Will rate instantly. Please answer fast $3.(25$ pts$)$ Fibonacci Heaps are data structures that implement Priority Queues with efficient amortized times. It is particularly useful to speedup algorithms that use DECREASE$-$KEY often. Recall that Fibonacci Heaps have a root list and that some of its nodes are marked. The potential of a heap $\backslash ($ H $\backslash )$ is defined as $\backslash (\backslash$Phi$($H$)=$t$($H$)+2$ m$($H$)\backslash ).$ nodes. list and $\backslash ($ m$($H$)\backslash )$ is the number of marked $($b$)$ For the following Fibonacci Hesp, perform the operation Exts $1,$ and that it costs $1$ unit to the initial "surgery" that splices a list into the root list costs is and that it costs $1$ unit to check each item in the root list during CONSOLIDATE. Wh$."$ of the operation? $($c$)$ What is the amortized cost of EXTRACT$-$MIN in a heap with $\backslash ($ n $\backslash )$ nodes? $($d$)$ For the following Fibonacci Heap, perform the operation DECREASE$-$KEY changing the key $26$ to $3.$ We consider that it costs one to move each node to the root list. What is the real and amortized costs of the operation? $($e$)$ What is the amortized cost of DECREASE$-$KEY in a heap with n nodes?