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A priority queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is: 10, 8, 5, 3, 2. Two new elements 1 and 7 are inserted into the heap in that order. The level-order traversal of the heap after the insertion of the elements is __________.
  • a)
     10, 8, 7, 3, 2, 1, 5
  • b)
     10, 8, 7, 2, 3, 1, 5
  • c)
     10, 8, 7, 1, 2, 3, 5
  • d)
     10, 8, 7, 5, 3, 2, 1
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A priority queue is implemented as a Max-Heap. Initially, it has 5 ele...
Given:
- The priority queue is implemented as a Max-Heap.
- The initial level-order traversal of the heap is: 10, 8, 5, 3, 2.

To Find:
- The level-order traversal of the heap after inserting the elements 1 and 7.

Solution:
To insert elements into a Max-Heap, we follow these steps:
1. Insert the element at the last position.
2. Compare the element with its parent.
3. If the element is greater than its parent, swap them.
4. Repeat steps 2 and 3 until the element is in its correct position.

Step 1: Inserting element 1
- The level-order traversal of the heap after inserting 1 at the last position is: 10, 8, 5, 3, 2, 1.

Step 2 and 3: Comparing and swapping element 1 with its parent
- Since 1 is smaller than its parent 10, no swap is required.
- The level-order traversal remains the same: 10, 8, 5, 3, 2, 1.

Step 1: Inserting element 7
- The level-order traversal of the heap after inserting 7 at the last position is: 10, 8, 5, 3, 2, 1, 7.

Step 2 and 3: Comparing and swapping element 7 with its parent
- Since 7 is greater than its parent 1, swap them.
- The level-order traversal becomes: 10, 8, 5, 3, 2, 7, 1.

Step 2 and 3: Comparing and swapping element 7 with its parent
- Since 7 is greater than its parent 2, swap them.
- The level-order traversal becomes: 10, 8, 7, 3, 2, 5, 1.

Step 2 and 3: Comparing and swapping element 7 with its parent
- Since 7 is greater than its parent 2, swap them.
- The level-order traversal becomes: 10, 8, 7, 3, 7, 5, 1.

Step 2 and 3: Comparing and swapping element 7 with its parent
- Since 7 is greater than its parent 3, swap them.
- The level-order traversal becomes: 10, 8, 7, 7, 3, 5, 1.

Step 2 and 3: Comparing and swapping element 7 with its parent
- Since 7 is greater than its parent 3, swap them.
- The level-order traversal becomes: 10, 8, 7, 7, 3, 5, 1.

Final Level-order Traversal:
- The level-order traversal of the heap after inserting the elements 1 and 7 is: 10, 8, 7, 7, 3, 5, 1.

Therefore, the correct option is (a) 10, 8, 7
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Community Answer
A priority queue is implemented as a Max-Heap. Initially, it has 5 ele...
Max heap: Root node value should be greater than child nodes.
Whenever we insert the new element in the heap, we will insert it at the last level of the heap.
After inserting the element if the max heap doesn't follow the property then we will apply heapify algorithm until we get the max heap.
Whenever insertion will be done in heap, it will always be inserted in the last level from left to right. So, we insert '1' and '7' as a child of node 5 now, we perform heapify algorithm until the heap property will satisfied and then we get the heap whose level order traversal is 10, 8, 7, 3, 2, 1, 5.
Initially heap has 10, 8, 5, 3, 2.
After insertion of 1:
No need to heapify as 5 is greater than 1.
After insertion of 7:
Heapify 5 as 7 is greater than 5.
No need to heapify any further as 10 is greater than 7:
Hence, the correct option is (A).
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A priority queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is: 10, 8, 5, 3, 2. Two new elements 1 and 7 are inserted into the heap in that order. The level-order traversal of the heap after the insertion of the elements is __________.a)10, 8, 7, 3, 2, 1, 5b)10, 8, 7, 2, 3, 1, 5c)10, 8, 7, 1, 2, 3, 5d)10, 8, 7, 5, 3, 2, 1Correct answer is option 'A'. Can you explain this answer?
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