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ANALYSIS OF ALGORITHMS AND ORDERS OF GROWTH

In Partial Fulfillment Of the requirements for the Degree

Bachelor of Science in Information Technology

School year 2011-2012

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Submitted By:

Dacutanan, Francis III C.

Submitted to:

Engr. Nelson Rodelas

Chapter I

Introduction

Algorithms are one of the few mathematical and logical constructs whose theoretical concept is being provided to represent for an instance in practical application by billions of people each day via the computer. Understanding the historical background, formulation, analysis and searching methods regarding algorithms is useful for those in the computer science field and curious outsiders including the other researchers upon studying in gaining an appreciation for what a computer can do as well as its limitations. Algorithms are expressed in a variety of ways; most commonly is natural languages, which are spoken languages. The other way that they are commonly expressed is through artificial languages such as mathematics and programming languages. They are also expressed, for learning purposes using flowcharts to illustrate the algorithmic concepts in academic settings understudy by many other researchers within this era of Information Technology. Searching algorithm methods will simply specify the exact context of element on a given list upon searching the desired element. Likewise, Binary search and linear/sequential search plays a big part that falls under this study. In computer science binary search is superior to sequential search. In addition, to know the complexity that an algorithm has, simply the analysis may take lead for it. Algorithm analysis can take on a number of forms, depending on the medium or language that a researcher will use, upon that it is expressed in. Regarding on the analysis of algorithm, Notations are included in this research which will enable to elaborate the complexity and growth of a function. Analysis in such manner is really a complex process that is gradually taken upon rigid logic and refined throughout testing, at varying levels of complexity. Overall, this study will guide the other researchers to know on how algorithms seemingly important to those who deals with computer. Let be this study shares information to inculcate with and be useful for the other researchers to build a concept for computer science and Information Technology field.

Chapter II

Statement of the problem

The objective of this study is to know what really an algorithm is. It will enable the other researchers to know the complexity and efficiency of algorithm in Mathematics and computers. It will also contribute a lot to computation and analysis moreover, how an algorithm works on computer and how the other researchers will analyze its functionality. Particularly, this study will help to answer the following questions: 1. What is an Algorithm?

1.1 Types of Algorithm

1.2 Properties of an Algorithm

2. How can we search algorithm in a list?

2.1 Binary search

2.2 Linear search

3. How can you compare Binary search to linear search? 3.1 size or length

3.2 speed

3.3 number of iterations

4. How do we analyze algorithm?

4.1 Execution time

4.2 number of statement

4.3 running time

5. How can we estimate the growth of a function?

5.1 asymptotic notations

5.2 Big O-Notation

6. What is problem complexity?

6.1 Definition

6.2 classifications

6.3 characteristics

Based upon the above questions, it will help the other researchers to know...