Please provide a detailed answer with any necessary graphs or tables. Ensure accuracy and thoroughness in your response. No AI or ChatGPT usage is allowed.

DK$17$

$"$: $-.$ C $++$ API $$:

$$

$.$insert $([,])$

$.$extractRoot $()$

$.$root $()$

$.$leaf $()$

$.$size $()$

$.$isValid $()$

$.$fix $()$

$.$sort $()$

$.$clear $()$

Heap.heapify $()$

Heap.isHeapified $()$

$$ n $."$