What does Quickselect return when run on the list (92, 69, 73, 86, 77, 45) with k = 2?

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BlackTom AI · Accepted Answer

The question asks: What does Quickselect return when run on the list (92, 69, 73, 86, 77, 45) with k = 2?

First, it's important to clarify the convention for k in Quickselect, because different sources use 1-based or 0-based indexing. If k is 1-based (the common textbook definition), k = 2 would mean the second smallest element. If k is 0-based, k = 2 would mean the third smallest element. The provided answer is 73, so we can infer which interpretation is being used.

Let's explore the data: the list elements are 92, 69, 73, 86, 77, 45.
- The sorted order of these values is: 45, 69, 73, 77, 86, 92.

If k = 2 were 1-based (second smallest), the result would be 69.
If k = 2 were 0-based (third smallest), the result would be 73.

Since the stated correct answer is 73, that aligns with the interpretation that k is treated as a 0-based index, i.e., k = 2 corresponds to the third smallest element.

Why 73 is the third smallest under this interpretation:
- After sorting, the three smallest elements are 45, 69, and 73.
- The third smallest among these is 73, which matches the given answer.

Now, consider potential misconceptions:
- If you assumed a 1-based convention and looked for the second smallest, you would get 69, which would contradict the provided answer.
- If you tried to apply Quickselect without understanding whether k is 0-based or 1-based, you might misidentify the target order statistic and select either the second or first smallest instead of the third.

In Quickselect implementations, always check the documentation or code to confirm whether k is 0-based or 1-based. In this case, the expected output of 73 corresponds to k = 2 being interpreted as the third smallest element (0-based indexing).

Summary: Given the answer is 73, the interpretation is that k is 0-based, so k = 2 selects the third smallest element of the list, which is 73.

CIS-279-OLH-CRN47413 Quiz: Chapter 3

What does Quickselect return when run on the list (92, 69, 73, 86, 77, 45) with k = 2?

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