Applying merge sort: Would the value in the box with the red cross be $71$? Does it matter whether we start at the bottom-left or bottom-right?

Question

I have the following diagram showing a case of merge sort:

I am trying to find the value that would be in the box with the red cross when applying merge sort in ascending order.

It seems to me that it would be $71$. If we start at the bottom-right, we have $[30, 71]$ for the first array. We then have the sorted arrays $[24, 30, 71]$ and $[49, 97]$. And then we combine these last two sorted arrays to get $[24, 30, 49, 71, 97]$. Therefore, the value in the box with the red cross would be $71$, right? And does it matter whether we start at the bottom-left or bottom-right? The result should be the same, right?

Answer 1

You don't need to simulate merge sort to figure out what that value will be. Since you know that mergesort is correct, and you're looking for the 4-th element in that subarray, you just need to find the element with rank $4$ among $\{71, 30, 24, 49, 97\}$, i.e., $71$.

This value is independent of the order in which you choose to execute the recursive calls (as long as you execute all the child calls before the parent one).