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When comparing two algorithms with time complexities O(n) and O(n2), which one is more efficient for large inputs?Group of answer choices

Question

When comparing two algorithms with time complexities O(n) and O(n^2), which one is more efficient for large inputs?

Group of answer choices

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Solution

The algorithm with time complexity O(n) is more efficient for large inputs.

Here's why:

  1. Time complexity is a concept in computer science that deals with the quantification of the amount of time taken by an algorithm to run, as a function of the size of the input to the program. It is usually expressed using Big O notation, which describes the upper bound of the time complexity in the worst case scenario.

  2. O(n) means that the time complexity or running time of an algorithm grows linearly with the size of the input data. In other words, if you double the size of the input, the running time will also double.

  3. O(n^2) means that the time complexity grows quadratically with the size of the input. So, if you double the size of the input, the running time will increase fourfold.

  4. Therefore, for large inputs, an algorithm with time complexity O(n) will be more efficient than an algorithm with time complexity O(n^2), because its running time increases at a slower rate as the size of the input increases.

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