Let H be a max$-$heap of size n$.$ Suppose we remove the leftmost branch of

H$.$

$1.$ How many elements will be left in H after the modification? Provide

your answer in terms of n$.[1$ point$]$

$2.$ Devise an algorithm to turn H into a max$-$heap. $[1$ point$]$

$3.$ What is the worst$-$case complexity of your algorithm?