Algorithm: An algorithm is step by step instructions to solve a given problem.
Why performance analysis?
There are many important things that should be taken care of, like user friendliness, modularity, security, maintainability, etc. Why to worry about performance?
Evaluation of an algorithm is required to find the most optimized solution for solving a given problem.
For example:
While travelling from Place A to Place B one needs to select the best mode of transport (Flight, Train , Bus etc) based upon the budget and urgency.
Given two algorithms for a task, how to find which one is better?
One way is – implement both the algorithms and run the two programs on your computer for different inputs and see which one takes less time. There are many problems with this approach.
1) It might be possible that for some inputs, first algorithm performs better than the second and vice versa.
2) Also for some inputs, first algorithm might perform better on one machine and the second works better on other machine for some other inputs.
Asymptotic Analysis is the big idea that handles above issues in analyzing algorithms. In Asymptotic Analysis, we evaluate the performance of an algorithm in terms of input size (we don’t measure the actual running time). We calculate, how does the time (or space) taken by an algorithm increase with the input size.
For example: Searching a given item in a sorted array.
There are 2 ways - Linear and Binary search.
To understand how Asymptotic Analysis solves the above mentioned problems in analyzing algorithms, let us say we run the Linear Search on a fast computer and Binary Search on a slow computer. For small values of input array size, the fast computer may take less time. But, after certain value of input array size, the Binary Search will definitely start taking less time compared to the Linear Search even though the Binary Search is being run on a slow machine.
The reason is the order of growth of Binary Search is logarithmic while that of Linear Search is linear. So the machine dependent constants can always be ignored after certain values of input size.
Does Asymptotic Analysis always work?
Asymptotic Analysis is not perfect, but that’s the best way available for analyzing algorithms.
Why performance analysis?
There are many important things that should be taken care of, like user friendliness, modularity, security, maintainability, etc. Why to worry about performance?
Evaluation of an algorithm is required to find the most optimized solution for solving a given problem.
For example:
While travelling from Place A to Place B one needs to select the best mode of transport (Flight, Train , Bus etc) based upon the budget and urgency.
Given two algorithms for a task, how to find which one is better?
One way is – implement both the algorithms and run the two programs on your computer for different inputs and see which one takes less time. There are many problems with this approach.
1) It might be possible that for some inputs, first algorithm performs better than the second and vice versa.
2) Also for some inputs, first algorithm might perform better on one machine and the second works better on other machine for some other inputs.
Asymptotic Analysis is the big idea that handles above issues in analyzing algorithms. In Asymptotic Analysis, we evaluate the performance of an algorithm in terms of input size (we don’t measure the actual running time). We calculate, how does the time (or space) taken by an algorithm increase with the input size.
For example: Searching a given item in a sorted array.
There are 2 ways - Linear and Binary search.
To understand how Asymptotic Analysis solves the above mentioned problems in analyzing algorithms, let us say we run the Linear Search on a fast computer and Binary Search on a slow computer. For small values of input array size, the fast computer may take less time. But, after certain value of input array size, the Binary Search will definitely start taking less time compared to the Linear Search even though the Binary Search is being run on a slow machine.
The reason is the order of growth of Binary Search is logarithmic while that of Linear Search is linear. So the machine dependent constants can always be ignored after certain values of input size.
Does Asymptotic Analysis always work?
Asymptotic Analysis is not perfect, but that’s the best way available for analyzing algorithms.
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