Table of Contents
by Aratrika Dutta
February 11, 2022
In this article, we will discuss the top important algorithms for competitive programming to boost coding knowledge
Programming is a challenging role and once you enter this field you will encounter new challenges and you may have to solve some problems which no one has solved before or their solution doesn’t exist anywhere. At that time you are expected to come up with a solution in the least possible time using your problem-solving and logical ability. Here comes competitive programming which is a mental sport enabling you to code a given problem under provided constraints. This article lists the top algorithms for competitive programming in 2022.
Under search algorithms there are two types of search approaches:
Linear Search Approach: A simple approach is to do a linear search. The time complexity of the Linear search is O(n). Another approach to perform the same task is using Binary Search.
Binary Search Approach: Binary Search is a searching algorithm used in a sorted array by repeatedly dividing the search interval in half. The idea of binary search is to use the information that the array is sorted and reduce the time complexity to O(log n).
Exponentiation by Squaring
Exponentiation by squaring or Binary exponentiation is a general method for fast computation of large positive integer powers of a number in O(log2N). Not only this but the method is also used for the computation of powers of polynomials and square matrices.
String Matching and Parsing
In computer science, pattern matching/searching is one of the most important problems. There has been a lot of research on the topic but we’ll enlist only two necessities for any programmer.
KMP Algorithm (String Matching)
Knuth-Morris-Pratt algorithm is used in cases where we have to match a short pattern in a long string. For instance, when we Ctrl+F a keyword in a document, we perform pattern matching in the whole document.
Regular Expression (String Parsing)
Many times we have to validate a string by parsing over a predefined restriction. It is heavily used in web development for URL parsing and matching.
Primality Testing Algorithms
There are deterministic and probabilistic ways of determining whether a given number is prime or not. Here are both deterministic and probabilistic (nondeterministic) ways.
Sieve of Eratosthenes (deterministic)
If there is a certain limit on the range of numbers, say determine all primes within range 100 to 1000 then Sieve is a way to go. The length of the range is a crucial factor because programmers have to allocate a certain amount of memory according to the range.
Fermat primality test and Miller–Rabin primality test (both are nondeterministic)
Both of these are compositeness tests. If a number is proved to be composite, then it sure isn’t a prime number. Miller-Rabin is a more sophisticated one than Fermat’s. Miller-Rabin also has a deterministic variant, but then it’s a game of trade between time complexity and accuracy of the algorithm.
In the field of computer science, sorting is the most thoroughly studied concept. The simple concept is to arrange the items of a list in a determined order. Though every major programming language has built-in sorting libraries, it comes in handy if you know how they work. Merge Sort, Quick Sort, Bucket Sort, Heap Sort, Counting Sort are the types of sorting that you might want to use depending upon the requirements.
Dynamic programming (DP) is a method for solving a complex problem by breaking it down into simpler subproblems. Programmers solve the subproblems, remember their results, and using them they make their way to solving the complex problem, quickly.
Hash lookup is currently the most widely used technique to find appropriate data by key or ID. Formerly, to look for indexes programmers used to rely on sorting and binary search but now they use hashing. The data structure is referred to as Hash-Map or Hash-Table or Dictionary that maps keys to values, efficiently. Performing value lookups can be done using keys. Idea is to use an appropriate hash function that does the key -> value mapping. Choosing a good hash function depends on the structure.
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