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國立臺灣大學 2026 · 考試 · 第 18 題

(4 points) Which of the following properties is true for some optimal prefix-free binary code and directly justifies the greedy choice made in the Huffman algorithm?

(A)
The two symbols with the lowest frequencies must appear at the same depth in the code tree.
(B)
The symbol with the lowest frequency must be assigned the longest codeword, but the symbol with the second lowest frequency need not.
(C)
All leaves at the maximum depth must correspond to symbols with the lowest frequency.
(D)
The two symbols with the lowest frequencies must have equal-length codewords but they need not share the same parent.
(E)
The two symbols with the lowest frequencies must be siblings at the maximum depth of the code tree.

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