# Category Archives: Theory

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## Prime factors of a number. [Prime Factorization]

Question: Given an integer N, find all the prime factors of the number. Input: N = 45 Output: 3 5 Finding prime factors of any numbers is a very important concept in number theory. One sample problem is available here in which we have to find the largest prime factor. The mathematical concept behind this problem is simple.… Read More »

## Find the first N prime numbers. (Method 4) [Sieve of Eratosthenes]

Question: Given an integer N, find the prime numbers in that range from 1 to N. Input: N = 25 Output: 2, 3, 5, 7, 11, 13, 17, 19, 23 We have several ways of finding prime numbers. Some of the methods are discussed in the these posts. Method 1 Method 2 Method 3 In this post we… Read More »

## Easiest way to change case of alphabets

Here we will discuss the easiest and most simple way to change case of alphabets. Hint : We will be using bit hacks. Often during our programming needs we need to change the case of alphabets. This can be a problem requirement or simply our need to solve the question. There are several ways to do it, but… Read More »

## Advanced level Bit Hacks

Here we shall discuss some high level Bit hacks that if used cleverly can really speed up your program execution time. We discussed some of the basic hacks in this post:- Low level bit hacks you must know. Please go through the post to get a little understanding of how the things work. Smart learners are anyways welcome… Read More »

## Low level Bit Hacks that you must know

Here we shall discuss some very low level Bit hacks that can really speed up your program execution time when used effectively. Every now and then we see bit level operators. Bit hacks are ingenious little programming tricks that manipulate integers in a smart and efficient manner. Instead of performing some operation (such as counting the 1 bits… Read More »

## Playing with Pointers

Question: What is a Pointer? What are its limitations? What are its benefits? How do we use it? What all operation we can perform using it? In this article we are going to discover answers to all these questions. Pointer is a variable that contain the address of another variable and that variable can be a structure, array… Read More »

## Unlocking the Enumeration/enum Mystery

What are enums actually? Enums provide an opportunity to the user to define a shorthand for fixed set of constants like months in a year, gender etc. Enumeration is the list of constant integer values, which means that the enum values can’t be modified. Here we are going to explain Enumeration usage rules and constraints in C language.… Read More »

## Symbol Table Implementations

Symbol Tables can be implemented in many ways and here are some of them. Unordered Array Implementation With this method, just maintaining an array is enough. It needs O(n) time for searching, insertion and deletion in the worst case. Ordered [Sorted] Array Implementation In this we maintain a sorted array of keys and values. Store in sorted order… Read More »

## Symbol Tables

Since childhood, we have all used a dictionary, and many of us have used a word processor (say Microsoft WORD) which comes with a spell checker. The spell checker is also a dictionary but limited. There are many real time examples for dictionaries and few of them are:- Spelling checker The data dictionary found in database management applications… Read More »

## How many binary trees are possible with n nodes?

Question: How many binary trees are possible with n nodes? Input: Nodes = 3 Output: Answer = 5 For, example consider a tree with 3 nodes (n = 3), it will have a maximum combination of 5 different trees In general, if there are n nodes, there exist (2n)!/(n+1)! different trees.