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Questions and Answers
What is the function of the Big-Oh notation in algorithm analysis?
Under what conditions can we say that f(n) is O(g(n))?
In the proof that 7n - 2 is O(n), what constants can be chosen to satisfy the definition of Big-Oh?
Which of the following statements correctly describes a characteristic of pseudocode in algorithm analysis?
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What is the meaning of 'c > 0' in the definition of Big-Oh notation?
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Study Notes
Asymptotic Notation
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A method for evaluating the running time of algorithms that simplifies analysis by focusing on the main factors affecting the running time.
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Aims to estimate the number of primitive operations executed up to a constant factor, regardless of the specific number of operations per statement.
Big-Oh Notation
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Used to characterize the running time of algorithms.
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Defined as follows:
- Let f ( n ) and g ( n ) be functions mapping nonnegative integers to real numbers.
- We say that f ( n ) is O ( g ( n ) ) if there is a real constant c > 0 and an integer constant n 0 ≥ 1 such that f ( n ) ≤ cg ( n ) for every integer n ≥ n 0.
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Often pronounced as “ f ( n ) is big-Oh of g ( n ) ” or “ f ( n ) is order g ( n ).”
Example
- 7 n − 2 is O ( n ) because we can find a real constant c > 0 and an integer constant n 0 ≥ 1 such that 7 n − 2 ≤ cn for every integer n ≥ n 0.
- For example, c = 7 and n 0 = 1 satisfies the condition.
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Description
This quiz covers Big-Oh notation, a critical method for analyzing the running time of algorithms. It simplifies the evaluation of algorithm efficiency by focusing on the dominant factors affecting performance. Test your understanding of its definitions and applications with this quiz.