Competitive Python

In this post we will explore and implement an algorithm which helps us verify that if the brackets are balanced or validly used. This is a very important application of stacks as a lot of programming languages use brackets very extensively in their syntax and one of the job of a compiler is to check if the brackets are balanced or not. For simplicity's sake we will just use a list with the methods append() and pop(). This will help us emulate a stack without actually needing to implement it. If you want to, you can go and learn about stacks on this link . A set of brackets can be called balanced if all of the brackets in it are properly matched. Examples of balanced brackets : (([]{}{})) ({{}}[]) Examples of unbalanced brackets : (([)]) {{}]}]]) So now getting to the algorithm, what we simply do is that we go through a string of brackets and check that for every closing bracket there is a properly nested opening bracket. This is how we do it - Convert the input string into a...

We are going to look at Dijkstra's two-stack algorithm and see how it's implemented. This algorithm is used to evaluate infix expressions. It uses stacks at its core, so if you don't know about stacks or if you'd want to learn more about them, click this link There are three types of expressions, Infix : Infix expressions are the ones where the operators are used between values, like a + b - c . Postfix : These are the expressions where operators are written after the values, like a b c +- , this translates to a + b - c in infix. Prefix : In these expressions, the operators are written before the values, for example + - a b c . This expression will also be equal to a + b - c in infix. Okay, so what this algorithm does is evaluate expressions like ( ( 3 + 4 ) * 83 ) . It starts by breaking down this expression into a list of stings and create two empty stack, one for housing the values and other for the operators. Then we go through the list one by one. Whenev...

Greedy Algorithms is an algorithmic paradigm just like divide and conquer is. It is a design technique that depends on locally optimal choices to produce an overall optimal solution. It makes a greedy choice at every step based on a condition and hopes that the choice it made will produce the most optimum solution. A lot of times this technique fails to generate algorithms that are optimal but it does make a lot of problems very very easy. Its used in several different algorithms, most famous of them being: Huffman Coding Dijstrika's Shortest path Kruskal’s Minimum Spanning Tree Greedy algorithms basically make up a solution step by step fashion choosing the next piece which offers the most immediate benefit. Some problems based on Greedy Algorithms are - Grocery Bagger School Assembly Boxing Chopsticks Receipt

Sieve of Eratosthenes is an algorithm that is used to generate all the primes up to a particular number . It is a very ancient algorithm but is very useful and also is a frequently seen in questions in competitive programming. This is a very elegant algorithm and is certainly better than trial division method . The idea behind this algorithm is to first select 2 and strike of all the multiples of because we know that they are composite. Then look for the next number that is not stricken off, it will definitely be a prime and then strike off all the multiples of that number. This goes on until the square of the number we select is greater than the limit that we assigned to it. As you will notice there is no need to go further because all of their multiple will already be stricken off by one or the other prime before it. To formalise the algorithm, it can be described as follows : Select the smallest prime from the list of all numbers upto n. Strike off all the multiples of the ...

Stack So, now we're going to talk about stack , a linear data structure and also we will see its implementation. In another post which will be linked below later will discuss its uses. So what is a stack ? Visualise a pile of coins or a stack of trays put one over the other. The item that has been put at the last has to be removed first as it is over all the other items. Hence, it is a data structure that works on LIFO (Last in First out) principle. Which simply means that the element that has been added the last will be removed first. It is a very useful data structure and has several applications like expression evaluation and HTML validat or or a bracket matching verifier . In this data structure we only have operations that take their effect only at one end of the list. Both, the front or the end of a list can be used to implement it but using the tail(back-end) of the list is more efficient. The main operation or methods on a stack are - Push : Adds element at the...

Sorting Why do we need to sort? Merge Sort Quick Sort Why do we need to sort? Sorting is among the most important, and well studied, of computing problems. Python does have a built in method for sorting a collection but it is very advance and highly optimised, it's known as timsort , even java's inbuilt sorting method uses this algorithm. A programmer should usually depend on built-in sorting functions than rolling out a search algorithm from scratch. But with that being said it is still imperative to have a deep understanding of how sorting algorithms functions as it makes you more and more aware about your program in terms of efficiency and space complexity We will see and study two of the quicker sorting algorithms, mergesort and quicksort .Both these algorithms work on divide and conquer design pattern. Merge Sort Merge sort is a recursive algorithm.It works by splitting the list into half and then calling mergesort on both the halves independently. Once the two...

Binary Search Okay, so how do you think we can search for a paticular element in an array? One obvious way will be to loop through the array and return true at which the element is found and to return false if it doesn't exist in the array. But the problem with this algorithm known as linear search is that it can very quickly turn out to be very costly in terms of space and time as this algorithm takes O(n) or linear time. This turns out to be highly costly for a large number of elements in an array. #Linear Search --> def linear_search(array , n ): for i in array: if i == n : return True So, the solution to this is to use an algorithm called binary search . Binary search is an algorithm that works on the divide and conquer technique and is also extremely efficient.It works on O(logn). But the only catch to this algorithm is that the array it is being applied on needs to be sorted . #Binary Search --> def binary_search(array, n ): #Setting up search ...

Analysis of Algorithms Why do we need to analyse algorithms? Well,every algorithm uses up resources and to figure out which algorithm is best in its class , we need to find out which algorithm takes up minimum resources while producing the desired results . You might wonder : There must be some way else to analyse and compare algorithms like based on the time it takes to execute, but that is a comparison that is machine dependent . The time taken by an algorithm will depend on the processor of the computer its being executed on . Hence , asymptotic analysis of algorithms is the best way to analyse algorithm. How to analyse algorithms? To analyse algorithms we use "Big-O" notation, here is a video by Harvard explaining Asymptotic Notation And here is an incredible text tutorial - Analysis For any queries leave a comment below and if you like the content, hit subscribe on top of the page to stay in the loop for further posts

WHY USE PYTHON FOR COMPETITIVE CODING Well a very good reason is that python is a language which radically cuts short the time you spend writing code ,rather you could spend that time thinking about the logic that is needed for the question. In these kind of competitions speed is necessary,I am not talking about the speed of the language but rather about the speed of the programmer.Python syntax is extremely clutter free and elegant which allows us to not get tangled up in complicated details of a programming language. Python also has a very vast variety of tools in its standard library and these tools can be very well utilised in competitive programming. Here's a list of a whole lot of other reasons why you would want to use python: Common inbuilt functions: Python has common functions like count,min,max,sorted etc.These functions allow you to easily go ahead and skip writing code for these trivial procedures which often prove to be very helpful,rest assured: Pytho...