Final Year Project Btech Computer Science

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Number theory Part-2

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Introduction Problems in competitive programming which involve Mathematics are are usually about number theory, or geometry. If you know number theory, that increases your ammo heavily in solving a lot of tougher problems, and helps you in getting a strong hold on a lot of other problems, too. Problems in competitive programming require insight, so just knowing some topics is not enough at all. All of the problems requires more or less math tough. For instance, solving large systems of equations and approximating solutions to differential equations.  Set Theory Before we proceed, let us get through the some common set operations. Q.) What is a Set? -In mathematics, a set is a collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}. Sets are one of the most fundamental con...
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Packages in Java

Packages In Java Package  in  Java  is a mechanism to encapsulate a group of classes, sub packages and interfaces. Packages are used for: Preventing naming conflicts. For example there can be two classes with name Employee in two packages, college.staff.cse.Employee and college.staff.ee.Employee Making searching/locating and usage of classes, interfaces, enumerations and annotations easier Providing controlled access: protected and default have package level access control. A protected member is accessible by classes in the same package and its subclasses. A default member (without any access specifier) is accessible by classes in the same package only. Packages can be considered as data encapsulation (or data-hiding). All we need to do is put related classes into packages. After that we can simply write a import a class from existing packages and use it in our program. A packages is container of group of related classes where some of the classes are acces...
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Number Theory Part-1

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Introduction: Problems in competitive programming which involve Mathematics are are usually about number theory, or geometry. If you know number theory, that increases your ammo heavily in solving a lot of tougher problems, and helps you in getting a strong hold on a lot of other problems, too. Problems in competitive programming require insight, so just knowing some topics is not enough at all. All of the problems requires more or less math tough. For instance, solving large systems of equations and approximating solutions to differential equations. Modulo: Modulo operation gives the remainder after division, when one number is divided by another. It is denoted by % sign. Example: We have two numbers 5 and 2, then 5%2 is 1 as when 5 is divided by 2, it leaves 1 as remainder. Properties: Some of the properties of modulo are: (a+b)%c = (a%c + b%c )%c. (a * b)%c = ((a%c) * (b%c))%c. Example: Let’s say a = 5, b = 3, c = 2. Then: 1) (5+3)%2 = 8%2 = 0. Similarly (5%2 ...
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