We say that a tree in a Fibonacci heap is path$-$like if all of its nodes

lie on a single downward path from the root. We say that a Fibonacci heap is path$-$like

if it contains exactly one tree, and that tree is path$-$like. In the following two parts,

assume that the keys associated with the Fibonacci heap are arbitrary integers.

$($a$)$ Exhibit a sequence of four Fibonacci heap operations that transforms

the empty Fibonacci heap into a $2-$node path$-$like Fibonacci heap.

$($b$)$ Let H be an i$-$node path$-$like Fibonacci heap, where i $>=2.$ Exhibit a

sequence of six Fibonacci heap operations that transforms H into an $($i $+1)-$node

path$-$like Fibonacci heap