Q$3.[$Prim$$s minimum spanning tree algorithm$]$ Solve Problem $8\mathrm{.}6$b from the Baase$$s textbook $($page $416).$

Execute Prim$$s minimum spanning tree algorithm by hand on the graph in Figure $($a$)[($a$)$ A weighted graph$],$ showing how the data structures evolve. Clearly indicate which edges become part of the minimum spinning tree and in what order.

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Start at vertex H$.$

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Q$4[25$ pts$.]$: $[$Dijkstra$$s shortest$-$path algorithm$]$ Solve Problem $8\mathrm{.}15$c from the Baase$$s textbook $($page $419).$

$$Figure $8\mathrm{.}13$ Digraph for Exercise $8\mathrm{.}15$

Here is the adjacency list $($with edge weights in parentheses$)$ for the digraph shown in Figure $8\mathrm{.}13[$see above$]$:

A: B$(4\mathrm{.}0),$ F$(2\mathrm{.}0)$

B: A$(1\mathrm{.}0),$ C$(3\mathrm{.}0),$ D$(4\mathrm{.}0)$

C: A$(6\mathrm{.}0),$ B$(3\mathrm{.}0),$ D$(7\mathrm{.}0)$

D: A$(6\mathrm{.}0),$ E$(2\mathrm{.}0)$

E: D$(5\mathrm{.}0)$

F: D$(2\mathrm{.}0),$ E$(3\mathrm{.}0)$

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c$.$ Execute Dijkstra$$s shortest$-$path algorithm by hand on this graph, showing how the data structures evolve, with s $=$ A$.$ Clearly indicate which edges become part of the shortest$-$path tree and in what order.

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Q$5[20$ pts$.]$: Show the Huffman tree and Encoding Table that results from the following distribution $($frequency$)$ of punctuation characters and digits: colon $(95),$ space $(313),$ newline $(70),$ comma $(35),1(221),2(164),3(57),5(241),6(153).$

Please provide answers in proper step by step. Do not provide AI answers. Also I want the answers to be hand written if not proper explanation and tables required.