Given an array apply the bottom$-$up heap construction

algorithm buildMinHeap $(A,7)$ to transform it into a min$-$heap. Please show the

updated array after each swap made during the downHeap procedure.

Follow the pseudocode provided from M$6$ slides:

buildMinHeap $(A,n$

for $i=(\frac{n}{2}-1)$ down to $0$

downHeap $(A,i$

downHeap $($A$,$ i$)$

smallest $=$ index of the smallest element among

$A[i]$ and its two children

if smallest $i$

swap $A[i]$ with smallest$]$

downHeap$($A$,$ smallest$)$