What is meant by Algorithm Analysis?
Algorithm analysis is an important part of computational complexity theory, which provides theoretical estimation for the required resources of an algorithm to solve a specific computational problem. Analysis of algorithms is the determination of the amount of time and space resources required to execute it.
Why Analysis of Algorithms is important?
- To predict the behavior of an algorithm without implementing it on a specific computer.
- It is much more convenient to have simple measures for the efficiency of an algorithm than to implement the algorithm and test the efficiency every time a certain parameter in the underlying computer system changes.
- It is impossible to predict the exact behavior of an algorithm. There are too many influencing factors.
- The analysis is thus only an approximation; it is not perfect.
- More importantly, by analyzing different algorithms, we can compare them to determine the best one for our purpose.
Types of Algorithm Analysis:
- Best case
- Worst case
- Average case
Basics on Analysis of Algorithms:
- What is algorithm and why analysis of it is important?
- Asymptotic Notation and Analysis (Based on input size) in Complexity Analysis of Algorithms
- Worst, Average and Best Case Analysis of Algorithms
- Types of Asymptotic Notations in Complexity Analysis of Algorithms
- How to Analyse Loops for Complexity Analysis of Algorithms
- How to analyse Complexity of Recurrence Relation
- Introduction to Amortized Analysis
- Analysis of Algorithms | Big-O analysis
- Difference between Big Oh, Big Omega and Big Theta
- Examples of Big-O analysis
- Difference between big O notations and tilde
- Analysis of Algorithms | Big – Ω (Big- Omega) Notation
- Analysis of Algorithms | Big – Θ (Big Theta) Notation
Some Advance topics:
- Types of Complexity Classes | P, NP, CoNP, NP hard and NP complete
- Can Run Time Complexity of a comparison-based sorting algorithm be less than N logN?
- Why does accessing an Array element take O(1) time?
- What is the time efficiency of the push(), pop(), isEmpty() and peek() operations of Stacks?
- Proof that Clique Decision problem is NP-Complete
- Proof that Independent Set in Graph theory is NP Complete
- Prove that a problem consisting of Clique and Independent Set is NP Complete
- Prove that Dense Subgraph is NP Complete by Generalisation
- Prove that Sparse Graph is NP-Complete
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