What are the parent and child indices for node 7 in the following max-heap?

Question

BlackTom AI · Accepted Answer

Here is the given question: 'What are the parent and child indices for node 7 in the following max-heap?' Note that the provided payload has an empty list for answer_options, and an answer field contains a single string: 'Parent index: 0; child indices: 5, 6'. Since there are no answer choices to analyze, I cannot compare multiple options directly. Instead, I will explain the standard way to determine parent and child indices in a max-heap and then apply it to node 7, highlighting how indexing convention affects the results.

First, recall common heap indexing conventions:
- 0-based indexing (root at index 0):
  - Parent of node at index i (i > 0) is at index floor((i - 1) / 2).
  - Left child of node at index i is at index 2*i + 1; right child is at index 2*i + 2.
- 1-based indexing (root at index 1):
  - Parent of node at index i (i > 1) is at index floor(i / 2).
  - Left child of node at index i is at index 2*i; right child is at index 2*i + 1.

Applying 0-based indexing to node 7:
- Parent index = floor((7 - 1) / 2) = floor(6 / 2) = 3.
- Left child index = 2*7 + 1 = 15; Right child index = 2*7 + 2 = 16.
Thus, under 0-based indexing, node 7 has parent 3 and children 15 and 16.

Applying 1-based indexing to node 7:
- Parent index = floor(7 / 2) = 3.
- Left child index = 2*7 = 14; Right child index = 2*7 + 1 = 15.
Thus, under 1-based indexing, node 7 has parent 3 and children 14 and 15.

Interpretation of the answer string 'Parent index: 0; child indices: 5, 6': this would correspond to a non-standard or inconsistent indexing scheme, since with both common conventions (0-based and 1-based) node 7’s parent is not 0 and its children are not 5 and 6. If the problem’s specific heap uses a different or custom indexing, you’d need to know that convention to verify the values. In typical heaps used in data structure courses, the results would be as shown above for the standard conventions.

If you can share the exact indexing convention used for this problem (0-based, 1-based, or another scheme), I can recompute the parent and child indices accordingly and confirm which values are correct.

What are the parent and child indices for node 7 in the following max-heap?

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