Lost a ton of time just getting on the same page about what Huffman encoding is and how the tree should be structured.
Start by clarifying the input format (e.g., a map of characters to frequencies) and the expected output (e.g., the root of the Huffman tree). Then explain the greedy algorithm: repeatedly extract the two nodes with the smallest frequencies, merge them into a new node with frequency equal to their sum, and insert it back into the min-heap until one node remains. Finally, discuss the time and space complexity and potential edge cases.
Pro tip: Mention that using a min-heap (priority queue) is optimal for efficiency, but if the frequencies are already sorted, a two-queue approach can achieve O(n) time. Also, clarify that the tree is not unique when frequencies tie, so any valid Huffman tree is acceptable.
Confirm the input format (e.g., a dictionary of characters and frequencies) and the expected output (e.g., the root node of the Huffman tree or the encoding map). Ask if the frequencies are given as a sorted list or if we need to handle sorting.
Decide to use a min-heap (priority queue) to efficiently extract the two smallest frequencies. Alternatively, if the input is sorted, consider using two queues for O(n) time. Explain the trade-offs.
Initialize a min-heap with all leaf nodes (each containing a character and its frequency). While the heap has more than one node, extract the two nodes with the smallest frequencies, create a new internal node with these two as children and frequency equal to their sum, and insert the new node back into the heap.
When only one node remains in the heap, that node is the root of the Huffman tree. Return it (or traverse the tree to generate Huffman codes if needed).
State that the time complexity is O(n log n) due to heap operations, and space complexity is O(n). Discuss edge cases: empty input, single character, and ties in frequencies (which can lead to different but valid trees).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.