Data Structures and Algorithms

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>Some rules for big-oh: 1. Ignore the lower order terms. 2. Ignore the coefficients of the highest-order term. 3. NO need to specify the base of logarithm If T1(N)=O f(N) & T2(N)=O g(N) T1(N)+T2(N) = max( O(f(N)), O(g(N)) ) T1(N)*T2(N) = O(f(N)* g(N))

NOTE:- ⚡Bounds are for the algorithms rather than programs or problems

Different Approaches :- 1. Empirical:- run an implemented system on real-word data. Notion of benchmarks. 2. Simulation:- run an implemented system on simulated data. 3. Analytical:- use theoretic-model data with a theoretical model system.

Machine Model Assumed: 1. Instructions are executed one after another, with no concurrent operations, Not parallel computers. 2. All operations execute in one unit of time(not the case in real computers) 3. We assume we have infinite memory and hence do not worry about page faulting. 4. Our model has fixed size(say 32 bit) integers and no fancy operations like matrix inversion, sorting. 5. One disk read counts same as addition even though addition is several orders of magnitude faster.

Factors affecting the running time: *Computer *Compiler *Algorithm used *Input to the Algorithm

*Analyzing an Algorithm* - Predicting the resources that the algorithm reset. - Resources include : - >Memory - >Communication bandwidth - >Computational time(usually most important)

Program = Data Structures + Algorithms

What is Algorithm? A clearly specified set of simple instructions on the data to be followed to solve a problem.

What is Data Structure? Method of organizing data