Design and Analysis of Algorithms

  • Last Updated : 13 Jul, 2022

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:

  1. Best case
  2. Worst case
  3. Average case

Basics on Analysis of Algorithms:

  1. What is algorithm and why analysis of it is important?
  2. Analysis of Algorithms | Set 1 (Asymptotic Analysis)
  3. Analysis of Algorithms | Set 2 (Worst, Average and Best Cases)
  4. Analysis of Algorithms | Set 3 (Asymptotic Notations)
  5. Analysis of Algorithms | Set 4 (Analysis of Loops)
  6. Analysis of Algorithm | Set 4 (Solving Recurrences)
  7. Analysis of Algorithm | Set 5 (Amortized Analysis Introduction)

Asymptotic Notations:

  1. Analysis of Algorithms | Big-O analysis
  2. Difference between Big Oh, Big Omega and Big Theta
  3. Examples of Big-O analysis
  4. Difference between big O notations and tilde
  5. Analysis of Algorithms | Big – Ω (Big- Omega) Notation
  6. Analysis of Algorithms | Big – Θ (Big Theta) Notation

Some Advance topics:

  1. Types of Complexity Classes | P, NP, CoNP, NP hard and NP complete
  2. Can Run Time Complexity of a comparison-based sorting algorithm be less than N logN?
  3. Why does accessing an Array element take O(1) time?
  4. What is the time efficiency of the push(), pop(), isEmpty() and peek() operations of Stacks?

Complexity Proofs:

  1. Proof that Clique Decision problem is NP-Complete
  2. Proof that Independent Set in Graph theory is NP Complete
  3. Prove that a problem consisting of Clique and Independent Set is NP Complete
  4. Prove that Dense Subgraph is NP Complete by Generalisation
  5. Prove that Sparse Graph is NP-Complete

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