The Best Algorithms for Competitive Programming Every Programmer Needs to Know in 2022


by Aratrika Dutta


February 11, 2022

In this article, we will discuss the most important algorithms for competitive programming to improve coding knowledge

Programming is a challenging role and once you enter this field you will encounter new challenges and you may need to solve problems that no one has solved before or whose solution does not exist anywhere. At that time, you are expected to find a solution in the shortest possible time using your problem-solving ability and logic. Here is the competitive programming which is a mental sport allowing to coded a given problem under the given constraints. This article lists the top algorithms for competitive programming in 2022.

Search algorithms

Under search algorithms, there are two types of search approaches:

Linear search approach: A simple approach is to perform a linear search. The time complexity of linear search is O(n). Another approach to perform the same task is to use binary search.

Binary search approach: Binary search is an algorithm used to search through 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 by and reduce the time complexity to O(log n).

Exponentiation by squaring

Exponentiation by squaring or binary exponentiation is a general method of quickly calculating large positive integer powers of a number in O(log2N). Not only that, but the method is also used for calculating the powers of polynomials and square matrices.

String matching and parsing

In computer science, pattern matching/searching is one of the most important problems. There’s been a lot of research on the subject, but we’ll pick out just two necessities for any programmer.

KMP algorithm (string matching)

The Knuth-Morris-Pratt algorithm is used in cases where we need to match a short pattern in a long string. For example, when we Ctrl+F a keyword in a document, we perform pattern matching throughout the document.

Regular expression (string parsing)

Many times we need to validate a string by parsing a predefined restriction. It is widely used in web development for URL parsing and matching.

Primality test algorithms

There are deterministic and probabilistic methods to determine whether a given number is prime or not. Here are both deterministic and probabilistic (non-deterministic) methods.

Sieve of Eratosthenes (deterministic)

If there is some limit on the range of numbers, say determining all prime numbers in the range 100 to 1000, then Sieve is a way to go. The length of the range is a crucial factor because programmers need to allocate a certain amount of memory based on the range.

Fermat primality test and Miller–Rabin primality test (both are nondeterministic)

Both of these tests are composition tests. If a number turns out to be composite, then it is definitely not a prime number. Miller-Rabin is more sophisticated than that of Fermat. Miller-Rabin also has a deterministic variant, but then it’s a trade-off between time complexity and algorithm accuracy.

Sorting algorithms

In the field of computing, sorting is the most studied concept. The simple concept is to arrange the elements of a list in a specific order. Although all major programming languages ​​have built-in sorting libraries, it comes in handy if you know how they work. Merge sort, quick sort, bucket sort, heap sort, and count sort are the sort types you can use depending on the need.

Dynamic programming

Dynamic Programming (DP) is a method for solving a complex problem by breaking it down into simpler sub-problems. Programmers solve subproblems, remember their results, and use them to quickly solve the complex problem.

hash

Hash searching is currently the most widely used technique for finding relevant data by key or ID. Previously, to find indexes, programmers relied on sorting and binary search, but now they use hashing. The data structure is called Hash-Map or Hash-Table or Dictionary which effectively maps keys to values. Value searches can be performed using keys. The idea is to use a proper hash function that does the key -> value mapping. Choosing a good hash function depends on the structure.

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