Most important type of Algorithms - GeeksforGeeks (2024)

What is an Algorithm?

An algorithm is a step-by-step procedure to solve a problem. A good algorithm should be optimized in terms of time and space. Different types of problems require different types of algorithmic techniques to be solved in the most optimized manner. There are many types of algorithms but the most important and fundamental algorithms that you must are discussed in this article.

1. Brute Force Algorithm:

This is the most basic and simplest type of algorithm. A Brute Force Algorithm is the straightforward approach to a problem i.e., the first approach that comes to our mind on seeing the problem. More technically it is just like iterating every possibility available to solve that problem.

Example:

If there is a lock of 4-digit PIN. The digits to be chosen from 0-9 then the brute force will be trying all possible combinations one by one like 0001, 0002, 0003, 0004, and so on until we get the right PIN. In the worst case, it will take 10,000 tries to find the right combination.

2. Recursive Algorithm:

This type of algorithm is based on recursion. In recursion, a problem is solved by breaking it into subproblems of the same type and calling own self again and again until the problem is solved with the help of a base condition.
Some common problem that is solved using recursive algorithms are Factorial of a Number, Fibonacci Series, Tower of Hanoi, DFS for Graph, etc.

a) Divide and Conquer Algorithm:

In Divide and Conquer algorithms, the idea is to solve the problem in two sections, the first section divides the problem into subproblems of the same type. The second section is to solve the smaller problem independently and then add the combined result to produce the final answer to the problem.
Some common problem that is solved using Divide and Conquers Algorithms are Binary Search, Merge Sort, Quick Sort, Strassen’s Matrix Multiplication, etc.

b) Dynamic Programming Algorithms:

This type of algorithm is also known as the memoization technique because in this the idea is to store the previously calculated result to avoid calculating it again and again. In Dynamic Programming, divide the complex problem into smaller overlapping subproblems and store the result for future use.
The following problems can be solved using the Dynamic Programming algorithm Knapsack Problem, Weighted Job Scheduling, Floyd Warshall Algorithm, etc.

c) Greedy Algorithm:

In the Greedy Algorithm, the solution is built part by part. The decision to choose the next part is done on the basis that it gives an immediate benefit. It never considers the choices that had been taken previously.
Some common problems that can be solved through the Greedy Algorithm are Dijkstra Shortest Path Algorithm, Prim’s Algorithm, Kruskal’s Algorithm, Huffman Coding, etc.

d) Backtracking Algorithm:

In Backtracking Algorithm, the problem is solved in an incremental way i.e. it is an algorithmic technique for solving problems recursively by trying to build a solution incrementally, one piece at a time, removing those solutions that fail to satisfy the constraints of the problem at any point of time.
Some common problems that can be solved through the Backtracking Algorithm are the Hamiltonian Cycle, M-Coloring Problem, N Queen Problem, Rat in Maze Problem, etc.

3. Randomized Algorithm:

In the randomized algorithm, we use a random number.it helps to decide the expected outcome. The decision to choose the random number so it gives the immediate benefit
Some common problems that can be solved through the Randomized Algorithm are Quicksort: In Quicksort we use the random number for selecting the pivot.

4. Sorting Algorithm:

The sorting algorithm is used to sort data in maybe ascending or descending order. Its also used for arranging data in an efficient and useful manner.
Some common problems that can be solved through the sorting Algorithm are Bubble sort, insertion sort, merge sort, selection sort, and quick sort are examples of the Sorting algorithm.

5. Searching Algorithm:

The searching algorithm is the algorithm that is used for searching the specific key in particular sorted or unsorted data. Some common problems that can be solved through the Searching Algorithm are Binary search or linear search is one example of a Searching algorithm.

6. Hashing Algorithm:

Hashing algorithms work the same as the Searching algorithm but they contain an index with a key ID i.e a key-value pair. In hashing, we assign a key to specific data.
Some common problems can be solved through the Hashing Algorithm in password verification.