Algorithms Classification
An Algorithm is a procedure to solve a particular problem in a finite number of steps for a finite-sized input.
Algorithms Classification
The algorithms can be classified in various ways. They are:
Implementation Method
Design Method
Design Approaches
Classification by Implementation Method
There are primarily three main categories into which an algorithm can be named in this type of classification. They are:
Recursion or Iteration
A recursive algorithm is an algorithm which calls itself again and again until a base condition is achieved whereas iterative algorithms use loops and/or data structures like stacks, queues to solve any problem.
Every recursive solution can be implemented as an iterative solution and vice versa.
Example
The Tower of Hanoi is implemented in a recursive fashion while Stock Span problem is implemented iteratively.
Exact or Approximate
Algorithms that are capable of finding an optimal solution for any problem are known as the exact algorithm.
For all those problems, where it is not possible to find the most optimized solution, an approximation algorithm is used.
Approximate algorithms are the type of algorithms that find the result as an average outcome of sub outcomes to a problem.
Example
For NP-Hard Problems, approximation algorithms are used. Sorting algorithms are the exact algorithms.
Serial or Parallel or Distributed Algorithms
In serial algorithms, one instruction is executed at a time while parallel algorithms are those in which we divide the problem into subproblems and execute them on different processors.
If parallel algorithms are distributed on different machines, then they are known as distributed algorithms.
Classification by Design Method
There are primarily three main categories into which an algorithm can be named in this type of classification. They are:
Greedy Method
In the greedy method, at each step, a decision is made to choose the local optimum, without thinking about the future consequences.
Example
Fractional Knapsack, Activity Selection.
Divide and Conquer
The Divide and Conquer strategy involves dividing the problem into sub-problem, recursively solving them, and then recombining them for the final answer.
Example
Merge sort, Quicksort.
Dynamic Programming
The approach of Dynamic programming is similar to divide and conquer.
The difference is that whenever we have recursive function calls with the same result, instead of calling them again we try to store the result in a data structure in the form of a table and retrieve the results from the table.
Thus, the overall time complexity is reduced.
Dynamicmeans we dynamically decide, whether to call a function or retrieve values from the table.
Example
0-1 Knapsack, subset-sum problem.
Linear Programming
In Linear Programming, there are inequalities in terms of inputs and maximizing or minimizing some linear functions of inputs.
Example
Maximum flow of Directed Graph
Reduction(Transform and Conquer)
In this method, we solve a difficult problem by transforming it into a known problem for which we have an optimal solution.
Basically, the goal is to find a reducing algorithm whose complexity is not dominated by the resulting reduced algorithms.
Example
Selection algorithm for finding the median in a list involves first sorting the list and then finding out the middle element in the sorted list. These techniques are also called transform and conquer.
Backtracking
This technique is very useful in solving combinatorial problems that have a single unique solution.
Where we have to find the correct combination of steps that lead to fulfillment of the task.
Such problems have multiple stages and there are multiple options at each stage.
This approach is based on exploring each available option at every stage one-by-one.
While exploring an option if a point is reached that doesn’t seem to lead to the solution, the program control backtracks one step, and starts exploring the next option.
In this way, the program explores all possible course of actions and finds the route that leads to the solution.
Example
N-queen problem, maize problem.
Branch and Bound
This technique is very useful in solving combinatorial optimization problem that have multiple solutions and we are interested in find the most optimum solution.
In this approach, the entire solution space is represented in the form of a state space tree.
As the program progresses each state combination is explored, and the previous solution is replaced by new one if it is not the optimal than the current solution.
Example
Job sequencing, Travelling salesman problem.
Classification by Design Approaches
There are two approaches for designing an algorithm. these approaches include
Top-Down Approach
In the top-down approach, a large problem is divided into small sub-problem and keep repeating the process of decomposing problems until the complex problem is solved.
Bottom-up approach
The bottom-up approach is also known as the reverse of top-down approaches. In approach different, part of a complex program is solved using a programming language and then this is combined into a complete program.
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