Given a set of characters with specific frequencies (A: 5, B: 9, C: 12, D: 13, E: 16, F: 45), explain the process of building a Huffman tree and assigning binary codes to each character. Describe the merging of nodes, the rearrangement of queues, and the tracing of paths to determine the codes. Use only text paragraphs; do not use a tree diagram or a table of codes.