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Complex?
What is complex?
Complexity is an abstract term that we use to denote the amount of time and effort that a problem or task takes to solve. The more time and effort required to solve the problem, the more complex the problem.
Complexity can be seen as the time it takes for a problem to get solved. As problems get more complex, it will take more time to get them solved.
How much time a problem takes to get solved is proportional to the complexity of the problem.
Methods
Some techniques for estimating complexity are:
Calculating the time complexity of a program by looking at the asymptotic worst-case running time.
Sorting an array.
Complexity vs Difficulty
Complexity is not the same thing as difficulty. Difficulty is the degree of difficulty of a task, and is typically expressed as a number of some kind, such as an operation's difficulty or an energy level. Complexity is also a factor in difficulty, in that more complex tasks usually take more time and effort to complete.
More technically, when the problem is expressed in the form of an algorithmic problem, one is dealing with the complexity of a computational problem and the other is a problem in probability.
History
Complexity was formally defined by Luis von Ahn, Hector Levesque, Joseph M. Mitchell, and Gerald Tesauro in 1999. They defined it as a combination of the following properties.
The task can be broken down into smaller tasks
Solving the smaller tasks takes less time
Solving the smaller tasks takes more time
The larger tasks are not easier to solve than the smaller tasks
The definition can be generalized by giving more examples of useful combinations.
See also
Algorithmic complexity
Probabilistic complexity
Turing machine
References ac619d1d87
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