Theory

Dynamic programming always reminds of a favorite quotation: Of the several different ways to solve a problem, dynamic programming is a paradigm where we tend to solve the problem as we move ahead and keep on learning. This is one of the techniques which even seasoned programmers find hard to implement. In this post we will try to address some of these fears and aim to have a better understanding of this approach. If you are new to problem solving and somehow landed at this post, it is recommended to…

We compare things all the time to determine which one is better over the other. The best example is when you are buying stuff online, we compare prices across websites, two different mobile phones, or even two different outfits. We know that there are different techniques of solving a problem in computer science: Brute Force Divide and Conquer Greedy Dynamic Programming Naturally, when we try to solve a problem with different methods, one would want to compare them. Once they are put side to side, we can then analyze which…

Greedy algorithms is a paradigm that describes the approach on how you can go about solving a problem. You might have heard about a lot of algorithmic techniques while learning how to solve problems in computer science. The others being: Brute Force Divide and Conquer Dynamic Programming In this post we shall understand what a greedy algorithm is and how can it be used to solve problems which don’t seem very trivial at the first glance. What is a Greedy Algorithm? What is the first thing that comes to your…

Brute force method would probably be the favorite algorithmic paradigm of every developer. The beauty of a brute force method is that it is pretty straightforward and if a solution to a problem exists, you are guaranteed to find it. This option is also the most exhaustive option as we might go through all the possibilities before arriving at the result. What is Brute Force Method? You might have heard the phrase “Brute force method to solve the problem”. What exactly do you mean by that? It simply means that…

What comes to your mind when you think about divide and conquer? Do you think about wars? A strategy? A way you can split up your forces and then conquer the enemy? I am here to tell you that is exactly right. Luckily, in computer science you don’t have to deal with weapons and artillery. There are several ways to approach a problem. Divide and conquer is one of them. In our case a problem statement is our enemy. We need to break it into parts (divide) and then solve…

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. We start with ‘2’ and keep dividing the original number to get rid of composite factors. Continue this process until the number is no longer divisible by 2. This means that at…

Question: Given an integer N, find the prime numbers in that range from 1 to N. Input: N = 25Output: 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 will find the first N prime numbers using the Sieve of Eratosthenes. This technique is helpful in scenarios when we have to give immediate results and we need to query the prime numbers…

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 what can be more beautiful than using bit hacks for the same. We discusses some of the BIT Hacks in these posts:- Low Level Bit Hacks Some advanced Bit Hacks Here I…

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 to proceed. ;-) BIT HACK 6: Turn off the rightmost 1-bit. Now it finally gets more interesting!!! Bit hacks #1 – #5 were kind of boring to be honest. This bit hack…

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 in an integer) by looping over individual bits, these programming nuggets do the same with one or two carefully chosen bitwise operations. To get things going I’ll assume that you know what…