Computer Algorithm and its analysis

Computer Algorithm

What is a computer algorithm?

Computer algorithm is a step-by-step method for solving a problem by using a computer.

Actually, there are various strategies to solve a problem including, dynamic programming, randomized way, divide & conquer and many more.

In fact, there is no rule that you must use particular way to solve a problem. Every time you may find new way to do it. We can consider this way as a new algorithm.

Generally, how to solve a problem using a computer?

In fact, there is a problem to solve . You should find your strategy for what you will do next. You make some drafts until getting the clear idea. This idea becomes as an algorithm. I can say that algorithm is a structured idea for the solution.

The structure of algorithm consists of inputs, outputs and some steps. What does it mean? Let’s see a following problem:

Problem: Let E be an array containing n entries without any order. We have to find the index of K, if K is in the array. Otherwise, algorithm should return -1.

Strategy: Compare K to each element until a match is found or the array is exhausted. If nothing is found, return -1.

Input: E array, K key, n entries (indexed 0, 1, …, n-1).

Output: Returns answer, the location of K or -1.

Step is a code to explain computer to solve the problem. You may use any programming language for it. In this case, we write only its function:

int Search(int[] E, int n, int K){
int ans, index;
ans = -1; 			

for (index = 0; index < n; index++)
   if (K == E[index])
   {
        ans = index; 	
        break;
   }		
return ans;
}

After getting some experience with algorithms, you may move on the analysis. Here you pay attention to correctness, time & space, and optimality. By continuing the answer above, we measure the amount of work which has been done by an algorithm.

Let W(n) be an a function. It is the maximum number of operation that algorithm performs on any input size n. For the given example it is W(n) = n. The worst cases happen when K is found at the end of the array or not in the array. Best case is also possible, if the E is ordered array.

2 thoughts on “Computer Algorithm and its analysis

  1. For large data linear or quadratic factors cannot be ignored, but for small data an asymptotically inefficient algorithm may be more efficient. This is particularly used in hybrid algorithms, like Timsort, which use an asymptotically efficient algorithm (here merge sort, with time complexity Theoretical computer science: introduction to Automata, computability, complexity, algorithmics, randomization, communication, and cryptography

  2. Algorithm analysis is important in practice because the accidental or unintentional use of an inefficient algorithm can significantly impact system performance. In time-sensitive applications, an algorithm taking too long to run can render its results outdated or useless. An inefficient algorithm can also end up requiring an uneconomical amount of computing power or storage in order to run, again rendering it practically useless. Analysis of algorithms typically focuses on the asymptotic performance, particularly at the elementary level, but in practical applications constant factors are important, and real-world data is in practice always limited in size. The limit is typically the size of addressable memory, so on 32-bit machines 2

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