$$: $4.$ Assume there is a max$-$heap of size $31$ whose values are distinct. The largest item in the max$-$heap must appear at index $1,$ and the second largest item...

$4.$ Assume there is a max$-$heap of size $31$ whose values are distinct. The largest item in the max$-$heap must appear at index $1,$ and the second largest item must be at index $2$ or index $3.$

$(1$ point$)$ Give the list of indices in the max$-$heap of size $31$ where the $k-$th largest item $($i$)$ can appear, and $($ii$)$ cannot appear, for $k=2,3,4.($assuming the item values to be distinct$)$

$(1$ point$)$ Give the list of indices in the max$-$heap of size $31$ where the $k-$th smallest item $($i$)$ can appear, and $($ii$)$ cannot appear, for $k=2,3,4.($assuming the item values to be distinct$)$