Let H be a binomial heap that intially contains n keys $($i$.$e$.,|$H$|=$ n$).$ In this

question, you will determine the $$amortized$($i$.$e$.,$ average$)$ cost of successively inserting k keys into H$.$

a$.$ Recall that $\backslash$alpha $($n$)$ is the number of $1$s in the binary representation of n$.$ Prove that binomial heap H

has exactly n $\backslash$alpha $($n$)$ edges.