Chapter 1 Functions of algorithms in computing

An algorithm is a series of computing steps used to convert input data into output results. An input sequence is called an instance of this Sorting Problem ). For a specific application, the following are the main considerations for choosing the Optimal Sorting Algorithm:

• Consider the number of data items to be sorted;
• These data items have been sorted;
• Possible restrictions on data item values;
• Type of the storage device to be used.

Which types of problems can the algorithm solve:

• Biological problems, DNA sequencing and analysis;
• Search engine, massive data management and manipulation;
• E-commerce, encryption and digital signature technologies;
• Commercial applications, allocation and scheduling of rare resources;
• The actual problem lies in the shortest path and the shortest route.

Efficiency is the root cause of different algorithm problems. As the scale of the problem increases, the gap will become insurmountable. Algorithms, like computer hardware, are a technology. The overall system performance depends not only on the selection of fast hardware, but also on the selection of effective algorithms. For each function f (n) and time t in the following table, find the maximum number of n problems that can be solved within the time t. Assume that the algorithm used to solve the problem requires f (n) milliseconds to solve the problem.

	1 second	1 minute	1 hour	1 day	1 month	1 year	1 Century
LgN	2 ^ 1000	Positive infinity	Positive infinity	Positive infinity	Positive infinity	Positive infinity	Positive infinity
Sqrt (n)	10 ^ 6	4.29E + 9	1.76E + 13	9.01E + 15
N	10 ^ 3	6E + 4	3.6E + 6	8.64E + 8
Nlgn	141	4896	204095	3.94E + 6
N ^ 2	32	245	1898	9296
N ^ 3	11	40	154	443
2 ^ n	10	16	22	27
N!	7	9	10	12