(c) A message of length x symbols is made from a set of 8 symbols drawn from a vocabulary shown below, with each symbol being coded using 3 binary bits: So, the message BADGE (x=5) would be coded as 001,000,011,110,100. This message requires a constant 3 bits/symbol. Analysis shows that in general usage, the symbols appear with the relative frequency as shown also in the table. (i) Construct a Huffman coding tree to determine the most efficient alternative coding for the symbols so as to minimise the number of bits/symbol to code a message. (ii) Determine the average number of bits/symbol required to code a message using this more efficient alternative coding. (d) A recursive algorithm is applied to some data A=(a1,,am) where m 3 and m is divisible by 3 . The running time T is characterised using the following recurrence equations: T(3)=c when the size of A is 3 T(m)=T(m3)+c otherwise Determine the running time complexity of this algorithm. Note that m is divisible by 3 and the problem size reduces by 3 for each recursion. (e) A student wishes to solve the Minimum Spanning Tree problem using a new algorithm they have devised. They decide to test their new algorithm against the well-known Kruskal and Prim algorithms. Discuss whether the new algorithm is guaranteed to produce an identical tree output as the Kruskal algorithm when provided with the same input graph