserved for the actual writing...

...Linear ProgrammingConcept Paper
There are two types of linear programming:
1. Linear Programming- involves no more than 2 variables, linear programming problems can be structured to minimize costs as well as maximize profits. Due to the increasing complexity of business organizations, the role of the management executive as a decision maker is becoming more and more difficult. Linear programming is a useful technique to solve such problems.
The necessary condition is that the data must be expressed in quantitative terms in the form of linear equations and inequalities. The general nature of the business problems in which linear programming can be effectively used are multifaceted. They include purchasing, transportation, job assignments, production scheduling and mixing. Linear programming provides a method of maximizing or minimizing a first degree function subject to certain environmental restrictions or constraints which are usually in the form of equations and inequalities.
2. Simplex method- is an algorithm for solving linear programming with any number of variables. Most real-world linear programming problems have more than two variables and thus are too complex for graphical solution. A procedure called the simplex method may be used to find the optimal solution to such problems. The simplex method is actually an...

...Base case If n = 0, return 1 Recursive step Calculate the factorial of n-1 Return n × (the factorial of n-1)
Example – Factorial
Code
int fact ( int n ) { if ( n == 0 ) return 1; return n * fact(n-1); }
// base case // recursive step
Requirements
Must have
Small version of problem solvable without recursion Strategy to simplify problem into 1 or more smaller subproblems Ability to calculate overall solution from solution(s) to subproblem(s)
MakingRecursion Work
Designing a correct recursive algorithm Verify
1. Base case is
Recognized correctly Solved correctly 2. Recursive case Solves 1 or more simpler subproblems Can calculate solution from solution(s) to subproblems
Uses principle of proof by induction
Proof By Induction
Mathematical technique A theorem is true for all n ≥ 0 if
1. Base case
Prove theorem is true for n = 0, and 2. Inductive step Assume theorem is true for n (inductive hypothesis) Prove theorem must be true for n+1
Recursion vs. Iteration
Problem may usually be solved either way
Both have advantages
Iterative algorithms
May be more efficient No additional function calls Run faster, use less memory
Recursion vs. Iteration
Recursive algorithms
Higher overhead Time to perform function call Memory for activation records (call stack) May be simpler algorithm Easier to understand, debug, maintain Natural for backtracking searches Suited for recursive data...

...ComputerProgramming:
Even Driven Programming:
This is the process where the flow of the program is determined by certain events such as:
* Senor output
* User actions i.e. mouse clicks, key presses
* Messages from other programs
* Threads
As users we have come across event driven program every day when we use a computer i.e. navigating through our computer user interface, also whilst playingcomputer games. By clicking on the mouse the computer picks up the event that has been made by this action, same goes for when we play computer games. This is because the events driven program picks up the actions that have been carried out, reads it then gives an output.
Event driven programming allows flexibility as it gives users full control whilst designing the program as they tell the program what it should do and at what time it should carry out the event. The key features of events driven program are:
* Service oriented - this means everything illustrated on the screen provides a service to the user.
* Time driven – this is where the event will only occur from the users input for example when they click on a button
* Event handlers – this is when a code is activated when an event occurs for example when a user clicks on a print preview button, when the button is pressed the code that is linked to the button is...