GATE CS 2014 Set 2 — Question 48
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Algorithms → Greedy Algorithms → Huffman Coding
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Question
Suppose P, Q, R, S, T are sorted sequences having lengths 20, 24, 30, 35, 50 respectively. They are to be merged into a single sequence by merging together two sequences at a time. The number of comparisons that will be needed in the worst case by the optimal algorithm for doing this is ____.
Correct answer
358 to 358
Solution
This problem asks for the number of comparisons in the worst case using the optimal merge pattern (Huffman coding strategy). Merging two sorted lists of size and requires at most comparisons in the worst case.Sorted lengths: 20, 24, 30, 35, 50Step 1: Merge the two smallest sequences (20 and 24).
.
- Size of new sequence:
- Comparisons:
- Current list of lengths: 30, 35, 44, 50
- Size of new sequence:
- Comparisons:
- Current list of lengths: 44, 50, 65
- Size of new sequence:
- Comparisons:
- Current list of lengths: 65, 94
- Size of new sequence:
- Comparisons:
.
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