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# ALGORITHM

## ALGORITHM

•  An Algorithm is a finite set of instruction that perform a particular task.

An Algorithm should satisfy following criteria.

• Input: Zero or more quantities are supplied externally.
• Output: At least one quantity is produced.
• Definiteness: Each instruction is clear and unambiguous.
• Finiteness: Algorithm must terminate after few steps.
• Effectiveness: Every instruction must be very basic.

ANALYSIS:

It means determining amount of resources (such as time and space) needed to execute it.

TIME COMPLEXITY:

• Time complexity of an algorithm is basically the execution time of a program.
• Time complexity of an algorithm depends on the number of machine instruction.

SPACE COMPLEXITY:

• Space complexity of an algorithm is basically the amount of computer memory required during program execution.

ASYMTOTIC NOTATION:

• BIG OH(O): f(n) is said to be big oh of g(n) that is f(n)=O(g(n)) iff there exists two positive constants n0 and c such that
F(n)<=cg(n) for all n>n0.
• BIG OMEGA(w): f(n) is said to be big omega of g(n) that is f(n)=w(g(n)) iff there exists two positive constants n0 and c such that
F(n)>=cg(n) for all n>n0.
• THETA(Θ): f(n) is said to be big oh of g(n) that is f(n)=Θ(g(n)) iff there exists two positive constants n0 and c such that
F(n)=cg(n) for all n>n0.

• Worst-case complexity:

It is defined by the maximum number of steps taken on any instance of size n.

• Best-case complexity:

It is defined by the maximum number of steps taken on any instance of size n.

• Average-case complexity:

It is defined by the average number of steps taken on any instance of size n.