Which of the following can be done in O(n)? (We have no pre-assumptions on the data we are given.)

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The question asks which operations can be performed in O(n) time without any preconditions about the data.
Option 1: Merging two ascending arrays, each of size n, to form a new ascending array. Using the standard merge procedure (two-pointer technique), you compare the heads of both arrays and copy the smaller element into the new array, advancing the corresponding pointer. This consumes exactly n + n elements and requires a single pass over both arrays, yielding O(n) time complexity. Because you only move through each input once, there’s no need to assume any extra structure beyond their sorted order.
Option 2: Inserting an element into a descending array of size n and building a new descending array. A straightforward approach is to scan the existing descending array to locate the correct insertion point for the new element, then copy elements into a new array with the element inserted at that point. This involves a single pass to find the position (potentially touching all n elements) and another pass to copy into the new array, which is O(n) time overall. Since there are no preconditions about the data beyond it being sorted in descending order, this method remains linear in n.
In both cases, the work grows linearly with the size of the input arrays, and no assumptions beyond the basic sorted order are required, so neither option exceeds O(n) time under the stated conditions.

CPSC_V 320 201/202/203 2024W2 Reading Quiz #2 (Asymptotic Analysis)

Which of the following can be done in O(n)? (We have no pre-assumptions on the data we are given.)

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