MS_6
Below is the Merge Sort discussed in lectures.
Consider the following segment of the merge function:

if j == len(S2) or (i S2[j]?

Question

MS_6
Below is the Merge Sort discussed in lectures.
Consider the following segment of the merge function:
   
    if j == len(S2) or (i  S2[j]?

BlackTom AI · Accepted Answer

Question restatement: The prompt shows a segment of the merge function from Merge Sort and asks how a certain conditional change would affect the overall behavior. The provided answer choices are:
- The list would be sorted in descending order.
- There would be no effect on the algorithm's behavior.
- The algorithm would no longer be stable.
- The time complexity would become O(n2)

Now, let’s evaluate each option in turn.

Option 1: The list would be sorted in descending order.
This option posits that the specific conditional change would flip the resulting overall order from ascending to descending. In a classic merge routine, the direction of ordering is determined by how the two sublists S1 and S2 are compared and merged. If the conditional used to select the next element from S1 or S2 is altered in a way that reverses the sense of the comparison (for example, replacing a less-than-or-equal check with a greater-than check, or otherwise inverting the comparison), the merged output could indeed end up in descending order rather than ascending. Since the fragment hints at a modified comparison between i and S2[j], such a change is plausible to cause a reversal of the final ordering. Therefore, describing the consequence as “the list would be sorted in descending order” aligns with how ordering is determined by the merge comparison.

Option 2: There would be no effect on the algorithm's behavior.
If the code modification actually changed the direction or logic of the comparison, the merge would produce a different ordering (ascending vs descending) or a different sequence of elements being pulled from S1 or S2. In either case, there is a behavioral impact. Claiming no effect would ignore the fundamental role of the merge comparison in determining order, so this option is incorrect.

Option 3: The algorithm would no longer be stable.
Stability in merge sort means equal elements preserve their relative order from the input across merges. A simple flip in the comparison direction could potentially affect stability only if equal elements are not handled carefully (e.g., if the code starts favoring one subarray over the other when elements are equal). However, the given scenario emphasizes a change that would alter the overall sorted order (as per Option 1), not explicitly the handling of equal elements. Without additional changes that specifically target the equal-case tie-breaking, it’s not guaranteed that stability would be lost. Therefore, this claim is not the most direct or guaranteed consequence of the described modification.

Option 4: The time complexity would become O(n2)
The time complexity of merge sort is dominated by the merging process across log n levels, yielding O(n log n). A single conditional change during merging does not change the asymptotic complexity to O(n^2); it would still perform the same number of comparisons and moves in the aggregate. Hence, this option is incorrect.

In summary, the most plausible consequence of altering the merge conditional as indicated is that the merged output would be sorted in descending order, rather than ascending, making Option 1 the correct characterization of the impact. The other options describe effects (no impact, changed stability, or worse asymptotic time) that are unsupported by how a change in the merge comparison typically influences Merge Sort.

MS_6 Below is the Merge Sort discussed in lectures. Consider the following segment of the merge function: if j == len(S2) or (i S2[j]?

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