From the given data below : a b b a a b b a a b which one of the following is not a word in the dictionary created by LZ-coding (the initial words are a, b) ?
b a a b
LZ (Lempel–Ziv–Welch) coding builds its dictionary while reading: it extends the current match w by the next symbol c; if wc is already a word it continues, otherwise it outputs w, adds wc as a new word and restarts with w = c.
Step 1 — Start with the dictionary {a, b} and trace the input a b b a a b b a a b:
| Current w | Next c | wc in dictionary? | New word added |
|---|---|---|---|
| a | b | no | ab |
| b | b | no | bb |
| b | a | no | ba |
| a | a | no | aa |
| a | b | yes (w = ab) | — |
| ab | b | no | abb |
| b | a | yes (w = ba) | — |
| ba | a | no | baa |
| a | b | yes (w = ab), input ends | — |
Step 2 — The final dictionary is {a, b, ab, bb, ba, aa, abb, baa}.
The words ab, bb and ba are all created during the trace, while the four-symbol string baab is never added — the longest new words are only three symbols long.
b a a b option is correct.
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