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Questions and Answers
What is the function of the Big-Oh notation in algorithm analysis?
What is the function of the Big-Oh notation in algorithm analysis?
- It provides an exact count of primitive operations.
- It measures the memory usage of algorithms.
- It categorizes algorithms by their input data type.
- It characterizes the main factors affecting an algorithm’s running time. (correct)
Under what conditions can we say that f(n) is O(g(n))?
Under what conditions can we say that f(n) is O(g(n))?
- If f(n) is strictly less than g(n) for all n.
- If f(n) is always greater than g(n) for large values of n.
- If f(n) grows at a constant rate independent of g(n).
- If there exist constants c > 0 and n0 such that f(n) ≤ c g(n) for all n ≥ n0. (correct)
In the proof that 7n - 2 is O(n), what constants can be chosen to satisfy the definition of Big-Oh?
In the proof that 7n - 2 is O(n), what constants can be chosen to satisfy the definition of Big-Oh?
- c = 8 and n0 = 3
- c = 6 and n0 = 1
- c = 5 and n0 = 2
- c = 7 and n0 = 1 (correct)
Which of the following statements correctly describes a characteristic of pseudocode in algorithm analysis?
Which of the following statements correctly describes a characteristic of pseudocode in algorithm analysis?
What is the meaning of 'c > 0' in the definition of Big-Oh notation?
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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