A text is made up of the characters A, B, C, D, E each occurring with the probability 0.08, 0.40, 0.25, 0.15 and 0.12 respectively. The optimal coding technique will have the average length of:

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UGC NET Computer Science (Paper 2) July 2018 Paper

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Answer 1

Concept:

Optimal coding technique merge the probabilities one by one starting from the lower one.

Explanation:

Characters are: A, B, C, D and E with probabilities 0.08, 0.40, 0.25, 0.15, 0.12 respectively.

Step 1: Merge 0.08 (A) and 0.12, (E)

Step 2: Merge 0.20 with 0.15(D)

Step 3: Merge 0.35 and 0.25 (C)

Step 4: Merge 0.60 with 0.40 (B), then assign 0 to all left edges and 1 to all right edges.

Code for A (0.08) = 1110 (length 4)

Code for B (0.40) = 0 (length 1)

Code for C (0.25) = 10(length 2)

Code for D (0.15) = 110 (length 3)

Code for E (0.12) = 1111 (length 4)

Average code length = [(0.08 × 4) + (0.40 × 1) + (0.25 × 2) + (0.15 × 3) + (0.12 × 4)] / 1 = 0.32 + 0.40 + 0.50 + 0.45 + 0. 48 = 2.15