Identify the max-heap that would result after inserting the value 60 into the following max-heap: 46 O 46 60 46 46 78 78 78 78 78 55 96 55 96 60 96 96 46 96 60 68 68 55 68 68 55 68 55
Identify the max-heap that would result after inserting the value 60 into the following max-heap: 46 O 46 60 46 46 78 78 78 78 78 55 96 55 96 60 96 96 46 96 60 68 68 55 68 68 55 68 55
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Transcribed Image Text:**Max-Heap Exercise**
**Objective:** Identify the max-heap that would result after inserting the value 60 into the following max-heap.
**Initial Max-Heap Structure:**
```
96
/ \
78 68
/ \
46 55
```
**Options for Max-Heap after Insertion:**
1. **Option A:**
```
96
/ \
78 68
/ \ /
46 55 60
```
2. **Option B:**
```
96
/ \
78 68
/ \ / \
60 46 55
```
3. **Option C:**
```
96
/ \
78 68
/ \
60 46
\
55
```
4. **Option D:**
```
96
/ \
78 68
/ \ /
60 55 46
```
**Explanation:**
- A max-heap is a binary tree where each parent node is greater than or equal to its child nodes.
- When inserting a new value, it is initially added at the leftmost available position to maintain complete binary tree properties.
- The heap property is then restored by comparing the new value with its parent node and swapping them if necessary. This process is repeated until the heap property is fully restored.
**Task:** Choose which of the options correctly represents the max-heap structure after inserting the value 60.
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