d$)$ Use the potential method to find the amortized cost per operation. Let $L_i$ be the list

after the $i-$th operation and let num $(L_i)$ be the number of items on $L_i.$ Use the following

potential function:

${}_i=$

$um(L_i)$

i$.$ First, show that this potential function is valid $($i$.$e$.{}_0=0$ and ${}_{i}0$ for all $i)$

ii$.$ Next use this potential function to calculate the amortized costs of Add and

Aggregate $($Recall that $a_i=c_i+{}_i-{}_{i-1},$ where $a_i,$ is the amortized cost of the $i-$th

operation and $c_i$ is the actual cost$)$