Answer:
Given that:
A= 40n^2
B = 2n^3
By given scenario:
40n^2=2n^3
dividing both sides by 2
20n^2=n^3
dividing both sides by n^2 we get
20 = n
Now putting n=20 in algorithms A and B:
A=40n^2
= 40 (20)^2
= 40 * (400)
A= 16000
B= 2n^3
= 2 (20)^3
= 2(8000)
B= 16000
Now as A and B got same on n = 20, then as given:
n0 <20 for n =20
Let us take n0 = 19, it will prove A is better than B.
We can also match the respective graphs of algorithms of A and B to see which one leads and which one lags, before they cross at n= 20.
The discipline of building hardware architectures, operating systems, and specialized algorithms for running a program on a cluster of processors is known as <u>parallel computing.</u>
<u></u>
<h3>What is Parallel Computing?</h3>
Parallel computing refers to the process of breaking down larger problems into smaller, independent, often similar parts that can be executed simultaneously by multiple processors communicating via shared memory, the results of which are combined upon completion as part of an overall algorithm. The primary goal of parallel computing is to increase available computation power for faster application processing and problem solving.
<h3>Types of parallel computing</h3>
There are generally four types of parallel computing, available from both proprietary and open source parallel computing vendors:
- Bit-level parallelism: increases processor word size, which reduces the quantity of instructions the processor must execute in order to perform an operation on variables greater than the length of the word.
- Instruction-level parallelism: the hardware approach works upon dynamic parallelism, in which the processor decides at run-time which instructions to execute in parallel; the software approach works upon static parallelism, in which the compiler decides which instructions to execute in parallel.
- Task parallelism: a form of parallelization of computer code across multiple processors that runs several different tasks at the same time on the same data.
- Superword-level parallelism: a vectorization technique that can exploit parallelism of inline code.
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