I knew this problem cold from prep so the heap-based build came out fine.
Start by clarifying the problem and edge cases, then explain the Huffman algorithm step-by-step: build a min-heap of nodes, repeatedly merge the two lowest-frequency nodes, and traverse the tree to assign codes. Emphasize the greedy choice and optimality, and discuss implementation details and complexity.
Pro tip: Mention that Huffman coding is optimal for symbol-by-symbol encoding and that using a min-heap gives O(n log n) time; also note that the code lengths satisfy the Kraft inequality and that ties can be broken arbitrarily without affecting optimality.
Restate the problem, confirm input/output format, and discuss edge cases like empty map, single symbol, or symbols with zero frequency.
Create leaf nodes for each symbol, insert into a min-heap by frequency, then repeatedly extract two minimum nodes, merge them into a new internal node, and reinsert until one node remains.
Traverse the tree from root to leaves, assigning '0' for left edges and '1' for right edges; the path to each leaf gives its prefix code.
Discuss time complexity O(n log n) and space O(n), and mention potential optimizations like using a sorted list or specialized heap for small alphabets.
Verify that codes are prefix-free, compare with fixed-length encoding, and discuss trade-offs like encoding/decoding speed vs. compression ratio.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.