Question

Consider the following max heap {50, 30, 20, 15, 10, 8, 16} Delete a node with value 50 . Draw the new heap after the deletion.

Answer 1

To delete the root node (value 50) from a max heap, replace it with the last element, then reheapify to maintain the max heap properties. The final max heap after deletion is: {30, 16, 20, 15, 10, 8}.

Step-by-step explanation:

To delete the node with value 50 from the given max heap {50, 30, 20, 15, 10, 8, 16}, we follow the heap deletion procedure. The first step is to replace the root node (value 50) with the last element in the heap, which is 16. After removing the 50, our heap looks like this: {16, 30, 20, 15, 10, 8}. Now we must reheapify.

The second step is to move the new root node down the heap until it's in the correct position. Here's how this process would look in steps:

1. 
   
3. 16 is swapped with the largest of its children (30), resulting in {30, 16, 20, 15, 10, 8}.
4. 
   
6. 16 is now a child node and must be compared with its children (15 and 10). Since 16 is already greater than both, no further moves are necessary.

This is the new max heap after deletion and reheapification: {30, 16, 20, 15, 10, 8}.