Design and Analysis Introduction

An algorithm is a set of steps of operations to solve a problem performing calculation, data processing, and automated reasoning tasks. An algorithm is an efficient method that can be expressed within finite amount of time and space.
An algorithm is the best way to represent the solution of a particular problem in a very simple and efficient way. If we have an algorithm for a specific problem, then we can implement it in any programming language, meaning that the algorithm is independent from any programming languages.
The important aspects of algorithm design include creating an efficient algorithm to solve a problem in an efficient way using minimum time and space.
To solve a problem, different approaches can be followed. Some of them can be efficient with respect to time consumption, whereas other approaches may be memory efficient. However, one has to keep in mind that both time consumption and memory usage cannot be optimized simultaneously. If we require an algorithm to run in lesser time, we have to invest in more memory and if we require an algorithm to run with lesser memory, we need to have more time.
The following steps are involved in solving computational problems.
Problem definition
Development of a model
Specification of an Algorithm
Designing an Algorithm
Checking the correctness of an Algorithm
Analysis of an Algorithm
Implementation of an Algorithm
Program testing
Documentation
The main characteristics of algorithms are as follows −
Algorithms must have a unique name
Algorithms must have a unique name
Algorithms should have explicitly defined set of inputs and outputs
Algorithms should have explicitly defined set of inputs and outputs
Algorithms are well-ordered with unambiguous operations
Algorithms are well-ordered with unambiguous operations
Algorithms halt in a finite amount of time. Algorithms should not run for infinity, i.e., an algorithm must end at some point
Algorithms halt in a finite amount of time. Algorithms should not run for infinity, i.e., an algorithm must end at some point
Pseudocode gives a high-level description of an algorithm without the ambiguity associated with plain text but also without the need to know the syntax of a particular programming language.
The running time can be estimated in a more general manner by using Pseudocode to represent the algorithm as a set of fundamental operations which can then be counted.
An algorithm is a formal definition with some specific characteristics that describes a process, which could be executed by a Turing-complete computer machine to perform a specific task. Generally, the word "algorithm" can be used to describe any high level task in computer science.
On the other hand, pseudocode is an informal and (often rudimentary) human readable description of an algorithm leaving many granular details of it. Writing a pseudocode has no restriction of styles and its only objective is to describe the high level steps of algorithm in a much realistic manner in natural language.
For example, following is an algorithm for Insertion Sort.
Algorithm: Insertion-Sort 
Input: A list L of integers of length n  
Output: A sorted list L1 containing those integers present in L 
Step 1: Keep a sorted list L1 which starts off empty  
Step 2: Perform Step 3 for each element in the original list L  
Step 3: Insert it into the correct position in the sorted list L1.  
Step 4: Return the sorted list 
Step 5: Stop

Here is a pseudocode which describes how the high level abstract process mentioned above in the algorithm Insertion-Sort could be described in a more realistic way.
for i <- 1 to length(A) 
   x <- A[i] 
   j <- i 
   while j > 0 and A[j-1] > x 
      A[j] <- A[j-1] 
      j <- j - 1 
   A[j] <- x

In this tutorial, algorithms will be presented in the form of pseudocode, that is similar in many respects to C, C++, Java, Python, and other programming languages.

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