Coding

Comments

Post a Comment

Popular posts from this blog

Number theory Part-2

Image
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...
Read more

Number Theory Part-1

Image
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 ...
Read more

Combinatorics Part-1

Image
Introduction Counting the objects that satisfy some criteria is a very common task in both TopCoder problems and in real-life situations. The myriad ways of counting the number of elements in a set is one of the main tasks in combinatorics, and I’ll try to describe some basic aspects of it in this tutorial. These methods are used in a range of applications, from discrete math and probability theory to statistics, physics, biology, and more. Combinatorial primitives Let’s begin with a quick overview of the basic rules and objects that we will reference later. The rule of sum The rule of product For example, if we have three towns — A, B and C — and there are 3 roads from A to B and 5 roads from B to C, then we can get from A to C through B in 3*5=15 different ways. These rules can be used for a finite collections of sets. Permutation without repetition When we choose k objects from n -element set in such a way that the order matters and each object can be ch...
Read more