Construct a heap with the following keys

$[$Hints: insert keys$/$ items to the heap one by one or construct the heap using bottom$-$up

approach$]$

$[20$ marks$]$

What will be the index value of the item with key $\text{'}25\text{'}$ for an array$-$based representation of

the heap shown in figure $1?$

$[10$ marks$]$

Figure $1$: Min heap showing the keys of the items

Perform remove min operation once on the heap shown in figure $1.$

Insert an item with key $\text{'}4\text{'}$ in the heap shown in figure $1.$

If there are $120$items in a heap, then calculate the maximum number of swap operations

needed for adding or removing an item from a heap.