If an algorithm has a time complexity of O(n^2), which of the following input sizes will cause the running time to increase the most?Doubling the input sizeTripling the input sizeHalving the input sizeKeeping the input size constantClear ResponseSave & Next
Question
If an algorithm has a time complexity of O(n^2), which of the following input sizes will cause the running time to increase the most?Doubling the input sizeTripling the input sizeHalving the input sizeKeeping the input size constantClear ResponseSave & Next
Solution
Tripling the input size will cause the running time to increase the most.
Here's why:
The time complexity of an algorithm, O(n^2), means that the running time of the algorithm increases quadratically with the size of the input.
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If you double the input size (2n), the new running time will be (2n)^2 = 4n^2. This is four times the original running time.
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If you triple the input size (3n), the new running time will be (3n)^2 = 9n^2. This is nine times the original running time.
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If you halve the input size (n/2), the new running time will be (n/2)^2 = n^2/4. This is one fourth of the original running time.
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If you keep the input size constant, the running time will also remain constant.
Therefore, tripling the input size will cause the greatest increase in running time.
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