Programming is a difficult role, and once you enter it, you will face new challenges and may be required to solve problems that no one has solved before or whose solution does not exist anywhere. At that point, you are expected to use your problem-solving and logical abilities to come up with a solution in the shortest amount of time possible. Here comes competitive programming, a mental sport that requires you to code a given problem within given constraints. So, we have curated a list of top competitive programming algorithms for 2022.
1. Search Algorithms
Search algorithms are designed to check or retrieve an element from any data structure where that element is being stored. They search for a target (key) in the search space.
There are two types of search approaches under search algorithms:
1. Linear Search : A linear search is a straightforward method. The linear search has a time complexity of O. (n). Binary Search is another method for accomplishing the same task.
Features:
It is used for unsorted and unordered small list of elements.
It has a time complexity of O(n), which means the time is linearly dependent on the number of elements, which is not bad, but not that good too.
It has a very simple implementation.
2. Binary Search: Binary Search is a searching algorithm that divides the search interval in half repeatedly in a sorted array. The idea behind binary search is to use the array's sorted information to reduce the time complexity to O. (log n).
Features:
It is great to search through large sorted arrays.
It has a time complexity of O(log n) which is a very good time complexity.
It has a simple implementation.
2. Exponentiation by Squaring
Exponentiation by squaring, also known as binary exponentiation, is a general method for computing large positive integer powers of a number in O(1) time (log2N). Not only that but the method is also used to compute polynomial powers and square matrices.
Exponentiating by squaring is an algorithm used for the fast computation of large integer powers of a number x. It is also known as the square-and-multiply algorithm or binary exponentiation. It implicitly uses the binary expansion of the exponent. It is of quite general use, for example in modular arithmetic.
It is used for quickly working out large integer powers of a number. It is also known as the square-and-multiply algorithm or binary exponentiation. It uses the binary expansion of the exponent.
3. String Parsing and Matching
String matching algorithms have greatly influenced computer science and play an essential role in various real-world problems. It helps in performing time-efficient tasks in multiple domains. These algorithms are useful in the case of searching a string within another string. String matching is also used in the Database schema, Network systems.
String Matching Algorithms can broadly be classified into two types of algorithms –
Exact String Matching Algorithms
Approximate String Matching Algorithms
Exact String Matching Algorithm
Exact string matching algorithms is to find one, several, or all occurrences of a defined string (pattern) in a large string (text or sequences) such that each matching is perfect. All alphabets of patterns must be matched to corresponding matched subsequence.
Approximate String Matching Algorithms
Approximate String Matching Algorithms (also known as Fuzzy String Searching) searches for substrings of the input string. More specifically, the approximate string matching approach is stated as follows: Suppose that we are given two strings, text T[1…n] and pattern P[1…m]. The task is to find all the occurrences of patterns in the text whose edit distance to the pattern is at most k.
Parsing Algorithm
Parsing, syntax analysis, or syntactic analysis is the process of analyzing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar. ... Some parsing algorithms may generate a parse forest or list of parse trees for a syntactically ambiguous input.
4. Algorithms for Primality Testing
A primality test is a test to determine whether or not a given number is prime, as opposed to actually decomposing the number into its constituent prime factors (which is known as prime factorization).
Primality tests come in two varieties:
Deterministic and
Probabilistic.
Deterministic tests determine with absolute certainty whether a number is prime. Examples of deterministic tests include the Lucas-Lehmer test and elliptic curve primality proving.
Probabilistic tests can potentially (although with very small probability) falsely identify a composite number as prime (although not vice versa). However, they are in general much faster than deterministic tests. Numbers that have passed a probabilistic prime test are therefore properly referred to as probable primes until their primality can be demonstrated deterministically.
5. Algorithms for Sorting
Sorting is the most thoroughly studied concept in the field of computer science. The basic idea is to arrange the items on a list in a specific order. Though every major programming language has built-in sorting libraries, knowing how they work comes in handy. Depending on the situation, sorting methods include Merge Sort, Quick Sort, Bucket Sort, Heap Sort, and Counting Sort.
Read More: Sorting Algorithm
6. Dynamic Programming
Dynamic programming (DP) is a technique for breaking down a complex problem into simpler subproblems. Programmers solve the subproblems, remember their results, and use them to solve the complex problem quickly.
The main use of dynamic programming is to solve optimization problems. Here, optimization problems mean that when we are trying to find out the minimum or the maximum solution of a problem. The dynamic programming guarantees to find the optimal solution of a problem if the solution exists.
The definition of dynamic programming says that it is a technique for solving a complex problem by first breaking into a collection of simpler subproblems, solving each subproblem just once, and then storing their solutions to avoid repetitive computations.
7. Hashing
Hash lookup is currently the most widely used technique for locating relevant data based on a key or ID. Previously, programmers relied on sorting and binary search to find indexes, but now they use hashing. The data structure is known as a Hash-Map, Hash-Table, or Dictionary, and it efficiently maps keys to values. Keys can be used to perform value lookups. The idea is to use a suitable hash function to perform the key -> value mapping. The structure influences the selection of a good hash function.
All hashing algorithms are:
Mathematical. Strict rules underlie the work an algorithm does, and those rules can’t be broken or adjusted.
Uniform. Choose one type of hashing algorithm, and data of any character count put through the system will emerge at a length predetermined by the program.
Consistent. The algorithm does just one thing (compress data) and nothing else.
One way. Once transformed by the algorithm, it’s nearly impossible to revert the data to its original state.
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