It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher Consider the following undirected, weighted graph: Provide your answer on the space

below... Use Dijkstra's Algorithm to find the shortest path and show all steps using a

table, as was performed during class. $(10$ points$)$

The figure above shows a network of roads. The number on each arc represents the length of

the road in Kilometers.

Us Dijkstra's algorithm to find the shortest path from to Node $1$ to $7$ and its length. Show all

steps. Use the similar algorithms as was performed during class

LZW is a data compression algorithm that reduces file size by

using a variable size dictionary. Apply the LZW compression

algorithm on the following string below: Show all steps as was shown

during class presentation.

Use the space provided below to write your answer. $(10$ points$)$

TOBEORNOTTOBEORTOBEORNOTOBEORNOT

than the second, into two like powers. I have discovered a truly marvelous proof of this, which this margin is too narrow to

contain $($Cubum$,$ autem in duos cubos, aut guadratoquadratum, in duos quadratoquadratos, et generaliter, nullam in infinitum

ultra quadratum potestatemin duos eiusdem nominis fas, dividere cuius, rei demonstrationem,mirabilem sane detexi.

Hanc marginis exiguitas, non saperet.$)$

Pierre de Fermat $($annotation on a copy of Diophantus' "Arithmetica"$).$

Answer All Questions. Make sure you show all work done for each problem. Please Do not rush and take your time in solving

each problem.

Draw the Binary Search tree that results from inserting the keys:

$3,9,1,7,4,5,8,3,7,11$ in that order into an initially empty tree. You are only required to show the final tree,

although drawing intermediate trees may result in partial credit. If you draw intermediate trees, please circle your

final tree for ANY credit. $(5$ points$)$

$1.$b Given the tree shown below. Draw what the tree would look like after deleting the value $9.$ Use one of the

methods for deleting described in class or in the slides. $(5$ points$)$

$1.$c$.$ Give traversals of the tree shown below: write the order of the traversals. $(5$ points$)$

In$-$Order: