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If an algorithm's time complexity is O(n2 log n), which of the following best describes its efficiency compared to an algorithm with a time complexity of O(n2)?

Question

If an algorithm's time complexity is O(n2 log n), which of the following best describes its efficiency compared to an algorithm with a time complexity of O(n2)?

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Solution

An algorithm with time complexity O(n^2 log n) is less efficient than an algorithm with time complexity O(n^2). This is because as the size of the input (n) increases, the algorithm with time complexity O(n^2 log n) will take more time to execute compared to the algorithm with time complexity O(n^2).

Here's a step-by-step comparison:

  1. O(n^2) means that the time it takes to complete increases quadratically with the size of the input. So if the input size doubles, the time it takes will increase by about four times.

  2. O(n^2 log n) means that the time it takes to complete increases more than quadratically with the size of the input. The exact increase depends on the value of log n, but it will always be more than the increase for O(n^2).

So, in comparison, the algorithm with time complexity O(n^2 log n) is less efficient than the one with O(n^2).

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