write the code for the same in cpp $,$ dont give the chat gpt answer $,$ Implementing a Min Heap $($array$-$based representation$)$:

Write code to create an empty heap.$(1$ Mark$)$

Implement insertion operation $($inserting an element into the heap$).(1\mathrm{.}5$ for insertion $+1\mathrm{.}5$ for heapify$)$

Implement deletion operation $($deleting the root element from the heap$).(1\mathrm{.}5$ for deletion $+1\mathrm{.}5$ for heapify$)$

Heap Operations:

Implement heapify operation $($ensuring the heap property is maintained after insertion or deletion$).$

Implement extract$-$min operation $($removing and returning the minimum element from the heap$).(1$ mark$)$

Implement heap sort using heap operations. $(1$ mark$)$

Heap Applications:

$[$ Practice question$]$Discuss and implement priority queues using heaps.

$[$ Practice question$]$ Explore other applications of heaps such as heap$-$based graph algorithms $($Dijkstra$$s algorithm, Prim$$s algorithm$).$

Please write a driver$($main$)$ function and call all the above functions appropriately from it$.(1$ mark$)$