$3(10$ pts$)$ For the Huffman encoding algorithm, use pseudo$-$code to implement the following.

$($a$)$ Nodes of the Huffman prefix tree.

The initial nodes store a symbol and its frequency, these are the leaf nodes. The two nodes with

the lowest frequencies are merged into a new node which stores their sum and references to the

two merged nodes, these nodes are the intermediate nodes. Indicate how the values stored in each

node can be retrieved.

$($b$)$ Retrieval and insertion.

Give the data structure for the storage of the nodes and how the two nodes with the lowest

frequencies are retrieved, merged and their merged node inserted.