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Which of the following asymptotic notations represents the worst-case time complexity of an algorithm?
- a)O(1)
- b)O(n)
- c)Θ(n)
- d)Ω(n)
Correct answer is option 'B'. Can you explain this answer?
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Which of the following asymptotic notations represents the worst-case ...
The O-notation represents the worst-case time complexity of an algorithm. It indicates that the time taken by the algorithm grows linearly with the input size.
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Which of the following asymptotic notations represents the worst-case ...
Explanation:
Asymptotic Notations:
Asymptotic notations are used to analyze the efficiency of algorithms in terms of their growth rate as the input size approaches infinity.
Worst-Case Time Complexity:
The worst-case time complexity of an algorithm represents the maximum time taken by the algorithm to complete for any input size. It provides an upper bound on the running time of the algorithm.
Options:
a) O(1): This represents constant time complexity, where the running time of the algorithm does not depend on the input size. It is the best-case scenario for time complexity.
b) O(n): This represents linear time complexity, where the running time of the algorithm grows linearly with the input size. It is the worst-case scenario for time complexity as the time taken increases proportionally with the input size.
c) Θ(n): This represents the average-case time complexity, where the running time of the algorithm grows linearly with the input size within a constant factor.
d) Ω(n): This represents the best-case time complexity, where the running time of the algorithm has a lower bound that grows linearly with the input size.
Conclusion:
In the given options, O(n) represents the worst-case time complexity of an algorithm as it indicates that the running time of the algorithm increases linearly with the input size, providing an upper bound on the time taken for any input.
Asymptotic Notations:
Asymptotic notations are used to analyze the efficiency of algorithms in terms of their growth rate as the input size approaches infinity.
Worst-Case Time Complexity:
The worst-case time complexity of an algorithm represents the maximum time taken by the algorithm to complete for any input size. It provides an upper bound on the running time of the algorithm.
Options:
a) O(1): This represents constant time complexity, where the running time of the algorithm does not depend on the input size. It is the best-case scenario for time complexity.
b) O(n): This represents linear time complexity, where the running time of the algorithm grows linearly with the input size. It is the worst-case scenario for time complexity as the time taken increases proportionally with the input size.
c) Θ(n): This represents the average-case time complexity, where the running time of the algorithm grows linearly with the input size within a constant factor.
d) Ω(n): This represents the best-case time complexity, where the running time of the algorithm has a lower bound that grows linearly with the input size.
Conclusion:
In the given options, O(n) represents the worst-case time complexity of an algorithm as it indicates that the running time of the algorithm increases linearly with the input size, providing an upper bound on the time taken for any input.
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Which of the following asymptotic notations represents the worst-case time complexity of an algorithm?a)O(1)b)O(n)c)Θ(n)d)Ω(n)Correct answer is option 'B'. Can you explain this answer?
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